⚠️ Warning: This is a draft ⚠️
This means it might contain formatting issues, incorrect code, conceptual problems, or other severe issues.
If you want to help to improve and eventually enable this page, please fork RosettaGit's repository and open a merge request on GitHub.
{{task|Fractals}}
;Task Produce an ASCII representation of a [[wp:Sierpinski triangle|Sierpinski triangle]] of order '''N'''.
;Example The Sierpinski triangle of order '''4''' should look like this:
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
;Related tasks
- [[Sierpinski triangle/Graphical]] for graphics images of this pattern.
- [[Sierpinski carpet]]
ACL2
(defun pascal-row (prev)
(if (endp (rest prev))
(list 1)
(cons (+ (first prev) (second prev))
(pascal-row (rest prev)))))
(defun pascal-triangle-r (rows prev)
(if (zp rows)
nil
(let ((curr (cons 1 (pascal-row prev))))
(cons curr (pascal-triangle-r (1- rows) curr)))))
(defun pascal-triangle (rows)
(cons (list 1)
(pascal-triangle-r rows (list 1))))
(defun print-odds-row (row)
(if (endp row)
(cw "~%")
(prog2$ (cw (if (oddp (first row)) "[]" " "))
(print-odds-row (rest row)))))
(defun print-spaces (n)
(if (zp n)
nil
(prog2$ (cw " ")
(print-spaces (1- n)))))
(defun print-odds (triangle height)
(if (endp triangle)
nil
(progn$ (print-spaces height)
(print-odds-row (first triangle))
(print-odds (rest triangle) (1- height)))))
(defun print-sierpenski (levels)
(let ((height (1- (expt 2 levels))))
(print-odds (pascal-triangle height)
height)))
Ada
This Ada example creates a string of the binary value for each line, converting the '0' values to spaces.
with Ada.Text_Io; use Ada.Text_Io;
with Ada.Strings.Fixed;
with Interfaces; use Interfaces;
procedure Sieteri_Triangles is
subtype Practical_Order is Unsigned_32 range 0..4;
function Pow(X : Unsigned_32; N : Unsigned_32) return Unsigned_32 is
begin
if N = 0 then
return 1;
else
return X * Pow(X, N - 1);
end if;
end Pow;
procedure Print(Item : Unsigned_32) is
use Ada.Strings.Fixed;
package Ord_Io is new Ada.Text_Io.Modular_Io(Unsigned_32);
use Ord_Io;
Temp : String(1..36) := (others => ' ');
First : Positive;
Last : Positive;
begin
Put(To => Temp, Item => Item, Base => 2);
First := Index(Temp, "#") + 1;
Last := Index(Temp(First..Temp'Last), "#") - 1;
for I in reverse First..Last loop
if Temp(I) = '0' then
Put(' ');
else
Put(Temp(I));
end if;
end loop;
New_Line;
end Print;
procedure Sierpinski (N : Practical_Order) is
Size : Unsigned_32 := Pow(2, N);
V : Unsigned_32 := Pow(2, Size);
begin
for I in 0..Size - 1 loop
Print(V);
V := Shift_Left(V, 1) xor Shift_Right(V,1);
end loop;
end Sierpinski;
begin
for N in Practical_Order loop
Sierpinski(N);
end loop;
end Sieteri_Triangles;
alternative using modular arithmetic:
with Ada.Command_Line;
with Ada.Text_IO;
procedure Main is
subtype Order is Natural range 1 .. 32;
type Mod_Int is mod 2 ** Order'Last;
procedure Sierpinski (N : Order) is
begin
for Line in Mod_Int range 0 .. 2 ** N - 1 loop
for Col in Mod_Int range 0 .. 2 ** N - 1 loop
if (Line and Col) = 0 then
Ada.Text_IO.Put ('X');
else
Ada.Text_IO.Put (' ');
end if;
end loop;
Ada.Text_IO.New_Line;
end loop;
end Sierpinski;
N : Order := 4;
begin
if Ada.Command_Line.Argument_Count = 1 then
N := Order'Value (Ada.Command_Line.Argument (1));
end if;
Sierpinski (N);
end Main;
{{out}}
XXXXXXXXXXXXXXXX
X X X X X X X X
XX XX XX XX
X X X X
XXXX XXXX
X X X X
XX XX
X X
XXXXXXXX
X X X X
XX XX
X X
XXXX
X X
XX
X
ALGOL 68
{{trans|python}} {{works with|ALGOL 68|Standard - no extensions to language used}} {{works with|ALGOL 68G|Any - tested with release mk15-0.8b.fc9.i386}}
PROC sierpinski = (INT n)[]STRING: (
FLEX[0]STRING d := "*";
FOR i TO n DO
[UPB d * 2]STRING next;
STRING sp := " " * (2 ** (i-1));
FOR x TO UPB d DO
STRING dx = d[x];
next[x] := sp+dx+sp;
next[UPB d+x] := dx+" "+dx
OD;
d := next
OD;
d
);
printf(($gl$,sierpinski(4)))
AppleScript
{{Trans|JavaScript}} {{Trans|Haskell}} Centering any previous triangle block over two adjacent duplicates:
-- SIERPINKSI TRIANGLE -------------------------------------------------------
-- sierpinski :: Int -> [String]
on sierpinski(n)
if n > 0 then
set previous to sierpinski(n - 1)
set padding to replicate(2 ^ (n - 1), space)
script alignedCentre
on |λ|(s)
concat(padding & s & padding)
end |λ|
end script
script adjacentDuplicates
on |λ|(s)
unwords(replicate(2, s))
end |λ|
end script
-- Previous triangle block centered,
-- and placed on 2 adjacent duplicates.
map(alignedCentre, previous) & map(adjacentDuplicates, previous)
else
{"*"}
end if
end sierpinski
-- TEST ----------------------------------------------------------------------
on run
unlines(sierpinski(4))
end run
-- GENERIC FUNCTIONS ---------------------------------------------------------
-- concat :: [[a]] -> [a] | [String] -> String
on concat(xs)
if length of xs > 0 and class of (item 1 of xs) is string then
set acc to ""
else
set acc to {}
end if
repeat with i from 1 to length of xs
set acc to acc & item i of xs
end repeat
acc
end concat
-- intercalate :: Text -> [Text] -> Text
on intercalate(strText, lstText)
set {dlm, my text item delimiters} to {my text item delimiters, strText}
set strJoined to lstText as text
set my text item delimiters to dlm
return strJoined
end intercalate
-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map
-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: Handler -> Script
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn
-- replicate :: Int -> a -> [a]
on replicate(n, a)
set out to {}
if n < 1 then return out
set dbl to {a}
repeat while (n > 1)
if (n mod 2) > 0 then set out to out & dbl
set n to (n div 2)
set dbl to (dbl & dbl)
end repeat
return out & dbl
end replicate
-- unlines, unwords :: [String] -> String
on unlines(xs)
intercalate(linefeed, xs)
end unlines
on unwords(xs)
intercalate(space, xs)
end unwords
{{Out}}
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
Or generating each line as an XOR / Rule 90 / Pascal triangle rewrite of the previous line. {{Trans|JavaScript}}
-- SIERPINSKI TRIANGLE BY XOR / RULE 90 --------------------------------------
-- sierpinskiTriangle :: Int -> String
on sierpinskiTriangle(intOrder)
-- A Sierpinski triangle of order N
-- is a Pascal triangle (of N^2 rows)
-- mod 2
-- pascalModTwo :: Int -> [[String]]
script pascalModTwo
on |λ|(intRows)
-- addRow [[Int]] -> [[Int]]
script addRow
-- nextRow :: [Int] -> [Int]
on nextRow(row)
-- The composition of AsciiBinary . mod two . add
-- is reduced here to a rule from
-- two parent characters above,
-- to the child character below.
-- Rule 90 also reduces to this XOR relationship
-- between left and right neighbours.
-- rule :: Character -> Character -> Character
script rule
on |λ|(a, b)
if a = b then
space
else
"*"
end if
end |λ|
end script
zipWith(rule, {" "} & row, row & {" "})
end nextRow
on |λ|(xs)
xs & {nextRow(item -1 of xs)}
end |λ|
end script
foldr(addRow, {{"*"}}, enumFromTo(1, intRows - 1))
end |λ|
end script
-- The centring foldr (fold right) below starts from the end of the list,
-- (the base of the triangle) which has zero indent.
-- Each preceding row has one more indent space than the row below it.
script centred
on |λ|(sofar, row)
set strIndent to indent of sofar
{triangle:strIndent & intercalate(space, row) & linefeed & ¬
triangle of sofar, indent:strIndent & space}
end |λ|
end script
triangle of foldr(centred, {triangle:"", indent:""}, ¬
pascalModTwo's |λ|(intOrder ^ 2))
end sierpinskiTriangle
-- TEST ----------------------------------------------------------------------
on run
set strTriangle to sierpinskiTriangle(4)
set the clipboard to strTriangle
strTriangle
end run
-- GENERIC FUNCTIONS ---------------------------------------------------------
-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
if m > n then
set d to -1
else
set d to 1
end if
set lst to {}
repeat with i from m to n by d
set end of lst to i
end repeat
return lst
end enumFromTo
-- foldr :: (a -> b -> a) -> a -> [b] -> a
on foldr(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from lng to 1 by -1
set v to |λ|(v, item i of xs, i, xs)
end repeat
return v
end tell
end foldr
-- intercalate :: Text -> [Text] -> Text
on intercalate(strText, lstText)
set {dlm, my text item delimiters} to {my text item delimiters, strText}
set strJoined to lstText as text
set my text item delimiters to dlm
return strJoined
end intercalate
-- min :: Ord a => a -> a -> a
on min(x, y)
if y < x then
y
else
x
end if
end min
-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: Handler -> Script
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn
-- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
on zipWith(f, xs, ys)
set lng to min(length of xs, length of ys)
set lst to {}
tell mReturn(f)
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, item i of ys)
end repeat
return lst
end tell
end zipWith
{{Out}}
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
ATS
(* ****** ****** *)
//
// How to compile:
//
// patscc -DATS_MEMALLOC_LIBC -o sierpinski sierpinski.dats
//
(* ****** ****** *)
//
#include
"share/atspre_staload.hats"
//
(* ****** ****** *)
#define SIZE 16
implement
main0 () =
{
//
var x: int
//
val () =
for (x := SIZE-1; x >= 0; x := x-1)
{
var i: int
val () =
for (i := 0; i < x; i := i+1)
{
val () = print_char(' ')
}
var y: int
val () =
for (y := 0; y + x < SIZE; y := y+1)
{
val y = g0int2uint_int_uint(y)
val x = g0int2uint_int_uint(x)
val () = print_string(if (x land y) != 0 then " " else "* ")
}
val ((*flushed*)) = print_newline()
}
//
} (* end of [main0] *)
AutoHotkey
ahk [http://www.autohotkey.com/forum/viewtopic.php?t=44657&postdays=0&postorder=asc&start=150 discussion]
Loop 6
MsgBox % Triangle(A_Index)
Triangle(n,x=0,y=1) { ; Triangle(n) -> string of dots and spaces of Sierpinski triangle
Static t, l ; put chars in a static string
If (x < 1) { ; when called with one parameter
l := 2*x := 1<<(n-1) ; - compute location, string size
VarSetCapacity(t,l*x,32) ; - allocate memory filled with spaces
Loop %x%
NumPut(13,t,A_Index*l-1,"char") ; - new lines in the end of rows
}
If (n = 1) ; at the bottom of recursion
Return t, NumPut(46,t,x-1+(y-1)*l,"char") ; - write "." (better at proportional fonts)
u := 1<<(n-2)
Triangle(n-1,x,y) ; draw smaller triangle here
Triangle(n-1,x-u,y+u) ; smaller triangle down-left
Triangle(n-1,x+u,y+u) ; smaller triangle down right
Return t
}
AWK
# WST.AWK - Waclaw Sierpinski's triangle contributed by Dan Nielsen
# syntax: GAWK -f WST.AWK [-v X=anychar] iterations
# example: GAWK -f WST.AWK -v X=* 2
BEGIN {
n = ARGV[1] + 0 # iterations
if (n !~ /^[0-9]+$/) { exit(1) }
if (n == 0) { width = 3 }
row = split("X,X X,X X,X X X X",A,",") # seed the array
for (i=1; i<=n; i++) { # build triangle
width = length(A[row])
for (j=1; j<=row; j++) {
str = A[j]
A[j+row] = sprintf("%-*s %-*s",width,str,width,str)
}
row *= 2
}
for (j=1; j<=row; j++) { # print triangle
if (X != "") { gsub(/X/,substr(X,1,1),A[j]) }
sub(/ +$/,"",A[j])
printf("%*s%s\n",width-j+1,"",A[j])
}
exit(0)
}
=={{header|BASH (feat. sed & tr)}}== This version completely avoids any number-theoretic workarounds. Instead, it repeatedly replaces characters by "blocks of characters". The strategy is in no way bash-specific, it would work with any other language just as well, but is particularly well suited for tools like sed and tr.
#!/bin/bash
# Basic principle:
#
#
# x -> dxd d -> dd s -> s
# xsx dd s
#
# In the end all 'd' and 's' are removed.
# 0x7F800000
function rec(){
if [ $1 == 0 ]
then
echo "x"
else
rec $[ $1 - 1 ] | while read line ; do
echo "$line" | sed "s/d/dd/g" | sed "s/x/dxd/g"
echo "$line" | sed "s/d/dd/g" | sed "s/x/xsx/g"
done
fi
}
rec $1 | tr 'dsx' ' *'
BASIC
{{works with|QBasic}} {{works with|FreeBASIC}}
DECLARE SUB triangle (x AS INTEGER, y AS INTEGER, length AS INTEGER, n AS INTEGER)
CLS
triangle 1, 1, 16, 5
SUB triangle (x AS INTEGER, y AS INTEGER, length AS INTEGER, n AS INTEGER)
IF n = 0 THEN
LOCATE y, x: PRINT "*";
ELSE
triangle x, y + length, length / 2, n - 1
triangle x + length, y, length / 2, n - 1
triangle x + length * 2, y + length, length / 2, n - 1
END IF
END SUB
Note: The total height of the triangle is 2 * parameter ''length''. It should be power of two so that the pattern matches evenly with the character cells. Value 16 will thus create pattern of 32 lines.
=
BBC BASIC
=
MODE 8
OFF
order% = 5
PROCsierpinski(0, 0, 2^(order%-1))
REPEAT UNTIL GET
END
DEF PROCsierpinski(x%, y%, l%)
IF l% = 0 THEN
PRINT TAB(x%,y%) "*";
ELSE
PROCsierpinski(x%, y%+l%, l% DIV 2)
PROCsierpinski(x%+l%, y%, l% DIV 2)
PROCsierpinski(x%+l%+l%, y%+l%, l% DIV 2)
ENDIF
ENDPROC
==={{header|IS-BASIC}}===
## Befunge
This is a version of the cellular automaton (''rule 90'') construction. The order, ''N'', is specified by the first number on the stack. It uses a single line of the playfield for the cell buffer, so the upper limit for ''N'' should be 5 on a standard Befunge-93 implementation. Interpreters with poor memory handling may not work with anything over 3, though, and a Befunge-98 interpreter should theoretically be unlimited.
```befunge>41+2
\#*1#2-#<:#\_$:1+v
v:$_:#`0#\\#00#:p#->#1<
>2/1\0p:2/\::>1-:>#v_1v
>8#4*#*+#+,#5^#5g0:< 1
vg11<\*g11!:g 0-1:::<p<
>!*+!!\0g11p\ 0p1-:#^_v
@$$_\#!:#::#-^#1\$,+55<
C
#include <stdio.h>
#define SIZE (1 << 4)
int main()
{
int x, y, i;
for (y = SIZE - 1; y >= 0; y--, putchar('\n')) {
for (i = 0; i < y; i++) putchar(' ');
for (x = 0; x + y < SIZE; x++)
printf((x & y) ? " " : "* ");
}
return 0;
}
Automaton
This solution uses a cellular automaton (''rule 90'') with a proper initial status.
#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>
#include <string.h>
#ifndef _POSIX_C_SOURCE
char *strdup(const char *s)
{
int l = strlen(s);
char *r = malloc(l+1);
memcpy(r, s, l+1);
return r;
}
#endif
#define truth(X) ((X)=='*'?true:false)
void rule_90(char *evstr)
{
int i;
int l = strlen(evstr);
bool s[3];
char *cp = strdup(evstr);
for(i=0;i < l; i++) {
s[1] = truth(cp[i]);
s[0] = (i-1) < 0 ? false : truth(cp[i-1]);
s[2] = (i+1) < l ? truth(cp[i+1]) : false;
if ( (s[0] && !s[2]) || (!s[0] && s[2]) ) {
evstr[i] = '*';
} else {
evstr[i] = ' ';
}
}
free(cp);
}
void sierpinski_triangle(int n)
{
int i;
int l = 1<<(n+1);
char *b = malloc(l+1);
memset(b, ' ', l);
b[l] = 0;
b[l>>1] = '*';
printf("%s\n", b);
for(i=0; i < l/2-1;i++) {
rule_90(b);
printf("%s\n", b);
}
free(b);
}
int main()
{
sierpinski_triangle(4);
return EXIT_SUCCESS;
}
C#
using System;
using System.Collections;
namespace RosettaCode {
class SierpinskiTriangle {
int len;
BitArray b;
public SierpinskiTriangle(int n) {
if (n < 1) {
throw new ArgumentOutOfRangeException("Order must be greater than zero");
}
len = 1 << (n+1);
b = new BitArray(len+1, false);
b[len>>1] = true;
}
public void Display() {
for (int j = 0; j < len / 2; j++) {
for (int i = 0; i < b.Count; i++) {
Console.Write("{0}", b[i] ? "*" : " ");
}
Console.WriteLine();
NextGen();
}
}
private void NextGen() {
BitArray next = new BitArray(b.Count, false);
for (int i = 0; i < b.Count; i++) {
if (b[i]) {
next[i - 1] = next[i - 1] ^ true;
next[i + 1] = next[i + 1] ^ true;
}
}
b = next;
}
}
}
namespace RosettaCode {
class Program {
static void Main(string[] args) {
SierpinskiTriangle t = new SierpinskiTriangle(4);
t.Display();
}
}
}
{{trans|C}} {{works with|C sharp|C#|6.0+}}
using static System.Console;
class Sierpinsky
{
static void Main(string[] args)
{
int order;
if(!int.TryParse(args.Length > 0 ? args[0] : "", out order)) order = 4;
int size = (1 << order);
for (int y = size - 1; y >= 0; y--, WriteLine())
{
for (int i = 0; i < y; i++) Write(' ');
for (int x = 0; x + y < size; x++)
Write((x & y) != 0 ? " " : "* ");
}
}
}
{{trans|OCaml}} {{works with|C sharp|C#|3.0+}}
using System;
using System.Collections.Generic;
using System.Linq;
class Program
{
public static List<String> Sierpinski(int n)
{
var lines = new List<string> { "*" };
string space = " ";
for (int i = 0; i < n; i++)
{
lines = lines.Select(x => space + x + space)
.Concat(lines.Select(x => x + " " + x)).ToList();
space += space;
}
return lines;
}
static void Main(string[] args)
{
foreach (string s in Sierpinski(4))
Console.WriteLine(s);
}
}
Or, with fold / reduce (a.k.a. aggregate):
using System;
using System.Collections.Generic;
using System.Linq;
class Program
{
static List<string> Sierpinski(int n)
{
return Enumerable.Range(0, n).Aggregate(
new List<string>(){"*"},
(p, i) => {
string SPACE = " ".PadRight((int)Math.Pow(2, i));
var temp = new List<string>(from x in p select SPACE + x + SPACE);
temp.AddRange(from x in p select x + " " + x);
return temp;
}
);
}
static void Main ()
{
foreach(string s in Sierpinski(4)) { Console.WriteLine(s); }
}
}
C++
{{works with|C++11}} A STL-centric recursive solution that uses the new lambda functions in C++11.
#include <iostream>
#include <string>
#include <list>
#include <algorithm>
#include <iterator>
using namespace std;
template<typename OutIt>
void sierpinski(int n, OutIt result)
{
if( n == 0 )
{
*result++ = "*";
}
else
{
list<string> prev;
sierpinski(n-1, back_inserter(prev));
string sp(1 << (n-1), ' ');
result = transform(prev.begin(), prev.end(),
result,
[sp](const string& x) { return sp + x + sp; });
transform(prev.begin(), prev.end(),
result,
[sp](const string& x) { return x + " " + x; });
}
}
int main()
{
sierpinski(4, ostream_iterator<string>(cout, "\n"));
return 0;
}
Clojure
{{trans|Ada}} {{trans|Common Lisp}} With a touch of Clojure's sequence handling.
(ns example
(:require [clojure.contrib.math :as math]))
; Length of integer in binary
; (copied from a private multimethod in clojure.contrib.math)
(defmulti #^{:private true} integer-length class)
(defmethod integer-length java.lang.Integer [n]
(count (Integer/toBinaryString n)))
(defmethod integer-length java.lang.Long [n]
(count (Long/toBinaryString n)))
(defmethod integer-length java.math.BigInteger [n]
(count (.toString n 2)))
(defn sierpinski-triangle [order]
(loop [size (math/expt 2 order)
v (math/expt 2 (- size 1))]
(when (pos? size)
(println
(apply str (map #(if (bit-test v %) "*" " ")
(range (integer-length v)))))
(recur
(dec size)
(bit-xor (bit-shift-left v 1) (bit-shift-right v 1))))))
(sierpinski-triangle 4)
COBOL
{{trans|Fortran}} and retains a more Fortran-like coding style than is really idiomatic in COBOL.
identification division.
program-id. sierpinski-triangle-program.
data division.
working-storage section.
01 sierpinski.
05 n pic 99.
05 i pic 999.
05 k pic 999.
05 m pic 999.
05 c pic 9(18).
05 i-limit pic 999.
05 q pic 9(18).
05 r pic 9.
procedure division.
control-paragraph.
move 4 to n.
multiply n by 4 giving i-limit.
subtract 1 from i-limit.
perform sierpinski-paragraph
varying i from 0 by 1 until i is greater than i-limit.
stop run.
sierpinski-paragraph.
subtract i from i-limit giving m.
multiply m by 2 giving m.
perform m times,
display space with no advancing,
end-perform.
move 1 to c.
perform inner-loop-paragraph
varying k from 0 by 1 until k is greater than i.
display ''.
inner-loop-paragraph.
divide c by 2 giving q remainder r.
if r is equal to zero then display ' * ' with no advancing.
if r is not equal to zero then display ' ' with no advancing.
compute c = c * (i - k) / (k + 1).
Common Lisp
(defun print-sierpinski (order)
(loop with size = (expt 2 order)
repeat size
for v = (expt 2 (1- size)) then (logxor (ash v -1) (ash v 1))
do (fresh-line)
(loop for i below (integer-length v)
do (princ (if (logbitp i v) "*" " ")))))
Printing each row could also be done by printing the integer in base 2 and replacing zeroes with spaces: (princ (substitute #\Space #\0 (format nil "~%~2,vR" (1- (* 2 size)) v)))
Replacing the iteration with for v = 1 then (logxor v (ash v 1)) produces a "right" triangle instead of an "equilateral" one.
Alternate approach:
(defun sierpinski (n)
(if (= n 0) '("*")
(nconc (mapcar (lambda (e) (format nil "~A~A~0@*~A" (make-string (expt 2 (1- n)) :initial-element #\ ) e)) (sierpinski (1- n)))
(mapcar (lambda (e) (format nil "~A ~A" e e)) (sierpinski (1- n))))))
(mapc #'print (sierpinski 4))
D
===Run-time Version===
void main() /*@safe*/ {
import std.stdio, std.algorithm, std.string, std.array;
enum level = 4;
auto d = ["*"];
foreach (immutable n; 0 .. level) {
immutable sp = " ".replicate(2 ^^ n);
d = d.map!(a => sp ~ a ~ sp).array ~
d.map!(a => a ~ " " ~ a).array;
}
d.join('\n').writeln;
}
{{out}}
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
===Compile-time Version=== Same output.
import std.string, std.range, std.algorithm;
string sierpinski(int level) pure nothrow /*@safe*/ {
auto d = ["*"];
foreach (immutable i; 0 .. level) {
immutable sp = " ".replicate(2 ^^ i);
d = d.map!(a => sp ~ a ~ sp).array ~
d.map!(a => a ~ " " ~ a).array;
}
return d.join('\n');
}
pragma(msg, 4.sierpinski);
void main() {}
Simple Version
{{trans|C}} Same output.
void showSierpinskiTriangle(in uint order) nothrow @safe @nogc {
import core.stdc.stdio: putchar;
foreach_reverse (immutable y; 0 .. 2 ^^ order) {
foreach (immutable _; 0 .. y)
' '.putchar;
foreach (immutable x; 0 .. 2 ^^ order - y) {
putchar((x & y) ? ' ' : '*');
' '.putchar;
}
'\n'.putchar;
}
}
void main() nothrow @safe @nogc {
4.showSierpinskiTriangle;
}
Alternative Version
This uses a different algorithm and shows a different output.
import core.stdc.stdio: putchar;
import std.algorithm: swap;
void showSierpinskiTriangle(in uint nLevels) nothrow @safe
in {
assert(nLevels > 0);
} body {
alias Row = bool[];
static void applyRules(in Row r1, Row r2) pure nothrow @safe @nogc {
r2[0] = r1[0] || r1[1];
r2[$ - 1] = r1[$ - 2] || r1[$ - 1];
foreach (immutable i; 1 .. r2.length - 1)
r2[i] = r1[i - 1] != r1[i] || r1[i] != r1[i + 1];
}
static void showRow(in Row r) nothrow @safe @nogc {
foreach (immutable b; r)
putchar(b ? '#' : ' ');
'\n'.putchar;
}
immutable width = 2 ^^ (nLevels + 1) - 1;
auto row1 = new Row(width);
auto row2 = new Row(width);
row1[width / 2] = true;
foreach (immutable _; 0 .. 2 ^^ nLevels) {
showRow(row1);
applyRules(row1, row2);
row1.swap(row2);
}
}
void main() @safe nothrow {
foreach (immutable i; 1 .. 6) {
i.showSierpinskiTriangle;
'\n'.putchar;
}
}
{{out}}
#
###
#
###
## ##
#######
#
###
## ##
#######
## ##
#### ####
## ## ## ##
###############
#
###
## ##
#######
## ##
#### ####
## ## ## ##
###############
## ##
#### ####
## ## ## ##
######## ########
## ## ## ##
#### #### #### ####
## ## ## ## ## ## ## ##
###############################
#
###
## ##
#######
## ##
#### ####
## ## ## ##
###############
## ##
#### ####
## ## ## ##
######## ########
## ## ## ##
#### #### #### ####
## ## ## ## ## ## ## ##
###############################
## ##
#### ####
## ## ## ##
######## ########
## ## ## ##
#### #### #### ####
## ## ## ## ## ## ## ##
################ ################
## ## ## ##
#### #### #### ####
## ## ## ## ## ## ## ##
######## ######## ######## ########
## ## ## ## ## ## ## ##
#### #### #### #### #### #### #### ####
## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
###############################################################
Delphi
{{trans|DWScript}}
program SierpinskiTriangle;
{$APPTYPE CONSOLE}
procedure PrintSierpinski(order: Integer);
var
x, y, size: Integer;
begin
size := (1 shl order) - 1;
for y := size downto 0 do
begin
Write(StringOfChar(' ', y));
for x := 0 to size - y do
begin
if (x and y) = 0 then
Write('* ')
else
Write(' ');
end;
Writeln;
end;
end;
begin
PrintSierpinski(4);
end.
DWScript
{{trans|E}}
procedure PrintSierpinski(order : Integer);
var
x, y, size : Integer;
begin
size := (1 shl order)-1;
for y:=size downto 0 do begin
Print(StringOfChar(' ', y));
for x:=0 to size-y do begin
if (x and y)=0 then
Print('* ')
else Print(' ');
end;
PrintLn('');
end;
end;
PrintSierpinski(4);
E
def printSierpinski(order, out) {
def size := 2**order
for y in (0..!size).descending() {
out.print(" " * y)
for x in 0..!(size-y) {
out.print((x & y).isZero().pick("* ", " "))
}
out.println()
}
}
? printSierpinski(4, stdout)
Non-ASCII version (quality of results will depend greatly on text renderer):
def printSierpinski(order, out) {
def size := 2**order
for y in (0..!size).descending() {
out.print(" " * y)
for x in 0..!(size-y) {
out.print((x & y).isZero().pick("◢◣", " "))
}
out.println()
}
}
Elixir
{{trans|Erlang}}
defmodule RC do
def sierpinski_triangle(n) do
f = fn(x) -> IO.puts "#{x}" end
Enum.each(triangle(n, ["*"], " "), f)
end
defp triangle(0, down, _), do: down
defp triangle(n, down, sp) do
newDown = (for x <- down, do: sp<>x<>sp) ++ (for x <- down, do: x<>" "<>x)
triangle(n-1, newDown, sp<>sp)
end
end
RC.sierpinski_triangle(4)
Elm
{{trans|Haskell}}
import String exposing (..)
import Html exposing (..)
import Html.Attributes as A exposing (..)
import Html.Events exposing (..)
import Html.App exposing (beginnerProgram)
import Result exposing (..)
sierpinski : Int -> List String
sierpinski n =
let down n = sierpinski (n - 1)
space n = repeat (2 ^ (n - 1)) " "
in case n of
0 -> ["*"]
_ -> List.map ((\st -> space n ++ st) << (\st -> st ++ space n)) (down n)
++ List.map (join " " << List.repeat 2) (down n)
main = beginnerProgram { model = "4", view = view, update = update }
update newStr oldStr = newStr
view : String -> Html String
view levelString =
div []
([ Html.form
[]
[ label [ myStyle ] [ text "Level: "]
, input
[ placeholder "triangle level."
, value levelString
, on "input" targetValue
, type' "number"
, A.min "0"
, myStyle
]
[]
]
] ++
[ pre [] (levelString
|> toInt
|> withDefault 0
|> sierpinski
|> List.map (\s -> div [] [text s]))
])
myStyle : Attribute msg
myStyle =
style
[ ("height", "20px")
, ("padding", "5px 0 0 5px")
, ("font-size", "1em")
, ("text-align", "left")
]
Link to live demo: http://dc25.github.io/sierpinskiElm/
Erlang
{{trans|OCaml}}
-module(sierpinski).
-export([triangle/1]).
triangle(N) ->
F = fun(X) -> io:format("~s~n",[X]) end,
lists:foreach(F, triangle(N, ["*"], " ")).
triangle(0, Down, _) -> Down;
triangle(N, Down, Sp) ->
NewDown = [Sp++X++Sp || X<-Down]++[X++" "++X || X <- Down],
triangle(N-1, NewDown, Sp++Sp).
Euphoria
{{trans|BASIC}}
procedure triangle(integer x, integer y, integer len, integer n)
if n = 0 then
position(y,x) puts(1,'*')
else
triangle (x, y+len, floor(len/2), n-1)
triangle (x+len, y, floor(len/2), n-1)
triangle (x+len*2, y+len, floor(len/2), n-1)
end if
end procedure
clear_screen()
triangle(1,1,8,4)
=={{header|F Sharp|F#}}==
let sierpinski n =
let rec loop down space n =
if n = 0 then
down
else
loop (List.map (fun x -> space + x + space) down @
List.map (fun x -> x + " " + x) down)
(space + space)
(n - 1)
in loop ["*"] " " n
let () =
List.iter (fun (i:string) -> System.Console.WriteLine(i)) (sierpinski 4)
Factor
{{trans|OCaml}}
USING: io kernel math sequences ;
IN: sierpinski
: iterate-triangle ( triange spaces -- triangle' )
[ [ dup surround ] curry map ]
[ drop [ dup " " glue ] map ] 2bi append ;
: (sierpinski) ( triangle spaces n -- triangle' )
dup 0 = [ 2drop "\n" join ] [
[
[ iterate-triangle ]
[ nip dup append ] 2bi
] dip 1 - (sierpinski)
] if ;
: sierpinski ( n -- )
[ { "*" } " " ] dip (sierpinski) print ;
FALSE
{{incorrect|FALSE|Different results with different interpreters (like http://morphett.info/false/false.html and http://www.quirkster.com/iano/js/false-js.html}}
[[$][$1&["*"]?$~1&[" "]?2/]#%"
"]s: { stars }
[$@$@|@@&~&]x: { xor }
[1\[$][1-\2*\]#%]e: { 2^n }
[e;!1\[$][\$s;!$2*x;!\1-]#%%]t:
4t;!
Forth
: stars ( mask -- )
begin
dup 1 and if [char] * else bl then emit
1 rshift dup
while space repeat drop ;
: triangle ( order -- )
1 swap lshift ( 2^order )
1 over 0 do
cr over i - spaces dup stars
dup 2* xor
loop 2drop ;
5 triangle
Fortran
{{works with|Fortran|90 and later}} This method calculates a Pascal's triangle and replaces every odd number with a * and every even number with a space. The limitation of this approach is the size of the numbers in the Pascal's triangle. Tryng to print an order 8 Sierpinski's triangle will overflow a 32 bit integer and an order 16 will overflow a 64 bit integer.
program Sierpinski_triangle
implicit none
call Triangle(4)
contains
subroutine Triangle(n)
implicit none
integer, parameter :: i64 = selected_int_kind(18)
integer, intent(in) :: n
integer :: i, k
integer(i64) :: c
do i = 0, n*4-1
c = 1
write(*, "(a)", advance="no") repeat(" ", 2 * (n*4 - 1 - i))
do k = 0, i
if(mod(c, 2) == 0) then
write(*, "(a)", advance="no") " "
else
write(*, "(a)", advance="no") " * "
end if
c = c * (i - k) / (k + 1)
end do
write(*,*)
end do
end subroutine Triangle
end program Sierpinski_triangle
GAP
# Using parity of binomial coefficients
SierpinskiTriangle := function(n)
local i, j, s, b;
n := 2^n - 1;
b := " ";
while Size(b) < n do
b := Concatenation(b, b);
od;
for i in [0 .. n] do
s := "";
for j in [0 .. i] do
if IsEvenInt(Binomial(i, j)) then
Append(s, " ");
else
Append(s, "* ");
fi;
od;
Print(b{[1 .. n - i]}, s, "\n");
od;
end;
SierpinskiTriangle(4);
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
gnuplot
Making and printing a text string, using bit-twiddling to decide whether each character should be a space or a star.
# Return a string space or star to print at x,y.
# Must have x<y. x<0 is the left side of the triangle.
# If x<-y then it's before the left edge and the return is a space.
char(x,y) = (y+x>=0 && ((y+x)%2)==0 && ((y+x)&(y-x))==0 ? "*" : " ")
# Return a string which is row y of the triangle from character
# position x through to the right hand end x==y, inclusive.
row(x,y) = (x<=y ? char(x,y).row(x+1,y) : "\n")
# Return a string of stars, spaces and newlines which is the
# Sierpinski triangle from row y to limit, inclusive.
# The first row is y=0.
triangle(y,limit) = (y <= limit ? row(-limit,y).triangle(y+1,limit) : "")
# Print rows 0 to 15, which is the order 4 triangle per the task.
print triangle(0,15)
Go
"Δ" (Greek capital letter delta) looks good for grain, as does Unicode triangle, "△". ASCII "." and "^" are pleasing. "/\", "´`", and "◢◣"" make interesting wide triangles.
package main
import (
"fmt"
"strings"
"unicode/utf8"
)
var order = 4
var grain = "*"
func main() {
t := []string{grain + strings.Repeat(" ", utf8.RuneCountInString(grain))}
for ; order > 0; order-- {
sp := strings.Repeat(" ", utf8.RuneCountInString(t[0])/2)
top := make([]string, len(t))
for i, s := range t {
top[i] = sp + s + sp
t[i] += s
}
t = append(top, t...)
}
for _, r := range t {
fmt.Println(r)
}
}
Groovy
Solution:
def stPoints;
stPoints = { order, base=[0,0] ->
def right = [base[0], base[1]+2**order]
def up = [base[0]+2**(order-1), base[1]+2**(order-1)]
(order == 0) \
? [base]
: (stPoints(order-1, base) + stPoints(order-1, right) + stPoints(order-1, up))
}
def stGrid = { order ->
def h = 2**order
def w = 2**(order+1) - 1
def grid = (0..<h).collect { (0..<w).collect { ' ' } }
stPoints(order).each { grid[it[0]][it[1]] = (order%10).toString() }
grid
}
Test:
stGrid(0).reverse().each { println it.sum() }
println()
stGrid(1).reverse().each { println it.sum() }
println()
stGrid(2).reverse().each { println it.sum() }
println()
stGrid(3).reverse().each { println it.sum() }
println()
stGrid(4).reverse().each { println it.sum() }
println()
stGrid(5).reverse().each { println it.sum() }
println()
stGrid(6).reverse().each { println it.sum() }
{{out}}
0
1
1 1
2
2 2
2 2
2 2 2 2
3
3 3
3 3
3 3 3 3
3 3
3 3 3 3
3 3 3 3
3 3 3 3 3 3 3 3
4
4 4
4 4
4 4 4 4
4 4
4 4 4 4
4 4 4 4
4 4 4 4 4 4 4 4
4 4
4 4 4 4
4 4 4 4
4 4 4 4 4 4 4 4
4 4 4 4
4 4 4 4 4 4 4 4
4 4 4 4 4 4 4 4
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
5
5 5
5 5
5 5 5 5
5 5
5 5 5 5
5 5 5 5
5 5 5 5 5 5 5 5
5 5
5 5 5 5
5 5 5 5
5 5 5 5 5 5 5 5
5 5 5 5
5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5
5 5 5 5
5 5 5 5
5 5 5 5 5 5 5 5
5 5 5 5
5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5
5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
6
6 6
6 6
6 6 6 6
6 6
6 6 6 6
6 6 6 6
6 6 6 6 6 6 6 6
6 6
6 6 6 6
6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6
6 6 6 6
6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6
6 6 6 6
6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
```
## Haskell
```haskell
sierpinski 0 = ["*"]
sierpinski n = map ((space ++) . (++ space)) down ++
map (unwords . replicate 2) down
where down = sierpinski (n - 1)
space = replicate (2 ^ (n - 1)) ' '
main = mapM_ putStrLn $ sierpinski 4
```
{{out}}
```txt
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
```
We can see how the approach above (centering a preceding block over two duplicates) generates a framing rectangle at each stage, by making the right padding (plus the extra space between duplicates) more distinct and visible:
```haskell
import Data.List (intercalate)
sierpinski :: Int -> [String]
sierpinski 0 = ["▲"]
sierpinski n =
concat $
(<$> sierpinski (n - 1)) <$> -- Previous triangle,
[ flip intercalate ([replicate (2 ^ (n - 1))] <*> " -") -- centred,
, (++) <*> ('+' :) -- above singly spaced duplicates.
]
main :: IO ()
main = mapM_ putStrLn $ sierpinski 4
```
{{Out}}
```txt
▲---------------
▲+▲--------------
▲-+ ▲-------------
▲+▲+▲+▲------------
▲---+ ▲-----------
▲+▲--+ ▲+▲----------
▲-+ ▲-+ ▲-+ ▲---------
▲+▲+▲+▲+▲+▲+▲+▲--------
▲-------+ ▲-------
▲+▲------+ ▲+▲------
▲-+ ▲-----+ ▲-+ ▲-----
▲+▲+▲+▲----+ ▲+▲+▲+▲----
▲---+ ▲---+ ▲---+ ▲---
▲+▲--+ ▲+▲--+ ▲+▲--+ ▲+▲--
▲-+ ▲-+ ▲-+ ▲-+ ▲-+ ▲-+ ▲-+ ▲-
▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲
```
Using bitwise and between x and y coords:
```haskell
import Data.Bits ((.&.))
sierpinski n = map row [m, m-1 .. 0] where
m = 2^n - 1
row y = replicate y ' ' ++ concatMap cell [0..m - y] where
cell x | y .&. x == 0 = " *"
| otherwise = " "
main = mapM_ putStrLn $ sierpinski 4
```
{{Trans|JavaScript}}
```Haskell
import Data.List (intersperse)
-- Top down, each row after the first is an XOR / Rule90 rewrite.
-- Bottom up, each line above the base is indented 1 more space.
sierpinski :: Int -> String
sierpinski = fst . foldr spacing ([], []) . rule90 . (2 ^)
where
rule90 = scanl next "*" . enumFromTo 1 . subtract 1
where
next = const . ((zipWith xor . (' ' :)) <*> (++ " "))
xor l r
| l == r = ' '
| otherwise = '*'
spacing x (s, w) = (concat [w, intersperse ' ' x, "\n", s], w ++ " ")
main :: IO ()
main = putStr $ sierpinski 4
```
Or simply as a right fold:
```haskell
sierpinski :: Int -> [String]
sierpinski n =
foldr
(\i xs ->
let s = replicate (2 ^ i) ' '
in fmap ((s ++) . (++ s)) xs ++ fmap ((++) <*> (' ' :)) xs)
["*"]
[n - 1,n - 2 .. 0]
main :: IO ()
main = (putStrLn . unlines. sierpinski) 4
```
{{Out}}
```txt
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
```
## Haxe
```haxe
class Main
{
static function main()
{
triangle(3);
}
static inline var SPACE = ' ';
static inline var STAR = '*';
static function triangle(o) {
var n = 1 << o;
var line = new Array();
for (i in 0...(n*2)) line[i] = SPACE;
line[n] = '*';
for (i in 0...n) {
Sys.println(line.join(''));
var u ='*';
var start = n - i;
var end = n + i + 1;
var t = SPACE;
for (j in start...end) {
t = (line[j-1] == line[j+1] ? SPACE : STAR);
line[j-1] = u;
u = t;
}
line[n+i] = t;
line[n+i+1] = STAR;
}
}
}
```
=={{header|Icon}} and {{header|Unicon}}==
This is a text based adaption of a program from the IPL and Icon Graphics book. The triangle is presented with a twist. Based on an idea from "Chaos and Fractals" by Peitgen, Jurgens, and Saupe.
```Icon
# text based adaptaion of
procedure main(A)
width := 2 ^ ( 1 + (order := 0 < integer(\A[1]) | 4)) # order of arg[1] or 4
write("Triangle order= ",order)
every !(canvas := list(width)) := list(width," ") # prime the canvas
every y := 1 to width & x := 1 to width do # traverse it
if iand(x - 1, y - 1) = 0 then canvas[x,y] := "*" # fill
every x := 1 to width & y := 1 to width do
writes((y=1,"\n")|"",canvas[x,y]," ") # print
end
```
{{libheader|Icon Programming Library}}
Adapted from [http://www.cs.arizona.edu/icon/library/src/gprogs/sier1.icn graphics/sier1.icn]
{{out|Sample output for order 3}}
```txt
Triangle order = 2
* * * * * * * *
* * * *
* * * *
* *
* * * *
* *
* *
*
```
## IDL
The only 'special' thing here is that the math is done in a byte array, filled with the numbers 32 and 42 and then output through a "string(array)" which prints the ascii representation of each individual element in the array.
```idl
pro sierp,n
s = (t = bytarr(3+2^(n+1))+32b)
t[2^n+1] = 42b
for lines = 1,2^n do begin
print,string( (s = t) )
for i=1,n_elements(t)-2 do if s[i-1] eq s[i+1] then t[i]=32b else t[i]=42b
end
end
```
## J
There are any number of succinct ways to produce this in J.
Here's one that exploits self-similarity:
```j
|. _31]\ ,(,.~ , ])^:4 ,: '* '
```
Here, (,.~ , ])^:4 ,: '* ' is the basic structure (with 4 iterations) and the rest of it is just formatting.
Here's one that leverages the relationship between Sierpinski's and Pascal's triangles:
```j
' *' {~ '1' = (- |."_1 [: ": 2 | !/~) i._16
```
Here, !/~ i._16 gives us [[Pascal's_triangle|pascal's triangle]] (and we want a power of 2 (or, for the formatting we are using here a negative of a power of 2) for the size of the square in which contains the triangle, and (2 + |/~) i._16 is a [[Boolean_values#J|boolean]] representation where the 1s correspond to odd values in pascal's triangle, and the rest is just formatting.
(Aside: it's popular to say that booleans are not integers, but this is a false representation of [[Greatest_common_divisor#J|George Boole's work]].)
## Java
{{trans|JavaScript}}
```java
public static void triangle(int n){
n= 1 << n;
StringBuilder line= new StringBuilder(); //use a "mutable String"
char t= 0;
char u= 0; // avoid warnings
for(int i= 0;i <= 2 * n;++i)
line.append(" "); //start empty
line.setCharAt(n, '*'); //with the top point of the triangle
for(int i= 0;i < n;++i){
System.out.println(line);
u= '*';
for(int j= n - i;j < n + i + 1;++j){
t= (line.charAt(j - 1) == line.charAt(j + 1) ? ' ' : '*');
line.setCharAt(j - 1, u);
u= t;
}
line.setCharAt(n + i, t);
line.setCharAt(n + i + 1, '*');
}
}
```
{{trans|Haskell}}
{{works with|Java|1.5+}}
```java
import java.util.*;
public class Sierpinski
{
public static List sierpinski(int n)
{
List down = Arrays.asList("*");
String space = " ";
for (int i = 0; i < n; i++) {
List newDown = new ArrayList();
for (String x : down)
newDown.add(space + x + space);
for (String x : down)
newDown.add(x + " " + x);
down = newDown;
space += space;
}
return down;
}
public static void main(String[] args)
{
for (String x : sierpinski(4))
System.out.println(x);
}
}
```
## JavaFX Script
{{trans|Python}}
```javafx
function sierpinski(n : Integer) {
var down = ["*"];
var space = " ";
for (i in [1..n]) {
down = [for (x in down) "{space}{x}{space}", for (x in down) "{x} {x}"];
space = "{space}{space}";
}
for (x in down) {
println("{x}")
}
}
sierpinski(4);
```
## JavaScript
### ES5
### =Functional=
Using a functional idiom of JavaScript, we can construct a Sierpinksi triangle as a Pascal triangle (mod 2),
mapping the binary pattern to centred strings.
```JavaScript
(function (order) {
// Sierpinski triangle of order N constructed as
// Pascal triangle of 2^N rows mod 2
// with 1 encoded as "▲"
// and 0 encoded as " "
function sierpinski(intOrder) {
return function asciiPascalMod2(intRows) {
return range(1, intRows - 1)
.reduce(function (lstRows) {
var lstPrevRow = lstRows.slice(-1)[0];
// Each new row is a function of the previous row
return lstRows.concat([zipWith(function (left, right) {
// The composition ( asciiBinary . mod 2 . add )
// reduces to a rule from 2 parent characters
// to a single child character
// Rule 90 also reduces to the same XOR
// relationship between left and right neighbours
return left === right ? " " : "▲";
}, [' '].concat(lstPrevRow), lstPrevRow.concat(' '))]);
}, [
["▲"] // Tip of triangle
]);
}(Math.pow(2, intOrder))
// As centred lines, from bottom (0 indent) up (indent below + 1)
.reduceRight(function (sofar, lstLine) {
return {
triangle: sofar.indent + lstLine.join(" ") + "\n" +
sofar.triangle,
indent: sofar.indent + " "
};
}, {
triangle: "",
indent: ""
}).triangle;
};
var zipWith = function (f, xs, ys) {
return xs.length === ys.length ? xs
.map(function (x, i) {
return f(x, ys[i]);
}) : undefined;
},
range = function (m, n) {
return Array.apply(null, Array(n - m + 1))
.map(function (x, i) {
return m + i;
});
};
// TEST
return sierpinski(order);
})(4);
```
Output (N=4)
```txt
▲
▲ ▲
▲ ▲
▲ ▲ ▲ ▲
▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
```
### =Imperative=
```javascript
function triangle(o) {
var n = 1 << o,
line = new Array(2 * n),
i, j, t, u;
for (i = 0; i < line.length; ++i) line[i] = ' ';
line[n] = '*';
for (i = 0; i < n; ++i) {
document.write(line.join('') + "\n");
u = '*';
for (j = n - i; j < n + i + 1; ++j) {
t = (line[j - 1] == line[j + 1] ? ' ' : '*');
line[j - 1] = u;
u = t;
}
line[n + i] = t;
line[n + i + 1] = '*';
}
}
document.write("
```txt
\n");
triangle(6);
document.write("
```
");
```
### ES6
Directly in terms of the built-in Array methods '''.map''', '''.reduce''', and '''.from''', and without much abstraction, possibly at the cost of some legibility:
```javascript
(() => {
'use strict';
// sierpinski :: Int -> String
const sierpinski = n =>
Array.from({
length: n
})
.reduce(
(xs, _, i) => {
const s = ' '.repeat(Math.pow(2, i));
return xs.map(x => s + x + s)
.concat(
xs.map(x => x + ' ' + x)
)
},
['*']
).join('\n');
// TEST -------------------------------------------
console.log(
sierpinski(4)
);
})();
```
{{Trans|Haskell}}
Centering any preceding triangle block over two adjacent duplicates:
```JavaScript
(() => {
'use strict';
// LINES OF SIERPINSKI TRIANGLE AT LEVEL N -------------------------------
// sierpinski :: Int -> [String]
const sierpTriangle = n =>
// Previous triangle centered with left and right padding,
(n > 0) ? concat(ap([
map(xs => intercalate(xs, ap(
[s => concat(replicate(Math.pow(2, (n - 1)), s))], [' ', '-']
))),
// above a pair of duplicates, placed one character apart.
map(xs => intercalate('+', [xs, xs]))
], [sierpTriangle(n - 1)])) : ['▲'];
// GENERIC FUNCTIONS -----------------------------------------------------
// replicate :: Int -> a -> [a]
const replicate = (n, a) => {
let v = [a],
o = [];
if (n < 1) return o;
while (n > 1) {
if (n & 1) o = o.concat(v);
n >>= 1;
v = v.concat(v);
}
return o.concat(v);
};
// curry :: ((a, b) -> c) -> a -> b -> c
const curry = f => a => b => f(a, b);
// map :: (a -> b) -> [a] -> [b]
const map = curry((f, xs) => xs.map(f));
// Apply a list of functions to a list of arguments
// <*> :: [(a -> b)] -> [a] -> [b]
const ap = (fs, xs) => //
[].concat.apply([], fs.map(f => //
[].concat.apply([], xs.map(x => [f(x)]))));
// unlines :: [String] -> String
const unlines = xs => xs.join('\n');
// intercalate :: String -> [a] -> String
const intercalate = (s, xs) => xs.join(s);
// concat :: [[a]] -> [a] || [String] -> String
const concat = xs => {
if (xs.length > 0) {
const unit = typeof xs[0] === 'string' ? '' : [];
return unit.concat.apply(unit, xs);
} else return [];
};
// TEST ------------------------------------------------------------------
return unlines(sierpTriangle(4));
})();
```
{{Out}}
```txt
▲---------------
▲+▲--------------
▲-+ ▲-------------
▲+▲+▲+▲------------
▲---+ ▲-----------
▲+▲--+ ▲+▲----------
▲-+ ▲-+ ▲-+ ▲---------
▲+▲+▲+▲+▲+▲+▲+▲--------
▲-------+ ▲-------
▲+▲------+ ▲+▲------
▲-+ ▲-----+ ▲-+ ▲-----
▲+▲+▲+▲----+ ▲+▲+▲+▲----
▲---+ ▲---+ ▲---+ ▲---
▲+▲--+ ▲+▲--+ ▲+▲--+ ▲+▲--
▲-+ ▲-+ ▲-+ ▲-+ ▲-+ ▲-+ ▲-+ ▲-
▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲+▲
```
Or constructed as 2^N lines of Pascal's triangle mod 2,
and mapped to centred {1:asterisk, 0:space} strings.
```JavaScript
(order => {
// sierpinski :: Int -> [Bool]
let sierpinski = intOrder => {
// asciiPascalMod2 :: Int -> [[Int]]
let asciiPascalMod2 = nRows =>
range(1, nRows - 1)
.reduce(sofar => {
let lstPrev = sofar.slice(-1)[0];
// The composition of (asciiBinary . mod 2 . add)
// is reduced here to a rule from two parent characters
// to a single child character.
// Rule 90 also reduces to the same XOR
// relationship between left and right neighbours.
return sofar
.concat([zipWith(
(left, right) => left === right ? ' ' : '*',
[' '].concat(lstPrev),
lstPrev.concat(' ')
)]);
}, [
['*'] // Tip of triangle
]);
// Reduce/folding from the last item (base of list)
// which has zero left indent.
// Each preceding row has one more indent space than the row beneath it
return asciiPascalMod2(Math.pow(2, intOrder))
.reduceRight((a, x) => {
return {
triangle: a.indent + x.join(' ') + '\n' + a.triangle,
indent: a.indent + ' '
}
}, {
triangle: '',
indent: ''
}).triangle
};
// zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
let zipWith = (f, xs, ys) =>
xs.length === ys.length ? (
xs.map((x, i) => f(x, ys[i]))
) : undefined,
// range(intFrom, intTo, optional intStep)
// Int -> Int -> Maybe Int -> [Int]
range = (m, n, step) => {
let d = (step || 1) * (n >= m ? 1 : -1);
return Array.from({
length: Math.floor((n - m) / d) + 1
}, (_, i) => m + (i * d));
};
return sierpinski(order);
})(4);
```
{{Out}}
```txt
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
```
## Julia
{{works with|Julia|0.6}}
```julia
function sierpinski(n, token::AbstractString="*")
x = fill(token, 1, 1)
for _ in 1:n
h, w = size(x)
s = fill(" ", h,(w + 1) ÷ 2)
t = fill(" ", h,1)
x = [[s x s] ; [x t x]]
end
return x
end
function printsierpinski(m::Matrix)
for r in 1:size(m, 1)
println(join(m[r, :]))
end
end
sierpinski(4) |> printsierpinski
```
## Kotlin
{{trans|C}}
```scala
// version 1.1.2
const val ORDER = 4
const val SIZE = 1 shl ORDER
fun main(args: Array) {
for (y in SIZE - 1 downTo 0) {
for (i in 0 until y) print(" ")
for (x in 0 until SIZE - y) print(if ((x and y) != 0) " " else "* ")
println()
}
}
```
{{out}}
```txt
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
```
## Liberty BASIC
```lb
nOrder=4
call triangle 1, 1, nOrder
end
SUB triangle x, y, n
IF n = 0 THEN
LOCATE x,y: PRINT "*";
ELSE
n=n-1
length=2^n
call triangle x, y+length, n
call triangle x+length, y, n
call triangle x+length*2, y+length, n
END IF
END SUB
```
## Logo
```logo
; Print rows of the triangle from 0 to :limit inclusive.
; limit=15 gives the order 4 form per the task.
; The range of :y is arbitrary, any rows of the triangle can be printed.
make "limit 15
for [y 0 :limit] [
for [x -:limit :y] [
type ifelse (and :y+:x >= 0 ; blank left of triangle
(remainder :y+:x 2) = 0 ; only "even" squares
(bitand :y+:x :y-:x) = 0 ; Sierpinski bit test
) ["*] ["| |] ; star or space
]
print []
]
```
## Lua
Ported from the list-comprehension Python version.
```lua
function sierpinski(depth)
lines = {}
lines[1] = '*'
for i = 2, depth+1 do
sp = string.rep(' ', 2^(i-2))
tmp = {}
for idx, line in ipairs(lines) do
tmp[idx] = sp .. line .. sp
tmp[idx+#lines] = line .. ' ' .. line
end
lines = tmp
end
return table.concat(lines, '\n')
end
print(sierpinski(4))
```
{{out}}
```txt
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
```
## Maple
```maple
S := proc(n)
local i, j, values, position;
values := [ seq(" ",i=1..2^n-1), "*" ];
printf("%s\n",cat(op(values)));
for i from 2 to 2^n do
position := [ ListTools:-SearchAll( "*", values ) ];
values := Array([ seq(0, i=1..2^n+i-1) ]);
for j to numelems(position) do
values[position[j]-1] := values[position[j]-1] + 1;
values[position[j]+1] := values[position[j]+1] + 1;
end do;
values := subs( { 2 = " ", 0 = " ", 1 = "*"}, values );
printf("%s\n",cat(op(convert(values, list))));
end do:
end proc:
```
{{out}}
```txt
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
```
## Mathematica
Cellular automaton (rule 90) based solution:
```mathematica
n=4;Grid[CellularAutomaton[90,{{1},0},2^n-1]/.{0->" ",1->"*"},ItemSize->All]
```
Using built-in function:
```mathematica
SierpinskiMesh[3]
```
## MATLAB
STRING was introduced in version R2016b.
```MATLAB
n = 4;
d = string('*');
for k = 0 : n - 1
sp = repelem(' ', 2 ^ k);
d = [sp + d + sp, d + ' ' + d];
end
disp(d.join(char(10)))
```
{{out}}
```txt
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
```
### Cellular Automaton Version
```MATLAB
n = 2 ^ 4 - 1;
tr = + ~(-n : n);
for k = 1:n
tr(k + 1, :) = bitget(90, 1 + filter2([4 2 1], tr(k, :)));
end
char(10 * tr + 32)
```
### Mixed Version
```matlab
spy(mod(abs(pascal(32,1)),2)==1)
```
## NetRexx
{{trans|Java}}
```NetRexx
/* NetRexx */
options replace format comments java crossref symbols nobinary
numeric digits 1000
runSample(arg)
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method runSample(arg) public static
BLACK_UPPOINTING_TRIANGLE = '\u25b2'
parse arg ordr filr .
if ordr = '' | ordr = '.' then ordr = 4
if filr = '' | filr = '.' then filler = BLACK_UPPOINTING_TRIANGLE
else filler = filr
drawSierpinskiTriangle(ordr, filler)
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method drawSierpinskiTriangle(ordr, filler = Rexx '^') public static
n = 1 * (2 ** ordr)
line = ' '.copies(2 * n)
line = line.overlay(filler, n + 1) -- set the top point of the triangle
loop row = 1 to n -- NetRexx arrays, lists etc. index from 1
say line.strip('t')
u = filler
loop col = 2 + n - row to n + row
cl = line.substr(col - 1, 1)
cr = line.substr(col + 1, 1)
if cl == cr then t = ' '
else t = filler
line = line.overlay(u, col - 1)
u = t
end col
j2 = n + row - 1
j3 = n + row
line = line.overlay(t, j2 + 1)
line = line.overlay(filler, j3 + 1)
end row
return
```
{{out}}
```txt
▲
▲ ▲
▲ ▲
▲ ▲ ▲ ▲
▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
```
## Nim
{{trans|C}}
```nim
const size = 1 shl 4 - 1
for y in countdown(size, 0):
for i in 0 .. space ^ x ^ space) down @
List.map (fun x -> x ^ " " ^ x) down)
(space ^ space)
(n - 1)
in loop ["*"] " " n
let () =
List.iter print_endline (sierpinski 4)
```
## Oforth
This solution uses a cellular automaton (rule 90 for triangle).
automat(rule, n) runs cellular automaton for rule "rule" for n generations.
```Oforth
: nextGen(l, r)
| i |
StringBuffer new
l size loop: i [
l at(i 1 -) '*' == 4 *
l at(i) '*' == 2 * +
l at(i 1 +) '*' == +
2 swap pow r bitAnd ifTrue: [ '*' ] else: [ ' ' ] over addChar
] ;
: automat(rule, n)
StringBuffer new " " <4 sierpinskiTriangle
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
ok
>
```
## Oz
```oz
declare
fun {NextTriangle Triangle}
Sp = {Spaces {Length Triangle}}
in
{Flatten
[{Map Triangle fun {$ X} Sp#X#Sp end}
{Map Triangle fun {$ X} X#" "#X end}
]}
end
fun {Spaces N} if N == 0 then nil else & |{Spaces N-1} end end
fun lazy {Iterate F X}
X|{Iterate F {F X}}
end
SierpinskiTriangles = {Iterate NextTriangle ["*"]}
in
{ForAll {Nth SierpinskiTriangles 5} System.showInfo}
```
## PARI/GP
{{trans|C}}
```parigp
Sierpinski(n)={
my(s=2^n-1);
forstep(y=s,0,-1,
for(i=1,y,print1(" "));
for(x=0,s-y,
print1(if(bitand(x,y)," ","*"))
);
print()
)
};
Sierpinski(4)
```
{{out}}
```txt
*
**
* *
****
* *
** **
* * * *
********
* *
** **
* * * *
**** ****
* * * *
** ** ** **
* * * * * * * *
****************
```
## Pascal
{{trans|C}}
{{works with|Free Pascal}}
```pascal
program Sierpinski;
function ipow(b, n : Integer) : Integer;
var
i : Integer;
begin
ipow := 1;
for i := 1 to n do
ipow := ipow * b
end;
function truth(a : Char) : Boolean;
begin
if a = '*' then
truth := true
else
truth := false
end;
```
```pascal
function rule_90(ev : String) : String;
var
l, i : Integer;
cp : String;
s : Array[0..1] of Boolean;
begin
l := length(ev);
cp := copy(ev, 1, l);
for i := 1 to l do begin
if (i-1) < 1 then
s[0] := false
else
s[0] := truth(ev[i-1]);
if (i+1) > l then
s[1] := false
else
s[1] := truth(ev[i+1]);
if ( (s[0] and not s[1]) or (s[1] and not s[0]) ) then
cp[i] := '*'
else
cp[i] := ' ';
end;
rule_90 := cp
end;
procedure triangle(n : Integer);
var
i, l : Integer;
b : String;
begin
l := ipow(2, n+1);
b := ' ';
for i := 1 to l do
b := concat(b, ' ');
b[round(l/2)] := '*';
writeln(b);
for i := 1 to (round(l/2)-1) do begin
b := rule_90(b);
writeln(b)
end
end;
```
```pascal
begin
triangle(4)
end.
```
## Perl
```perl
sub sierpinski {
my ($n) = @_;
my @down = '*';
my $space = ' ';
foreach (1..$n) {
@down = (map("$space$_$space", @down), map("$_ $_", @down));
$space = "$space$space";
}
return @down;
}
print "$_\n" foreach sierpinski 4;
```
## Perl 6
{{trans|Perl}}
```perl6
sub sierpinski ($n) {
my @down = '*';
my $space = ' ';
for ^$n {
@down = |("$space$_$space" for @down), |("$_ $_" for @down);
$space x= 2;
}
return @down;
}
.say for sierpinski 4;
```
## Phix
{{Trans|C}}
```Phix
procedure sierpinski(integer n)
integer lim = power(2,n)-1
for y=lim to 0 by -1 do
puts(1,repeat(' ',y))
for x=0 to lim-y do
puts(1,iff(and_bits(x,y)?" ":"* "))
end for
puts(1,"\n")
end for
end procedure
for i=1 to 5 do
sierpinski(i)
end for
```
{{out}}
*
* *
*
* *
* *
* * * *
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
```
## PicoLisp
{{trans|Python}}
```PicoLisp
(de sierpinski (N)
(let (D '("*") S " ")
(do N
(setq
D (conc
(mapcar '((X) (pack S X S)) D)
(mapcar '((X) (pack X " " X)) D) )
S (pack S S) ) )
D ) )
(mapc prinl (sierpinski 4))
```
## PL/I
```PL/I
sierpinski: procedure options (main); /* 2010-03-30 */
declare t (79,79) char (1);
declare (i, j, k) fixed binary;
declare (y, xs, ys, xll, xrr, ixrr, limit) fixed binary;
t = ' ';
xs = 40; ys = 1;
/* Make initial triangle */
call make_triangle (xs, ys);
y = ys + 4;
xll = xs-4; xrr = xs+4;
do k = 1 to 3;
limit = 0;
do forever;
ixrr = xrr;
do i = xll to xll+limit by 8;
if t(y-1, i) = ' ' then
do;
call make_triangle (i, y);
if t(y+3,i-5) = '*' then
t(y+3,i-4), t(y+3,ixrr+4) = '*';
call make_triangle (ixrr, y);
end;
ixrr = ixrr - 8;
end;
xll = xll - 4; xrr = xrr + 4;
y = y + 4;
limit = limit + 8;
if xll+limit > xs-1 then leave;
end;
t(y-1,xs) = '*';
end;
/* Finished generation; now print the Sierpinski triangle. */
put edit (t) (skip, (hbound(t,2)) a);
make_triangle: procedure (x, y);
declare (x, y) fixed binary;
declare i fixed binary;
do i = 0 to 3;
t(y+i, x-i), t(y+i, x+i) = '*';
end;
do i = x-2 to x+2; /* The base of the triangle. */
t(y+3, i) = '*';
end;
end make_triangle;
end sierpinski;
```
## Pop11
Solution using line buffer in an integer array oline, 0 represents ' '
(space), 1 represents '*' (star).
```pop11
define triangle(n);
lvars k = 2**n, j, l, oline, nline;
initv(2*k+3) -> oline;
initv(2*k+3) -> nline;
for l from 1 to 2*k+3 do 0 -> oline(l) ; endfor;
1 -> oline(k+2);
0 -> nline(1);
0 -> nline(2*k+3);
for j from 1 to k do
for l from 1 to 2*k+3 do
printf(if oline(l) = 0 then ' ' else '*' endif);
endfor;
printf('\n');
for l from 2 to 2*k+2 do
(oline(l-1) + oline(l+1)) rem 2 -> nline(l);
endfor;
(oline, nline) -> (nline, oline);
endfor;
enddefine;
triangle(4);
```
Alternative solution, keeping all triangle as list of strings
```pop11
define triangle2(n);
lvars acc = ['*'], spaces = ' ', j;
for j from 1 to n do
maplist(acc, procedure(x); spaces >< x >< spaces ; endprocedure)
<> maplist(acc, procedure(x); x >< ' ' >< x ; endprocedure) -> acc;
spaces >< spaces -> spaces;
endfor;
applist(acc, procedure(x); printf(x, '%p\n'); endprocedure);
enddefine;
triangle2(4);
```
## PostScript
This draws the triangles in a string-rewrite fashion, where all edges form a single polyline. 9 page document showing progession.
```postscript
%!PS-Adobe-3.0
%%BoundingBox 0 0 300 300
/F { 1 0 rlineto } def
/+ { 120 rotate } def
/- {-120 rotate } def
/v {.5 .5 scale } def
/^ { 2 2 scale } def
/!0{ dup 1 sub dup -1 eq not } def
/X { !0 { v X + F - X - F + X ^ } { F } ifelse pop } def
0 1 8 { 300 300 scale 0 1 12 div moveto
X + F + F fill showpage } for
%%EOF
```
## PowerShell
{{Trans|JavaScript}}
```powershell
function triangle($o) {
$n = [Math]::Pow(2, $o)
$line = ,' '*(2*$n+1)
$line[$n] = '█'
$OFS = ''
for ($i = 0; $i -lt $n; $i++) {
Write-Host $line
$u = '█'
for ($j = $n - $i; $j -lt $n + $i + 1; $j++) {
if ($line[$j-1] -eq $line[$j+1]) {
$t = ' '
} else {
$t = '█'
}
$line[$j-1] = $u
$u = $t
}
$line[$n+$i] = $t
$line[$n+$i+1] = '█'
}
}
```
## Prolog
Works with SWI-Prolog;
```Prolog
sierpinski_triangle(N) :-
Len is 2 ** (N+1) - 1,
length(L, Len),
numlist(1, Len, LN),
maplist(init(N), L, LN),
atomic_list_concat(L, Line),
writeln(Line),
NbTours is 2**N - 1,
loop(NbTours, LN, Len, L).
init(N, Cell, Num) :-
( Num is 2 ** N + 1 -> Cell = *; Cell = ' ').
loop(0, _, _, _) :- !.
loop(N, LN, Len, L) :-
maplist(compute_next_line(Len, L), LN, L1),
atomic_list_concat(L1, Line),
writeln(Line),
N1 is N - 1,
loop(N1, LN, Len, L1).
compute_next_line(Len, L, I, V) :-
I1 is I - 1,
I2 is I+1,
( I = 1 -> V0 = ' '; nth1(I1, L, V0)),
nth1(I, L, V1),
( I = Len -> V2 = ' '; nth1(I2, L, V2)),
rule_90(V0, V1, V2, V).
rule_90('*','*','*', ' ').
rule_90('*','*',' ', '*').
rule_90('*',' ','*', ' ').
rule_90('*',' ',' ', '*').
rule_90(' ','*','*', '*').
rule_90(' ','*',' ', ' ').
rule_90(' ',' ','*', '*').
rule_90(' ',' ',' ', ' ').
```
{{out}}
```txt
?- sierpinski_triangle(4).
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
true
```
## PureBasic
```PureBasic
Procedure Triangle (X,Y, Length, N)
If N = 0
DrawText( Y,X, "*",#Blue)
Else
Triangle (X+Length, Y, Length/2, N-1)
Triangle (X, Y+Length, Length/2, N-1)
Triangle (X+Length, Y+Length*2, Length/2, N-1)
EndIf
EndProcedure
OpenWindow(0, 100, 100,700,500 ,"Sierpinski triangle", #PB_Window_SystemMenu |1)
StartDrawing(WindowOutput(0))
DrawingMode(#PB_2DDrawing_Transparent )
Triangle(10,10,120,5)
StopDrawing()
Repeat
Until WaitWindowEvent()=#PB_Event_CloseWindow
End
```
## Python
```python
def sierpinski(n):
d = ["*"]
for i in xrange(n):
sp = " " * (2 ** i)
d = [sp+x+sp for x in d] + [x+" "+x for x in d]
return d
print "\n".join(sierpinski(4))
```
Or, using fold / reduce {{works with|Python|3.x}}
```python
import functools
def sierpinski(n):
def aggregate(TRIANGLE, I):
SPACE = " " * (2 ** I)
return [SPACE+X+SPACE for X in TRIANGLE] + [X+" "+X for X in TRIANGLE]
return functools.reduce(aggregate, range(n), ["*"])
print("\n".join(sierpinski(4)))
```
and fold/reduce, wrapped as concatMap, can provide the list comprehensions too:
```python
from functools import (reduce)
from operator import (add)
# sierpinski :: Int -> String
def sierpinski(n):
def go(xs, i):
s = ' ' * (2 ** i)
return concatMap(lambda x: [s + x + s])(xs) + (
concatMap(lambda x: [x + ' ' + x])(xs)
)
return '\n'.join(reduce(go, range(n), '*'))
# concatMap :: (a -> [b]) -> [a] -> [b]
def concatMap(f):
return lambda xs: (
reduce(add, map(f, xs), [])
)
print(sierpinski(4))
```
Use Python's long integer and bit operator to make an infinite triangle:
```python
x = 1
while True:
print(bin(x)[2:].replace('0', ' '))
x ^= x<<1
```
## R
Based on C# but using some of R's functionality to abbreviate code where possible.
```r
sierpinski.triangle = function(n) {
len <- 2^(n+1)
b <- c(rep(FALSE,len/2),TRUE,rep(FALSE,len/2))
for (i in 1:(len/2))
{
cat(paste(ifelse(b,"*"," "),collapse=""),"\n")
n <- rep(FALSE,len+1)
n[which(b)-1]<-TRUE
n[which(b)+1]<-xor(n[which(b)+1],TRUE)
b <- n
}
}
sierpinski.triangle(5)
```
Shortened to a function of one line.
```r
sierpinski.triangle = function(n) {
c(paste(ifelse(b<<- c(rep(FALSE,2^(n+1)/2),TRUE,rep(FALSE,2^(n+1)/2)),"*"," "),collapse=""),replicate(2^n-1,paste(ifelse(b<<-xor(c(FALSE,b[1:2^(n+1)]),c(b[2:(2^(n+1)+1)],FALSE)),"*"," "),collapse="")))
}
cat(sierpinski.triangle(5),sep="\n")
```
## Racket
```Racket
#lang racket
(define (sierpinski n)
(if (zero? n)
'("*")
(let ([spaces (make-string (expt 2 (sub1 n)) #\space)]
[prev (sierpinski (sub1 n))])
(append (map (λ(x) (~a spaces x spaces)) prev)
(map (λ(x) (~a x " " x)) prev)))))
(for-each displayln (sierpinski 5))
```
## REXX
```rexx
/*REXX program constructs and displays a Sierpinski triangle of up to around order 10k.*/
parse arg n mark . /*get the order of Sierpinski triangle.*/
if n=='' | n=="," then n=4 /*Not specified? Then use the default.*/
if mark=='' then mark= "*" /*MARK was specified as a character. */
if length(mark)==2 then mark=x2c(mark) /* " " " in hexadecimal. */
if length(mark)==3 then mark=d2c(mark) /* " " " " decimal. */
numeric digits 12000 /*this should handle the biggy numbers.*/
/* [↓] the blood-'n-guts of the pgm. */
do j=0 for n*4; !=1; z=left('', n*4 -1-j) /*indent the line to be displayed. */
do k=0 for j+1 /*construct the line with J+1 parts. */
if !//2==0 then z=z' ' /*it's either a blank, or ··· */
else z=z mark /* ··· it's one of 'em thar characters.*/
!=! * (j-k) % (k+1) /*calculate handy-dandy thing-a-ma-jig.*/
end /*k*/ /* [↑] finished constructing a line. */
say z /*display a line of the triangle. */
end /*j*/ /* [↑] finished showing triangle. */
/*stick a fork in it, we're all done. */
```
'''output''' when using the default input of order: 4
(Shown at three quarter size.)
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
```
'''output''' when using the input of: 8 1e
(Shown at half size.)
▲
▲ ▲
▲ ▲
▲ ▲ ▲ ▲
▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
```
'''output''' when using the input of: 32 db
(Shown at one tenth size.)
█
█ █
█ █
█ █ █ █
█ █
█ █ █ █
█ █ █ █
█ █ █ █ █ █ █ █
█ █
█ █ █ █
█ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █
█ █ █ █
█ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █
█ █ █ █
█ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █
█ █ █ █
█ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
```
Output with an input of '''64''' can be viewed at: [[Sierpinski triangle/REXX output 64]]
## Ring
```ring
# Project : Sierpinski triangle
norder=4
xy = list(40)
for i = 1 to 40
xy[i] = " "
next
triangle(1, 1, norder)
for i = 1 to 36
see xy[i] + nl
next
func triangle(x, y, n)
if n = 0
xy[y] = left(xy[y],x-1) + "*" + substr(xy[y],x+1)
else
n=n-1
length=pow(2,n)
triangle(x, y+length, n)
triangle(x+length, y, n)
triangle(x+length*2, y+length, n)
ok
```
Output:
```txt
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
```
## Ruby
From the command line:
```ruby
ruby -le'16.times{|y|print" "*(15-y),*(0..y).map{|x|~y&x>0?" ":" *"}}'
```
or, {{trans|Python}}
```ruby
def sierpinski_triangle(n)
triangle = ["*"]
n.times do |i|
sp = " " * (2**i)
triangle = triangle.collect {|x| sp + x + sp} +
triangle.collect {|x| x + " " + x}
end
triangle
end
puts sierpinski_triangle(4)
```
Using fold / reduce (aka. inject):
```ruby
def sierpinski_triangle(n)
(0...n).inject(["*"]) {|triangle, i|
space = " " * (2**i)
triangle.map {|x| space + x + space} + triangle.map {|x| x + " " + x}
}
end
puts sierpinski_triangle(4)
```
## Run BASIC
```runbasic
nOrder=4
dim xy$(40)
for i = 1 to 40
xy$(i) = " "
next i
call triangle 1, 1, nOrder
for i = 1 to 36
print xy$(i)
next i
end
SUB triangle x, y, n
IF n = 0 THEN
xy$(y) = left$(xy$(y),x-1) + "*" + mid$(xy$(y),x+1)
ELSE
n=n-1
length=2^n
call triangle x, y+length, n
call triangle x+length, y, n
call triangle x+length*2, y+length, n
END IF
END SUB
```
```txt
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
```
## Scala
The Ruby command-line version (on Windows):
```scala
scala -e "for(y<-0 to 15){println(\" \"*(15-y)++(0 to y).map(x=>if((~y&x)>0)\" \"else\" *\")mkString)}"
```
The Forth version:
```scala
def sierpinski(n: Int) {
def star(n: Long) = if ((n & 1L) == 1L) "*" else " "
def stars(n: Long): String = if (n == 0L) "" else star(n) + " " + stars(n >> 1)
def spaces(n: Int) = " " * n
((1 << n) - 1 to 0 by -1).foldLeft(1L) {
case (bitmap, remainingLines) =>
println(spaces(remainingLines) + stars(bitmap))
(bitmap << 1) ^ bitmap
}
}
```
The Haskell version:
```scala
def printSierpinski(n: Int) {
def sierpinski(n: Int): List[String] = {
lazy val down = sierpinski(n - 1)
lazy val space = " " * (1 << (n - 1))
n match {
case 0 => List("*")
case _ => (down map (space + _ + space)) :::
(down map (List.fill(2)(_) mkString " "))
}
}
sierpinski(n) foreach println
}
```
## Scheme
{{trans|Haskell}}
```scheme
(define (sierpinski n)
(for-each
(lambda (x) (display (list->string x)) (newline))
(let loop ((acc (list (list #\*))) (spaces (list #\ )) (n n))
(if (zero? n)
acc
(loop
(append
(map (lambda (x) (append spaces x spaces)) acc)
(map (lambda (x) (append x (list #\ ) x)) acc))
(append spaces spaces)
(- n 1))))))
```
## Seed7
```seed7
$ include "seed7_05.s7i";
const func array string: sierpinski (in integer: n) is func
result
var array string: parts is 1 times "*";
local
var integer: i is 0;
var string: space is " ";
var array string: parts2 is 0 times "";
var string: x is "";
begin
for i range 1 to n do
parts2 := 0 times "";
for x range parts do
parts2 &:= [] (space & x & space);
end for;
for x range parts do
parts2 &:= [] (x & " " & x);
end for;
parts := parts2;
space &:= space;
end for;
end func;
const proc: main is func
begin
writeln(join(sierpinski(4), "\n"));
end func;
```
## Sidef
```ruby
func sierpinski_triangle(n) {
var triangle = ['*']
{ |i|
var sp = (' ' * 2**i)
triangle = (triangle.map {|x| sp + x + sp} +
triangle.map {|x| x + ' ' + x})
} * n
triangle.join("\n")
}
say sierpinski_triangle(4)
```
## Swift
{{trans|Java}}
import Foundation
// Easy get/set of charAt
extension String {
subscript(index:Int) -> String {
get {
var array = Array(self)
var charAtIndex = array[index]
return String(charAtIndex)
}
set(newValue) {
var asChar = Character(newValue)
var array = Array(self)
array[index] = asChar
self = String(array)
}
}
}
func triangle(var n:Int) {
n = 1 << n
var line = ""
var t = ""
var u = ""
for (var i = 0; i <= 2 * n; i++) {
line += " "
}
line[n] = "*"
for (var i = 0; i < n; i++) {
println(line)
u = "*"
for (var j = n - i; j < n + i + 1; j++) {
t = line[j-1] == line[j + 1] ? " " : "*"
line[j - 1] = u
u = t
}
line[n + i] = t
line[n + i + 1] = "*"
}
}
```
## Tcl
{{trans|Perl}}
```tcl
package require Tcl 8.5
proc map {lambda list} {
foreach elem $list {
lappend result [apply $lambda $elem]
}
return $result
}
proc sierpinski_triangle n {
set down [list *]
set space " "
for {set i 1} {$i <= $n} {incr i} {
set down [concat \
[map [subst -nocommands {x {expr {"$space[set x]$space"}}}] $down] \
[map {x {expr {"$x $x"}}} $down] \
]
append space $space
}
return [join $down \n]
}
puts [sierpinski_triangle 4]
```
=={{header|TI-83 BASIC}}==
Uses Wolfram Rule 90.
```ti83b
PROGRAM:SIRPNSKI
:ClrHome
:Output(1,8,"^")
:{0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0}→L1
:{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}→L2
:L2→L3
:For(X,2,8,1)
:For(Y,2,17,1)
:If L1(Y-1)
:Then
:4→N
:End
:If L1(Y)
:Then
:N+2→N
:End
:If L1(Y+1)
:Then
:N+1→N
:End
:If N=1 or N=3 or N=4 or N=6
:Then
:1→L2(Y)
:Output(X,Y-1,"^")
:End
:0→N
:End
:L2→L1
:L3→L2
:End
```
## uBasic/4tH
Input "Triangle order: ";n
n = 2^n
For y = n - 1 To 0 Step -1
For i = 0 To y
Print " ";
Next
x = 0
For x = 0 Step 1 While ((x + y) < n)
If AND (x,y) Then
Print " ";
Else
Print "* ";
EndIf
Next
Print
Next
End
```
## Unlambda
```Unlambda
```ci``s``s`ks``s`k`s``s`kc``s``s``si`kr`k. `k.*k
`k``s``s``s``s`s`k`s``s`ksk`k``s``si`kk`k``s`kkk
`k``s`k`s``si`kk``s`kk``s``s``s``si`kk`k`s`k`s``s`ksk`k`s`k`s`k`si``si`k`ki
`k``s`k`s``si`k`ki``s`kk``s``s``s``si`kk`k`s`k`s`k`si`k`s`k`s``s`ksk``si`k`ki
`k`ki``s`k`s`k`si``s`kkk
```
This produces an infinite, left-justified triangle:
*
**
* *
****
* *
** **
* * * *
********
* *
** **
* * * *
**** ****
* * * *
** ** ** **
* * * * * * * *
****************
* *
** **
* * * *
**** ****
* * * *
** ** ** **
* * * * * * * *
******** ********
* * * *
** ** ** **
* * * * * * * *
**** **** **** ****
* * * * * * * *
** ** ** ** ** ** ** **
* * * * * * * * * * * * * * * *
********************************
* *
** **
* * * *
........
```
## Ursala
the straightforward recursive solution
```Ursala
#import nat
triangle = ~&a^?\<<&>>! ^|RNSiDlrTSPxSxNiCK9xSx4NiCSplrTSPT/~& predecessor
```
the cheeky cellular automaton solution
```Ursala
#import std
#import nat
rule = -$<0,&,0,0,&,0,0,0>@rSS zipp0*ziD iota8
evolve "n" = @iNC ~&x+ rep"n" ^C\~& @h rule*+ swin3+ :/0+ --<0>
sierpinski = iota; --<&>@NS; iota; ^H/evolve@z @NS ^T/~& :/&
```
an example of each (converting from booleans to characters)
```Ursala
#show+
examples = mat0 ~&?(`*!,` !)***
```
{{out}}
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
```
## VBA
{{Trans|Phix}}
```vb
Sub sierpinski(n As Integer)
Dim lim As Integer: lim = 2 ^ n - 1
For y = lim To 0 Step -1
Debug.Print String$(y, " ")
For x = 0 To lim - y
Debug.Print IIf(x And y, " ", "# ");
Next
Debug.Print
Next y
End Sub
Public Sub main()
Dim i As Integer
For i = 1 To 5
sierpinski i
Next i
End Sub
```
{{out}}
#
# #
#
# #
# #
# # # #
#
# #
# #
# # # #
# #
# # # #
# # # #
# # # # # # # #
#
# #
# #
# # # #
# #
# # # #
# # # #
# # # # # # # #
# #
# # # #
# # # #
# # # # # # # #
# # # #
# # # # # # # #
# # # # # # # #
# # # # # # # # # # # # # # # #
#
# #
# #
# # # #
# #
# # # #
# # # #
# # # # # # # #
# #
# # # #
# # # #
# # # # # # # #
# # # #
# # # # # # # #
# # # # # # # #
# # # # # # # # # # # # # # # #
# #
# # # #
# # # #
# # # # # # # #
# # # #
# # # # # # # #
# # # # # # # #
# # # # # # # # # # # # # # # #
# # # #
# # # # # # # #
# # # # # # # #
# # # # # # # # # # # # # # # #
# # # # # # # #
# # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
```
## VBScript
{{trans|PowerShell}}
```vb
Sub triangle(o)
n = 2 ^ o
Dim line()
ReDim line(2*n)
line(n) = "*"
i = 0
Do While i < n
WScript.StdOut.WriteLine Join(line,"")
u = "*"
j = n - i
Do While j < (n+i+1)
If line(j-1) = line(j+1) Then
t = " "
Else
t = "*"
End If
line(j-1) = u
u = t
j = j + 1
Loop
line(n+i) = t
line(n+i+1) = "*"
i = i + 1
Loop
End Sub
triangle(4)
```
## Vedit macro language
### Iterative
{{trans|JavaScript}}
The macro writes the fractal into an edit buffer where it can be viewed and saved to file if required.
This allows creating images larger than screen, the size is only limited by free disk space.
```vedit
#3 = 16 // size (height) of the triangle
Buf_Switch(Buf_Free) // Open a new buffer for output
Ins_Char(' ', COUNT, #3*2+2) // fill first line with spaces
Ins_Newline
Line(-1) Goto_Col(#3)
Ins_Char('*', OVERWRITE) // the top of triangle
for (#10=0; #10 < #3-1; #10++) {
BOL Reg_Copy(9,1) Reg_Ins(9) // duplicate the line
#20 = '*'
for (#11 = #3-#10; #11 < #3+#10+1; #11++) {
Goto_Col(#11-1)
if (Cur_Char==Cur_Char(2)) { #21=' ' } else { #21='*' }
Ins_Char(#20, OVERWRITE)
#20 = #21
}
Ins_Char(#21, OVERWRITE)
Ins_Char('*', OVERWRITE)
}
```
### Recursive
{{trans|BASIC}}
Vedit macro language does not have recursive functions, so some pushing and popping is needed to implement recursion.
```vedit
#1 = 1 // x
#2 = 1 // y
#3 = 16 // length (height of the triangle / 2)
#4 = 5 // depth of recursion
Buf_Switch(Buf_Free) // Open a new buffer for output
Ins_Newline(#3*2) // Create as many empty lines as needed
Call("Triangle") // Draw the triangle
BOF
Return
:Triangle:
if (#4 == 0) {
Goto_Line(#2)
EOL Ins_Char(' ', COUNT, #1-Cur_Col+1) // add spaces if needed
Goto_Col(#1)
Ins_Char('*', OVERWRITE)
} else {
Num_Push(1,4)
#2 += #3; #3 /= 2; #4--; Call("Triangle")
Num_Pop(1,4)
Num_Push(1,4)
#1 += #3; #3 /= 2; #4--; Call("Triangle")
Num_Pop(1,4)
Num_Push(1,4)
#1 += 2*#3; #2 += #3; #3 /= 2; #4--; Call("Triangle")
Num_Pop(1,4)
}
Return
```
## X86 Assembly
Translation of XPL0. Assemble with tasm, tlink /t
```asm
.model tiny
.code
.486
org 100h
start: xor ebx, ebx ;S1:= 0
mov edx, 8000h ;S2:= $8000
mov cx, 16 ;for I:= Size downto 1
tri10: mov ebx, edx ; S1:= S2
tri15: test edx, edx ; while S2#0
je tri20
mov al, '*' ; ChOut
test dl, 01h ; if S2&1 then '*' else ' '
jne tri18
mov al, ' '
tri18: int 29h
shr edx, 1 ; S2>>1
jmp tri15
tri20: mov al, 0Dh ;new line
int 29h
mov al, 0Ah
int 29h
shl ebx, 1 ;S2:= S2 xor S1<<1
xor edx, ebx
shr ebx, 2 ;S2:= S2 xor S1>>1
xor edx, ebx
loop tri10 ;next I
ret
end start
```
{{out}}
```txt
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
```
## XPL0
```XPL0
code ChOut=8, CrLf=9;
def Order=4, Size=1<>1];
CrLf(0);
S2:= S2 xor S1<<1;
S2:= S2 xor S1>>1;
];
]
```
{{out}}
```txt
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
```
## Yabasic
{{trans|Phix}}
```Yabasic
sub rep$(n, c$)
local i, s$
for i = 1 to n
s$ = s$ + c$
next
return s$
end sub
sub sierpinski(n)
local lim, y, x
lim = 2**n - 1
for y = lim to 0 step -1
print rep$(y, " ");
for x = 0 to lim-y
if and(x, y) then print " "; else print "* "; end if
next
print
next
end sub
for i = 1 to 5
sierpinski(i)
next
```
## zkl
{{trans|D}}
```zkl
level,d := 3,T("*");
foreach n in (level + 1){
sp:=" "*(2).pow(n);
d=d.apply('wrap(a){ String(sp,a,sp) }).extend(
d.apply(fcn(a){ String(a," ",a) }));
}
d.concat("\n").println();
```
{{out}}
```txt
*
* *
* *
* * * *
* *
* * * *
* * * *
* * * * * * * *
* *
* * * *
* * * *
* * * * * * * *
* * * *
* * * * * * * *
* * * * * * * *
* * * * * * * * * * * * * * * *
```