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This means it might contain formatting issues, incorrect code, conceptual problems, or other severe issues.
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{{task}}
Draw a Cantor set. See details: [https://en.wikipedia.org/wiki/Cantor_set Cantor set]
11l
{{trans|Python}}
V WIDTH = 81
V HEIGHT = 5
F cantor(start, len, index)
V seg = len I/ 3
I seg == 0
R
L(it) 0 .< :HEIGHT - index
V i = index + it
L(jt) 0 .< seg
V j = start + seg + jt
V pos = i * :WIDTH + j
:lines[pos] = ‘ ’
cantor(start, seg, index + 1)
cantor(start + seg * 2, seg, index + 1)
V lines = [‘*’] * (WIDTH * HEIGHT)
cantor(0, WIDTH, 1)
L(i) 0 .< HEIGHT
V beg = WIDTH * i
print((lines[beg .< beg + WIDTH]).join(‘’))
{{out}}
*********************************************************************************
*************************** ***************************
********* ********* ********* *********
*** *** *** *** *** *** *** ***
* * * * * * * * * * * * * * * *
ALGOL 68
BEGIN
# draw a Cantor Set using ASCII #
INT lines = 5; # number of lines for the set #
# we must choose the line width so that the width of each segment is #
# divisible by 3 ( except for the final line where the segment width will #
# be 1 ) #
INT set width = 3 ^ ( lines - 1 );
[ set width ]CHAR set;
# start with a complete line #
FOR i TO set width DO set[ i ] := "#" OD;
print( ( set, newline ) );
# repeatedly modify the line, replacing the middle third of each segment #
# with blanks #
INT segment width := set width OVER 3;
WHILE segment width > 0 DO
INT set pos := 1;
WHILE set pos < ( set width - segment width ) DO
set pos +:= segment width;
FOR char pos FROM set pos TO ( set pos + segment width ) - 1 DO
set[ char pos ] := " "
OD;
set pos +:= segment width
OD;
print( ( set, newline ) );
segment width OVERAB 3
OD
END
{{out}}
#################################################################################
########################### ###########################
######### ######### ######### #########
### ### ### ### ### ### ### ###
# # # # # # # # # # # # # # # #
ALGOL W
Based on the Algol 68 sample.
begin
% draw a Cantor Set using ASCII %
integer LINES; % number of lines for the set %
integer setWidth; % width of each line of the set %
% we must choose the line width so that the width of each segment is %
% divisible by 3 ( except for the final line where the segment width will %
% be 1 ) %
LINES := 5;
setWidth := round( 3 ** ( LINES - 1 ) );
begin % start new block so the array can have computed bounds %
logical array set ( 1 :: setWidth );
integer segmentWidth;
% start with a complete line %
for i := 1 until setWidth do set( i ) := true;
segmentWidth := setWidth;
for l := 1 until LINES do begin
% print the latest line, all lines start with a "#" %
write( "#" );
for i := 2 until setWidth do writeon( if set( i ) then "#" else " " );
% modify the line, replacing the middle third of each segment %
% with blanks, unless this was the last line %
if l < LINES then begin
integer setPos;
segmentWidth := segmentWidth div 3;
setPos := 1;
while setPos < ( setWidth - segmentWidth ) do begin
setPos := setPos + segmentWidth;
for charPos := setPos until ( setPos + segmentWidth ) - 1 do set( charPos ) := false;
setPos := setPos + segmentWidth
end while_setPos_in_range ;
end if_l_lt_LINES
end for_l
end
end.
{{out}}
#################################################################################
########################### ###########################
######### ######### ######### #########
### ### ### ### ### ### ### ###
# # # # # # # # # # # # # # # #
AppleScript
-- cantor :: [String] -> [String] on cantor(xs) script go on |λ|(s) set m to (length of s) div 3 set blocks to text 1 thru m of s if "█" = text 1 of s then {blocks, replicate(m, space), blocks} else {s} end if end |λ| end script concatMap(go, xs) end cantor -- showCantor :: Int -> String on showCantor(n) unlines(map(my concat, ¬ take(n, iterate(cantor, ¬ {replicate(3 ^ (n - 1), "█")})))) end showCantor -- TEST --------------------------------------------------- on run showCantor(5) end run -- GENERIC ------------------------------------------------ -- concat :: [[a]] -> [a] -- concat :: [String] -> String on concat(xs) set lng to length of xs if 0 < lng and string is class of (item 1 of xs) then set acc to "" else set acc to {} end if repeat with i from 1 to lng set acc to acc & item i of xs end repeat acc end concat -- concatMap :: (a -> [b]) -> [a] -> [b] on concatMap(f, xs) set lng to length of xs set acc to {} tell mReturn(f) repeat with i from 1 to lng set acc to acc & |λ|(item i of xs, i, xs) end repeat end tell return acc end concatMap -- 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 :: First-class m => (a -> b) -> m (a -> b) on mReturn(f) if class of f is script then f else script property |λ| : f end script end if end mReturn -- iterate :: (a -> a) -> a -> Gen [a] on iterate(f, x) script property v : missing value property g : mReturn(f)'s |λ| on |λ|() if missing value is v then set v to x else set v to g(v) end if return v end |λ| end script end iterate -- replicate :: Int -> String -> String on replicate(n, s) set out to "" if n < 1 then return out set dbl to s 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 -- take :: Int -> [a] -> [a] -- take :: Int -> String -> String on take(n, xs) set c to class of xs if list is c then if 0 < n then items 1 thru min(n, length of xs) of xs else {} end if else if string is c then if 0 < n then text 1 thru min(n, length of xs) of xs else "" end if else if script is c then set ys to {} repeat with i from 1 to n set v to xs's |λ|() if missing value is v then return ys else set end of ys to v end if end repeat return ys else missing value end if end take -- unlines :: [String] -> String on unlines(xs) set {dlm, my text item delimiters} to ¬ {my text item delimiters, linefeed} set str to xs as text set my text item delimiters to dlm str end unlines
{{Out}}
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AWK
# syntax: GAWK -f CANTOR_SET.AWK
# converted from C
BEGIN {
WIDTH = 81
HEIGHT = 5
for (i=0; i<HEIGHT; ++i) {
for (j=0; j<WIDTH; ++j) {
lines[i][j] = "*"
}
}
cantor(0,WIDTH,1)
for (i=0; i<HEIGHT; ++i) {
for (j=0; j<WIDTH; ++j) {
printf("%s",lines[i][j])
}
printf("\n")
}
exit(0)
}
function cantor(start,leng,indx, i,j,seg) {
seg = int(leng/3)
if (seg == 0) { return }
for (i=indx; i<HEIGHT; ++i) {
for (j=start+seg; j<start+seg*2; ++j) {
lines[i][j] = " "
}
}
cantor(start,seg,indx+1)
cantor(start+seg*2,seg,indx+1)
}
{{out}}
*********************************************************************************
*************************** ***************************
********* ********* ********* *********
*** *** *** *** *** *** *** ***
* * * * * * * * * * * * * * * *
BASIC256
{{trans|FreeBASIC}}
global ancho, alto, intervalo
ancho = 81 : alto = 5
dim intervalo(alto, ancho)
subroutine Cantor()
for i = 0 to alto - 1
for j = 0 to ancho - 1
intervalo[i, j] = "■"
next j
next i
end subroutine
subroutine ConjCantor(inicio, longitud, indice)
segmento = longitud / 3
if segmento = 0 then return
for i = indice to alto - 1
for j = inicio + segmento to inicio + segmento * 2 - 1
intervalo[i, j] = " "
next j
next i
call ConjCantor(inicio, segmento, indice + 1)
call ConjCantor(inicio + segmento * 2, segmento, indice + 1)
end subroutine
call Cantor()
call ConjCantor(0, ancho, 1)
for i = 0 to alto - 1
for j = 0 to ancho - 1
print intervalo[i, j];
next j
print
next i
End
{{out}}
Igual que la entrada de FreeBASIC.
C
Translated from Kotlin.
#include <stdio.h> #define WIDTH 81 #define HEIGHT 5 char lines[HEIGHT][WIDTH]; void init() { int i, j; for (i = 0; i < HEIGHT; ++i) { for (j = 0; j < WIDTH; ++j) lines[i][j] = '*'; } } void cantor(int start, int len, int index) { int i, j, seg = len / 3; if (seg == 0) return; for (i = index; i < HEIGHT; ++i) { for (j = start + seg; j < start + seg * 2; ++j) lines[i][j] = ' '; } cantor(start, seg, index + 1); cantor(start + seg * 2, seg, index + 1); } void print() { int i, j; for (i = 0; i < HEIGHT; ++i) { for (j = 0; j < WIDTH; ++j) printf("%c", lines[i][j]); printf("\n"); } } int main() { init(); cantor(0, WIDTH, 1); print(); return 0; }
{{output}}
*********************************************************************************
*************************** ***************************
********* ********* ********* *********
*** *** *** *** *** *** *** ***
* * * * * * * * * * * * * * * *
C++
Translated from D.
#include <iostream> const int WIDTH = 81; const int HEIGHT = 5; char lines[WIDTH*HEIGHT]; void cantor(int start, int len, int index) { int seg = len / 3; if (seg == 0) return; for (int i = index; i < HEIGHT; i++) { for (int j = start + seg; j < start + seg * 2; j++) { int pos = i * WIDTH + j; lines[pos] = ' '; } } cantor(start, seg, index + 1); cantor(start + 2 * seg, seg, index + 1); } int main() { // init for (int i = 0; i < WIDTH*HEIGHT; i++) { lines[i] = '*'; } // calculate cantor(0, WIDTH, 1); // print for (int i = 0; i < HEIGHT*WIDTH; i += WIDTH) { printf("%.*s\n", WIDTH, lines + i); } return 0; }
{{out}}
*********************************************************************************
*************************** ***************************
********* ********* ********* *********
*** *** *** *** *** *** *** ***
* * * * * * * * * * * * * * * *
C#
Translated from Java.
using System; namespace CantorSet { class Program { const int WIDTH = 81; const int HEIGHT = 5; private static char[,] lines = new char[HEIGHT, WIDTH]; static Program() { for (int i = 0; i < HEIGHT; i++) { for (int j = 0; j < WIDTH; j++) { lines[i, j] = '*'; } } } private static void Cantor(int start, int len, int index) { int seg = len / 3; if (seg == 0) return; for (int i = index; i < HEIGHT; i++) { for (int j = start + seg; j < start + seg * 2; j++) { lines[i, j] = ' '; } } Cantor(start, seg, index + 1); Cantor(start + seg * 2, seg, index + 1); } static void Main(string[] args) { Cantor(0, WIDTH, 1); for (int i = 0; i < HEIGHT; i++) { for (int j = 0; j < WIDTH; j++) { Console.Write(lines[i,j]); } Console.WriteLine(); } } } }
{{out}}
*********************************************************************************
*************************** ***************************
********* ********* ********* *********
*** *** *** *** *** *** *** ***
* * * * * * * * * * * * * * * *
D
{{trans|C}}
import std.stdio; enum WIDTH = 81; enum HEIGHT = 5; char[WIDTH*HEIGHT] lines; void cantor(int start, int len, int index) { int seg = len / 3; if (seg == 0) return; for (int i=index; i<HEIGHT; i++) { for (int j=start+seg; j<start+seg*2; j++) { int pos = i*WIDTH + j; lines[pos] = ' '; } } cantor(start, seg, index+1); cantor(start+seg*2, seg, index+1); } void main() { // init lines[] = '*'; // calculate cantor(0, WIDTH, 1); // print for (int i=0; i<HEIGHT; i++) { int beg = WIDTH * i; writeln(lines[beg..beg+WIDTH]); } }
{{out}}
*********************************************************************************
*************************** ***************************
********* ********* ********* *********
*** *** *** *** *** *** *** ***
* * * * * * * * * * * * * * * *
Factor
USING: grouping.extras io kernel math sequences
sequences.repeating ;
IN: rosetta-code.cantor-set
CONSTANT: width 81
CONSTANT: depth 5
: cantor ( n -- seq )
dup 0 = [ drop { 0 1 } ]
[ 1 - cantor [ 3 / ] map dup [ 2/3 + ] map append ] if ;
! Produces a sequence of lengths from a Cantor set, depending on
! width. Even indices are solid; odd indices are blank.
! e.g. 2 cantor gaps -> { 9 9 9 27 9 9 9 }
!
: gaps ( seq -- seq )
[ width * ] map [ - abs ] 2clump-map ;
: print-cantor ( n -- )
cantor gaps [ even? "#" " " ? swap repeat ] map-index
concat print ;
depth <iota> [ print-cantor ] each
{{out}}
#################################################################################
########################### ###########################
######### ######### ######### #########
### ### ### ### ### ### ### ###
# # # # # # # # # # # # # # # #
Forth
Where is says [email protected] it should say c@, but I'm not keen on writing it as c@ in the actual code.
warnings off
4 \ iterations
: ** 1 swap 0 ?DO over * LOOP nip ;
3 swap ** constant width \ Make smallest step 1
create string here width char # fill width allot
: print string width type cr ;
\ Overwrite string with new holes of size 'length'.
\ Pointer into string at TOS.
create length width ,
: reduce length dup @ 3 / swap ! ;
: done? dup string - width >= ;
: hole? dup c@ bl = ;
: skip length @ + ;
: whipe dup length @ bl fill skip ;
: step hole? IF skip skip skip ELSE skip whipe skip THEN ;
: split reduce string BEGIN step done? UNTIL drop ;
\ Main
: done? length @ 1 <= ;
: step split print ;
: go print BEGIN step done? UNTIL ;
go bye
Output:
#################################################################################
########################### ###########################
######### ######### ######### #########
### ### ### ### ### ### ### ###
# # # # # # # # # # # # # # # #
FreeBASIC
Const ancho = 81
Const alto = 5
Dim Shared intervalo(alto, ancho) As String
Dim As Integer i, j
Sub Cantor()
Dim As Integer i, j
For i = 0 To alto - 1
For j = 0 To ancho - 1
intervalo(i, j) = Chr(254)
Next j
Next i
End Sub
Sub ConjCantor(inicio As Integer, longitud As Integer, indice As Integer)
Dim As Integer i, j
Dim segmento As Integer = longitud / 3
If segmento = 0 Then Return
For i = indice To alto - 1
For j = inicio + segmento To inicio + segmento * 2 - 1
intervalo(i, j) = Chr(32)
Next j
Next i
ConjCantor(inicio, segmento, indice + 1)
ConjCantor(inicio + segmento * 2, segmento, indice + 1)
End Sub
Cantor()
ConjCantor(0, ancho, 1)
For i = 0 To alto - 1
For j = 0 To ancho - 1
Print intervalo(i, j);
Next j
Print
Next i
End
{{out}}
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Go
{{trans|Kotlin}}
package main import "fmt" const ( width = 81 height = 5 ) var lines [height][width]byte func init() { for i := 0; i < height; i++ { for j := 0; j < width; j++ { lines[i][j] = '*' } } } func cantor(start, len, index int) { seg := len / 3 if seg == 0 { return } for i := index; i < height; i++ { for j := start + seg; j < start + 2 * seg; j++ { lines[i][j] = ' ' } } cantor(start, seg, index + 1) cantor(start + seg * 2, seg, index + 1) } func main() { cantor(0, width, 1) for _, line := range lines { fmt.Println(string(line[:])) } }
{{out}}
*********************************************************************************
*************************** ***************************
********* ********* ********* *********
*** *** *** *** *** *** *** ***
* * * * * * * * * * * * * * * *
Haskell
Interval bars
{{Trans|Python}} (Functional version)
import Data.Bool (bool) cantor :: [(Bool, Int)] -> [(Bool, Int)] cantor = (go =<<) where go (bln, n) = let m = quot n 3 in bool [(bln, n)] [(True, m), (False, m), (True, m)] (bln && 1 < n) cantorLines :: Int -> String cantorLines n = unlines $ showCantor <$> take n (iterate cantor [(True, 3 ^ (n - 1))]) showCantor :: [(Bool, Int)] -> String showCantor = (uncurry (flip replicate . bool ' ' '*') =<<) main :: IO () main = putStrLn $ cantorLines 5
{{Out}}
*********************************************************************************
*************************** ***************************
********* ********* ********* *********
*** *** *** *** *** *** *** ***
* * * * * * * * * * * * * * * *
Or, using strings for the model as well as the display:
import Data.Bool (bool) cantor :: [String] -> [String] cantor = (go =<<) where go x = let m = quot (length x) 3 block = take m x in bool [x] [block, replicate m ' ', block] ('█' == head x) cantorLines :: Int -> String cantorLines n = unlines $ concat <$> take n (iterate cantor [replicate (3 ^ (n - 1)) '█']) main :: IO () main = putStrLn $ cantorLines 5
{{Out}}
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Dual representation
Intervals as fraction pairs, and intervals as graphic bars:
import Data.Ratio (Ratio, (%), numerator, denominator) import Data.List (intercalate, mapAccumL, maximumBy) import Data.Bool (bool) cantor :: (Rational, Rational) -> [[(Rational, Rational)]] cantor = let go (x, y) = let r = (y - x) / 3 in [(x, x + r), (y - r, y)] in iterate (>>= go) . return main :: IO () main = do let xs = take 4 $ cantor (0, 1) (putStrLn . unlines) $ intervalRatios <$> xs putStrLn $ intervalBars xs -- DISPLAY FUNCTIONS --------------------------------------------------- intervalBars :: [[(Rational, Rational)]] -> String intervalBars xs = let go w xs = concat . snd $ mapAccumL (\a (rx, ry) -> let (wx, wy) = (w * rx, w * ry) in ( wy -- Accumulator – end of previous interval. , replicate (floor (wx - a)) ' ' -- Preceding gap, and ++ replicate (floor (wy - wx)) '█' -- interval bar. )) 0 xs d = maximum $ (denominator . fst) <$> last xs in unlines $ go (d % 1) <$> xs intervalRatios :: [(Rational, Rational)] -> String intervalRatios xs = let go (rx, ry) = intercalate ", " $ showRatio <$> [rx, ry] in '(' : intercalate ") (" (go <$> xs) ++ ")" showRatio :: Rational -> String showRatio r = let d = denominator r in show (numerator r) ++ bool [] ('/' : show d) (1 /= d)
{{Out}}
(0, 1)
(0, 1/3) (2/3, 1)
(0, 1/9) (2/9, 1/3) (2/3, 7/9) (8/9, 1)
(0, 1/27) (2/27, 1/9) (2/9, 7/27) (8/27, 1/3) (2/3, 19/27) (20/27, 7/9) (8/9, 25/27) (26/27, 1)
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=={{header|IS-BASIC}}==
## J
The argument to the cantor_dust monad is an integer that describes the depth of the dust. Shown here are results for cantor_dust 2 and for cantor_dust 3 . It works by checking for 1 digits in the base 3 representation of the coordinates. These background coordinates are plotted with # character using ASCII art. 1j1 #"1 expands the lines to improve aspect ratio on character cell (console) display. }:"1 curtails the extra space character line by line. < draws a pretty box.
```J
odometer =: [: (4 $. $.) $&1
cantor_dust =: monad define
shape =. ,~ 3 ^ y
a =. shape $ ' '
i =. odometer shape
< (}:"1) 1j1 #"1 '#' (([: <"1 [: ;/"1 (#~ 1 e."1 [: (,/"2) 3 3&#:)) i)}a
)
cantor_dust 2
┌─────────────────┐
│ # # # # # │
│# # # # # # # # #│
│ # # # # # │
│# # # # # # # # #│
│# # # # # # # # #│
│# # # # # # # # #│
│ # # # # # │
│# # # # # # # # #│
│ # # # # # │
└─────────────────┘
cantor_dust 3
┌─────────────────────────────────────────────────────┐
│ # # # # # # # # # # # # # # # │
│# # # # # # # # # # # # # # # # # # # # # # # # # # #│
│ # # # # # # # # # # # # # # # │
│# # # # # # # # # # # # # # # # # # # # # # # # # # #│
│# # # # # # # # # # # # # # # # # # # # # # # # # # #│
│# # # # # # # # # # # # # # # # # # # # # # # # # # #│
│ # # # # # # # # # # # # # # # │
│# # # # # # # # # # # # # # # # # # # # # # # # # # #│
│ # # # # # # # # # # # # # # # │
│ # # # # # # # # # # # # # # # │
│# # # # # # # # # # # # # # # # # # # # # # # # # # #│
│ # # # # # # # # # # # # # # # │
│# # # # # # # # # # # # # # # # # # # # # # # # # # #│
│# # # # # # # # # # # # # # # # # # # # # # # # # # #│
│# # # # # # # # # # # # # # # # # # # # # # # # # # #│
│ # # # # # # # # # # # # # # # │
│# # # # # # # # # # # # # # # # # # # # # # # # # # #│
│ # # # # # # # # # # # # # # # │
│ # # # # # # # # # # # # # # # │
│# # # # # # # # # # # # # # # # # # # # # # # # # # #│
│ # # # # # # # # # # # # # # # │
│# # # # # # # # # # # # # # # # # # # # # # # # # # #│
│# # # # # # # # # # # # # # # # # # # # # # # # # # #│
│# # # # # # # # # # # # # # # # # # # # # # # # # # #│
│ # # # # # # # # # # # # # # # │
│# # # # # # # # # # # # # # # # # # # # # # # # # # #│
│ # # # # # # # # # # # # # # # │
└─────────────────────────────────────────────────────┘
With an `x' argument cantor_dust generalizes to higher dimensions. Try 3 cantor_dust 2
cantor_dust =: 2&$: :(dyad define)
shape =. x # 3 ^ y
a =. shape $ ' '
i =. odometer shape
< (}:"1) 1j1 #"1 '#' (([: <"1 [: ;/"1 (#~ 1 e."1 [: (,/"2) 3 3&#:)) i)} a
)
Java
{{trans|Kotlin}}
public class App { private static final int WIDTH = 81; private static final int HEIGHT = 5; private static char[][] lines; static { lines = new char[HEIGHT][WIDTH]; for (int i = 0; i < HEIGHT; i++) { for (int j = 0; j < WIDTH; j++) { lines[i][j] = '*'; } } } private static void cantor(int start, int len, int index) { int seg = len / 3; if (seg == 0) return; for (int i = index; i < HEIGHT; i++) { for (int j = start + seg; j < start + seg * 2; j++) { lines[i][j] = ' '; } } cantor(start, seg, index + 1); cantor(start + seg * 2, seg, index + 1); } public static void main(String[] args) { cantor(0, WIDTH, 1); for (int i = 0; i < HEIGHT; i++) { for (int j = 0; j < WIDTH; j++) { System.out.print(lines[i][j]); } System.out.println(); } } }
{{out}}
*********************************************************************************
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*** *** *** *** *** *** *** ***
* * * * * * * * * * * * * * * *
JavaScript
{{Trans|Python}} (Functional version) {{Trans|Haskell}}
(() => { 'use strict'; const main = () => { // cantor :: [(Bool, Int)] -> [(Bool, Int)] const cantor = xs => { const go = ([bln, n]) => bln && 1 < n ? (() => { const lng = Math.floor(n / 3); return [ [true, lng], [false, lng], [true, lng] ] })() : [ [bln, n] ]; return concatMap(go, xs); }; // cantorLines :: Int -> String const cantorLines = n => unlines( map(showCantor, take(n, iterate( cantor, [ [true, Math.pow(3, n - 1)] ] ) ) ) ); // showCantor :: [(Bool, Int)] -> String const showCantor = xs => concat(map( ([bln, n]) => replicate(n, bln ? '*' : ' '), xs )); console.log( cantorLines(5) ); }; // GENERIC FUNCTIONS ---------------------------------- // concat :: [[a]] -> [a] // concat :: [String] -> String const concat = xs => 0 < xs.length ? (() => { const unit = 'string' !== typeof xs[0] ? ( [] ) : ''; return unit.concat.apply(unit, xs); })() : []; // concatMap :: (a -> [b]) -> [a] -> [b] const concatMap = (f, xs) => xs.reduce((a, x) => a.concat(f(x)), []); // iterate :: (a -> a) -> a -> Gen [a] function* iterate(f, x) { let v = x; while (true) { yield(v); v = f(v); } } // map :: (a -> b) -> [a] -> [b] const map = (f, xs) => xs.map(f); // replicate :: Int -> String -> String const replicate = (n, s) => s.repeat(n); // take :: Int -> [a] -> [a] // take :: Int -> String -> String const take = (n, xs) => 'GeneratorFunction' !== xs.constructor.constructor.name ? ( xs.slice(0, n) ) : [].concat.apply([], Array.from({ length: n }, () => { const x = xs.next(); return x.done ? [] : [x.value]; })); // unlines :: [String] -> String const unlines = xs => xs.join('\n'); // MAIN --- return main(); })();
{{Out}}
*********************************************************************************
*************************** ***************************
********* ********* ********* *********
*** *** *** *** *** *** *** ***
* * * * * * * * * * * * * * * *
Or, using strings for the model as well as the display: {{Trans|Haskell}}
(() => { 'use strict'; const main = () => showCantor(5); // showCantor :: Int -> String const showCantor = n => unlines(map(concat, take(n, iterate( cantor, [replicate(Math.pow(3, n - 1), '█')] ) ) )); // cantor :: [String] -> [String] const cantor = xs => { const go = s => { const m = Math.floor(s.length / 3), blocks = take(m, s); return '█' === s[0] ? ( [blocks, replicate(m, ' '), blocks] ) : [s]; }; return concatMap(go, xs); }; // GENERIC FUNCTIONS ---------------------------- // concat :: [[a]] -> [a] // concat :: [String] -> String const concat = xs => 0 < xs.length ? (() => { const unit = 'string' !== typeof xs[0] ? ( [] ) : ''; return unit.concat.apply(unit, xs); })() : []; // concatMap :: (a -> [b]) -> [a] -> [b] const concatMap = (f, xs) => xs.reduce((a, x) => a.concat(f(x)), []); // iterate :: (a -> a) -> a -> Gen [a] function* iterate(f, x) { let v = x; while (true) { yield(v); v = f(v); } } // map :: (a -> b) -> [a] -> [b] const map = (f, xs) => xs.map(f); // replicate :: Int -> String -> String const replicate = (n, s) => s.repeat(n); // take :: Int -> [a] -> [a] // take :: Int -> String -> String const take = (n, xs) => 'GeneratorFunction' !== xs.constructor.constructor.name ? ( xs.slice(0, n) ) : [].concat.apply([], Array.from({ length: n }, () => { const x = xs.next(); return x.done ? [] : [x.value]; })); // unlines :: [String] -> String const unlines = xs => xs.join('\n'); // MAIN --- return main(); })();
{{Out}}
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Dual representation
{{Trans|Haskell}} {{Trans|Python}}
Cantor ternary intervals rendered both as lists of ratio pairs, and as graphic bars. In the case of languages like Javascript which lack a built-in Ratio type, or standard Fraction/Ratio library, rendering stages of the set elaboration as lists of fraction pairs may take more work than rendering them as graphic lines.
(() => { 'use strict'; // main :: IO () const main = () => { const xs = take(4, iterate(cantor, [Tuple(0, 1)])); console.log( unlines(map(intervalRatios, xs)) + '\n', ); console.log( intervalBars(xs) ); }; // cantor :: [(Rational, Rational)] -> [(Rational, Rational)] const cantor = xs => { const go = tpl => { const [r1, r2] = map(rational, Array.from(tpl)); const third = ratioDiv(ratioMinus(r2, r1), 3); return [ Tuple(r1, ratioPlus(r1, third)), Tuple(ratioMinus(r2, third), r2) ]; }; return concatMap(go, xs); }; // intervalRatios :: [(Rational, Rational)] -> String const intervalRatios = xs => { const go = tpl => map(compose(showRatio, rational), Array.from(tpl) ).join(', '); return '(' + map(go, xs).join(') (') + ')'; }; // intervalBars :: [[(Rational, Rational)]] -> String const intervalBars = xs => { const go = w => xs => concat(snd(mapAccumL( (a, tpl) => { const [wx, wy] = map( r => ratioMult(w, rational(r)), Array.from(tpl) ); return Tuple( wy, replicateString(floor(ratioMinus(wx, a)), ' ') + replicateString(floor(ratioMinus(wy, wx)), '█') ); }, 0, xs ))); const d = maximum(map(x => fst(x).d, last(xs))); return unlines(map(go(ratio(d, 1)), xs)); }; // GENERIC FUNCTIONS ---------------------------------- // Tuple (,) :: a -> b -> (a, b) const Tuple = (a, b) => ({ type: 'Tuple', '0': a, '1': b, length: 2 }); // abs :: Num -> Num const abs = Math.abs; // compose (<<<) :: (b -> c) -> (a -> b) -> a -> c const compose = (f, g) => x => f(g(x)); // concat :: [[a]] -> [a] // concat :: [String] -> String const concat = xs => 0 < xs.length ? (() => { const unit = 'string' !== typeof xs[0] ? ( [] ) : ''; return unit.concat.apply(unit, xs); })() : []; // concatMap :: (a -> [b]) -> [a] -> [b] const concatMap = (f, xs) => xs.reduce((a, x) => a.concat(f(x)), []); // floor :: Num -> Int const floor = x => { const nr = ( 'Ratio' !== x.type ? ( properFraction ) : properFracRatio )(x), n = nr[0]; return 0 > nr[1] ? n - 1 : n; }; // foldl1 :: (a -> a -> a) -> [a] -> a const foldl1 = (f, xs) => 1 < xs.length ? xs.slice(1) .reduce(f, xs[0]) : xs[0]; // fst :: (a, b) -> a const fst = tpl => tpl[0]; // gcd :: Int -> Int -> Int const gcd = (x, y) => { const _gcd = (a, b) => (0 === b ? a : _gcd(b, a % b)), abs = Math.abs; return _gcd(abs(x), abs(y)); }; // iterate :: (a -> a) -> a -> Gen [a] function* iterate(f, x) { let v = x; while (true) { yield(v); v = f(v); } } // last :: [a] -> a const last = xs => 0 < xs.length ? xs.slice(-1)[0] : undefined; // lcm :: Int -> Int -> Int const lcm = (x, y) => (x === 0 || y === 0) ? 0 : Math.abs(Math.floor(x / gcd(x, y)) * y); // map :: (a -> b) -> [a] -> [b] const map = (f, xs) => xs.map(f); // 'The mapAccumL function behaves like a combination of map and foldl; // it applies a function to each element of a list, passing an accumulating // parameter from left to right, and returning a final value of this // accumulator together with the new list.' (See Hoogle) // mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y]) const mapAccumL = (f, acc, xs) => xs.reduce((a, x, i) => { const pair = f(a[0], x, i); return Tuple(pair[0], a[1].concat(pair[1])); }, Tuple(acc, [])); // maximum :: Ord a => [a] -> a const maximum = xs => 0 < xs.length ? ( foldl1((a, x) => x > a ? x : a, xs) ) : undefined; // properFracRatio :: Ratio -> (Int, Ratio) const properFracRatio = nd => { const [q, r] = Array.from(quotRem(nd.n, nd.d)); return Tuple(q, ratio(r, nd.d)); }; // properFraction :: Real -> (Int, Real) const properFraction = n => { const i = Math.floor(n) + (n < 0 ? 1 : 0); return Tuple(i, n - i); }; // quot :: Int -> Int -> Int const quot = (n, m) => Math.floor(n / m); // quotRem :: Int -> Int -> (Int, Int) const quotRem = (m, n) => Tuple(Math.floor(m / n), m % n); // ratio :: Int -> Int -> Ratio Int const ratio = (x, y) => { const go = (x, y) => 0 !== y ? (() => { const d = gcd(x, y); return { type: 'Ratio', 'n': quot(x, d), // numerator 'd': quot(y, d) // denominator }; })() : undefined; return go(x * signum(y), abs(y)); }; // ratioDiv :: Rational -> Rational -> Rational const ratioDiv = (n1, n2) => { const [r1, r2] = map(rational, [n1, n2]); return ratio(r1.n * r2.d, r1.d * r2.n); }; // ratioMinus :: Rational -> Rational -> Rational const ratioMinus = (n1, n2) => { const [r1, r2] = map(rational, [n1, n2]); const d = lcm(r1.d, r2.d); return ratio( (r1.n * (d / r1.d)) - (r2.n * (d / r2.d)), d ); }; // ratioMult :: Rational -> Rational -> Rational const ratioMult = (n1, n2) => { const [r1, r2] = map(rational, [n1, n2]); return ratio(r1.n * r2.n, r1.d * r2.d); }; // ratioPlus :: Rational -> Rational -> Rational const ratioPlus = (n1, n2) => { const [r1, r2] = map(rational, [n1, n2]); const d = lcm(r1.d, r2.d); return ratio( (r1.n * (d / r1.d)) + (r2.n * (d / r2.d)), d ); }; // rational :: Num a => a -> Rational const rational = x => isNaN(x) ? x : ratio(x, 1); // replicateString :: Int -> String -> String const replicateString = (n, s) => s.repeat(n); // showRatio :: Ratio -> String const showRatio = r => 'Ratio' !== r.type ? ( r.toString() ) : r.n.toString() + ( 1 !== r.d ? ( '/' + r.d.toString() ) : '' ); // signum :: Num -> Num const signum = n => 0 > n ? -1 : (0 < n ? 1 : 0); // snd :: (a, b) -> b const snd = tpl => tpl[1]; // take :: Int -> [a] -> [a] // take :: Int -> String -> String const take = (n, xs) => 'GeneratorFunction' !== xs.constructor.constructor.name ? ( xs.slice(0, n) ) : [].concat.apply([], Array.from({ length: n }, () => { const x = xs.next(); return x.done ? [] : [x.value]; })); // unlines :: [String] -> String const unlines = xs => xs.join('\n'); // MAIN --- return main(); })();
{{Out}}
(0, 1)
(0, 1/3) (2/3, 1)
(0, 1/9) (2/9, 1/3) (2/3, 7/9) (8/9, 1)
(0, 1/27) (2/27, 1/9) (2/9, 7/27) (8/27, 1/3) (2/3, 19/27) (20/27, 7/9) (8/9, 25/27) (26/27, 1)
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Julia
{{trans|AWK}}
const width = 81 const height = 5 function cantor!(lines, start, len, idx) seg = div(len, 3) if seg > 0 for i in idx+1:height, j in start + seg + 1: start + seg * 2 lines[i, j] = ' ' end cantor!(lines, start, seg, idx + 1) cantor!(lines, start + 2 * seg, seg, idx + 1) end end lines = fill(UInt8('#'), height, width) cantor!(lines, 0, width, 1) for i in 1:height, j in 1:width print(Char(lines[i, j]), j == width ? "\n" : "") end
{{out}}
#################################################################################
########################### ###########################
######### ######### ######### #########
### ### ### ### ### ### ### ###
# # # # # # # # # # # # # # # #
Kotlin
Simple terminal drawing.
// Version 1.2.31 const val WIDTH = 81 const val HEIGHT = 5 val lines = List(HEIGHT) { CharArray(WIDTH) { '*' } } fun cantor(start: Int, len: Int, index: Int) { val seg = len / 3 if (seg == 0) return for (i in index until HEIGHT) { for (j in start + seg until start + seg * 2) lines[i][j] = ' ' } cantor(start, seg, index + 1) cantor(start + seg * 2, seg, index + 1) } fun main(args: Array<String>) { cantor(0, WIDTH, 1) lines.forEach { println(it) } }
{{output}}
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********* ********* ********* *********
*** *** *** *** *** *** *** ***
* * * * * * * * * * * * * * * *
Lua
{{trans|python}}
local WIDTH = 81 local HEIGHT = 5 local lines = {} function cantor(start, length, index) -- must be local, or only one side will get calculated local seg = math.floor(length / 3) if 0 == seg then return nil end -- remove elements that are not in the set for it=0, HEIGHT - index do i = index + it for jt=0, seg - 1 do j = start + seg + jt pos = WIDTH * i + j lines[pos] = ' ' end end -- left side cantor(start, seg, index + 1) -- right side cantor(start + seg * 2, seg, index + 1) return nil end -- initialize the lines for i=0, WIDTH * HEIGHT do lines[i] = '*' end -- calculate cantor(0, WIDTH, 1) -- print the result sets for i=0, HEIGHT-1 do beg = WIDTH * i for j=beg, beg+WIDTH-1 do if j <= WIDTH * HEIGHT then io.write(lines[j]) end end print() end
{{out}}
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*** *** *** *** *** *** *** ***
* * * * * * * * * * * * * * * *
=={{header|Modula-2}}== {{trans|Kotlin}}
MODULE Cantor;
FROM Terminal IMPORT Write,WriteLn,ReadChar;
CONST
WIDTH = 81;
HEIGHT = 5;
VAR
lines : ARRAY[0..HEIGHT] OF ARRAY[0..WIDTH] OF CHAR;
PROCEDURE Init;
VAR i,j : CARDINAL;
BEGIN
FOR i:=0 TO HEIGHT DO
FOR j:=0 TO WIDTH DO
lines[i,j] := '*'
END
END
END Init;
PROCEDURE Cantor(start,len,index : CARDINAL);
VAR i,j,seg : CARDINAL;
BEGIN
seg := len DIV 3;
IF seg=0 THEN RETURN END;
FOR i:=index TO HEIGHT-1 DO
j := start+seg;
FOR j:=start+seg TO start+seg*2-1 DO
lines[i,j] := ' '
END
END;
Cantor(start, seg, index+1);
Cantor(start+seg*2, seg, index+1)
END Cantor;
PROCEDURE Print;
VAR i,j : CARDINAL;
BEGIN
FOR i:=0 TO HEIGHT-1 DO
FOR j:=0 TO WIDTH-1 DO
Write(lines[i,j])
END;
WriteLn
END
END Print;
BEGIN
Init;
Cantor(0,WIDTH,1);
Print;
ReadChar;
END Cantor.
Perl
{{trans|Perl 6}}
use strict; use feature 'say'; sub cantor { our($height) = @_; my $width = 3 ** ($height - 1); our @lines = ('#' x $width) x $height; sub trim_middle_third { my($len, $start, $index) = @_; my $seg = int $len / 3 or return; for my $i ( $index .. $height - 1 ) { for my $j ( 0 .. $seg - 1 ) { substr $lines[$i], $start + $seg + $j, 1, ' '; } } trim_middle_third( $seg, $start + $_, $index + 1 ) for 0, $seg * 2; } trim_middle_third( $width, 0, 1 ); @lines; } say for cantor(5);
{{Out}}
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Perl 6
{{trans|Kotlin}}
sub cantor ( Int $height ) {
my $width = 3 ** ($height - 1);
my @lines = ( "\c[FULL BLOCK]" x $width ) xx $height;
my sub _trim_middle_third ( $len, $start, $index ) {
my $seg = $len div 3
or return;
for ( $index ..^ $height ) X ( 0 ..^ $seg ) -> ( $i, $j ) {
@lines[$i].substr-rw( $start + $seg + $j, 1 ) = ' ';
}
_trim_middle_third( $seg, $start + $_, $index + 1 ) for 0, $seg * 2;
}
_trim_middle_third( $width, 0, 1 );
return @lines;
}
.say for cantor(5);
{{Out}}
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Phix
Based on Algol 68, but even simpler, shorter, and sweeter!
integer n = 5,
w = power(3,n-1),
len = w
string line = repeat('#',w)&"\n"
while 1 do
puts(1,line)
if len=1 then exit end if
len /= 3
integer pos = 1
while pos<(w-len) do
pos += len
line[pos..pos+len-1] = ' '
pos += len
end while
end while
{{out}}
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########################### ###########################
######### ######### ######### #########
### ### ### ### ### ### ### ###
# # # # # # # # # # # # # # # #
Python
Imperative
WIDTH = 81 HEIGHT = 5 lines=[] def cantor(start, len, index): seg = len / 3 if seg == 0: return None for it in xrange(HEIGHT-index): i = index + it for jt in xrange(seg): j = start + seg + jt pos = i * WIDTH + j lines[pos] = ' ' cantor(start, seg, index + 1) cantor(start + seg * 2, seg, index + 1) return None lines = ['*'] * (WIDTH*HEIGHT) cantor(0, WIDTH, 1) for i in xrange(HEIGHT): beg = WIDTH * i print ''.join(lines[beg : beg+WIDTH])
{{out}}
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********* ********* ********* *********
*** *** *** *** *** *** *** ***
* * * * * * * * * * * * * * * *
Functional
Separating ''(Bool, Int)'' model from ''String'' display: {{Works with|Python|3.7}}
'''Cantor set – separating model from display''' from functools import (reduce) import itertools # cantor :: [(Bool, Int)] -> [(Bool, Int)] def cantor(xs): '''A Cantor segmentation step.''' def go(tpl): (bln, n) = tpl m = n // 3 return [ (True, m), (False, m), (True, m) ] if bln and (1 < n) else [tpl] return concatMap(go)(xs) # cantorLines :: Int -> String def cantorLines(n): '''A text block display of n Cantor-segmented lines. ''' m = n - 1 repeat = itertools.repeat return '\n'.join( [showCantor(x) for x in ( reduce( lambda a, f: a + [f(a[-1])], repeat(cantor, m), [[(True, 3 ** m)]] ) )] ) # showCantor :: [(Bool, Int)] -> String def showCantor(xs): '''A text block display of a list of Cantor line segments. ''' return ''.join( concatMap(lambda tpl: tpl[1] * ('█' if tpl[0] else ' '))( xs ) ) # main :: IO () def main(): '''Testing to depth 5''' print( cantorLines(5) ) # GENERIC ------------------------------------------------------------- # concatMap :: (a -> [b]) -> [a] -> [b] def concatMap(f): '''A concatenated list over which a function has been mapped. The list monad can be derived by using a function f which wraps its output in a list, (using an empty list to represent computational failure).''' chain = itertools.chain return lambda xs: list( chain.from_iterable(map(f, xs)) ) # MAIN --- if __name__ == '__main__': main()
{{Out}}
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Or, using strings for both model and display: {{Trans|JavaScript}} {{Trans|Haskell}} {{Works with|Python|3.7}}
'''Cantor set – strings as both model and display.''' from itertools import (chain, islice) # cantorLines :: Int -> String def cantorLines(n): '''N levels of cantor segmentation, obtained and displayed in the form of lines of block characters. ''' return '\n'.join( [''.join(x) for x in islice( iterate(cantor)( [3 ** (n - 1) * '█'] ), n )] ) # cantor :: [String] -> [String] def cantor(xs): '''A cantor line derived from its predecessor.''' def go(s): m = len(s) // 3 blocks = s[0:m] return [ blocks, m * ' ', blocks ] if '█' == s[0] else [s] return concatMap(go)(xs) # MAIN ---------------------------------------------------- # main :: IO () def main(): '''Testing cantor line generation to level 5''' print( cantorLines(5) ) # GENERIC ------------------------------------------------- # concatMap :: (a -> [b]) -> [a] -> [b] def concatMap(f): '''A concatenated list over which a function has been mapped. The list monad can be derived by using a function f which wraps its output in a list, (using an empty list to represent computational failure).''' return lambda xs: list( chain.from_iterable(map(f, xs)) ) # iterate :: (a -> a) -> a -> Gen [a] def iterate(f): '''An infinite list of repeated applications of f to x. ''' def go(x): v = x while True: yield v v = f(v) return lambda x: go(x) # MAIN --- if __name__ == '__main__': main()
{{Out}}
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===Dual representations – fractional and graphic=== {{Works with|Python|3.7}}
'''A Cantor set generator, and two different representations of its output. ''' from itertools import (islice, chain) from functools import (reduce) from fractions import Fraction # cantor :: Generator [[(Fraction, Fraction)]] def cantor(): '''A non-finite stream of successive Cantor partitions of the line, in the form of lists of fraction pairs. ''' def go(xy): (x, y) = xy third = Fraction(y - x, 3) return [(x, x + third), (y - third, y)] xs = [(0, 1)] while True: yield xs xs = concatMap(go)(xs) # fractionLists :: [(Fraction, Fraction)] -> String def fractionLists(xs): '''A fraction pair representation of a Cantor-partitioned line. ''' def go(xy): return ', '.join(map(showRatio, xy)) return ' '.join('(' + go(x) + ')' for x in xs) # intervalBars :: [(Fraction, Fraction)] -> String def intervalBars(w): '''A block diagram representation of a Cantor-partitioned line. ''' def go(xs): def show(a, tpl): [x, y] = [int(w * r) for r in tpl] return ( y, # Accumulator - end of previous interval (' ' * (x - a)) + ('█' * (y - x)) # A gap + an interval bar ) return mapAccumL(show)(0)(xs) return lambda xs: ''.join(go(xs)[1]) # TEST ---------------------------------------------------- # main :: IO () def main(): '''Testing the generation of successive Cantor subdivisions of the line, and displaying them both as lines of fraction pairs and as graphic interval bars. ''' xs = list(islice(cantor(), 4)) w = max(xy[1].denominator for xy in xs[-1]) print( '\n'.join(map(fractionLists, xs)), '\n' ) print( '\n'.join(map(intervalBars(w), xs)) ) # GENERIC ----------------------------------------------------- # concatMap :: (a -> [b]) -> [a] -> [b] def concatMap(f): '''A concatenated list over which a function has been mapped. The list monad can be derived by using a function f which wraps its output in a list, (using an empty list to represent computational failure).''' return lambda xs: list( chain.from_iterable(map(f, xs)) ) # mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y]) def mapAccumL(f): '''A tuple of an accumulation and a list derived by a combined map and fold, with accumulation from left to right. ''' def go(a, x): tpl = f(a[0], x) return (tpl[0], a[1] + [tpl[1]]) return lambda acc: lambda xs: ( reduce(go, xs, (acc, [])) ) # showRatio :: Ratio -> String def showRatio(r): '''String representation of the ratio r.''' d = r.denominator return str(r.numerator) + ( '/' + str(d) if 1 != d else '' ) # MAIN --- if __name__ == '__main__': main()
{{Out}}
(0, 1)
(0, 1/3) (2/3, 1)
(0, 1/9) (2/9, 1/3) (2/3, 7/9) (8/9, 1)
(0, 1/27) (2/27, 1/9) (2/9, 7/27) (8/27, 1/3) (2/3, 19/27) (20/27, 7/9) (8/9, 25/27) (26/27, 1)
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Racket
{{trans|Kotlin}}
#lang racket/base
;; {trans|Kotlin}}
(define current-width (make-parameter 81))
(define current-height (make-parameter 5))
(define (Cantor_set (w (current-width)) (h (current-height)))
(define lines (build-list h (λ (_) (make-bytes w (char->integer #\#)))))
(define (cantor start len index)
(let* ((seg (quotient len 3))
(seg-start (+ start seg))
(seg-end (+ seg-start seg)))
(unless (zero? seg)
(for* ((i (in-range index h))
(j (in-range seg-start seg-end)))
(bytes-set! (list-ref lines i) j (char->integer #\space)))
(cantor start seg (add1 index))
(cantor seg-end seg (add1 index)))))
(cantor 0 w 1)
lines)
(module+ main
(for-each displayln (Cantor_set)))
{{out}}
*********************************************************************************
*************************** ***************************
********* ********* ********* *********
*** *** *** *** *** *** *** ***
* * * * * * * * * * * * * * * *
REXX
/*REXX program displays an ASCII diagram of a Canter Set as a set of (character) lines. */
w= linesize() /*obtain the width of the display term.*/
if w==0 then w=81 /*Can't obtain width? Use the default.*/
do lines=0; _=3**lines /*calculate powers of three (# lines).*/
if _>w then leave /*Too large? We passed the max value. */
#=_ /*this value of a width─of─line is OK. */
end /*lines*/ /* [↑] calculate a useable line width.*/
w= # /*use the (last) useable line width. */
$= copies('■', #) /*populate the display line with blocks*/
do j=0 until #==0 /*show Cantor set as a line of chars. */
if j>0 then do k=#+1 by #+# to w /*skip 1st line blanking.*/
$=overlay(left('', #), $, k) /*blank parts of a line. */
end /*j*/
say $ /*display a line of the Cantor Set. */
#= # % 3 /*the part (thirds) to be blanked out. */
end /*j*/ /*stick a fork in it, we're all done. */
This REXX program makes use of '''linesize''' REXX program (or BIF) which is used to determine the screen width (or linesize) of the terminal (console).
Some REXXes don't have this BIF, so the '''linesize.rex''' REXX program is included here ──► [[LINESIZE.REX]].
{{out|output|text= when using the default size of the terminal width of 100:}}
(Shown at half size.)
■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■
■■■■■■■■■■■■■■■■■■■■■■■■■■■ ■■■■■■■■■■■■■■■■■■■■■■■■■■■
■■■■■■■■■ ■■■■■■■■■ ■■■■■■■■■ ■■■■■■■■■
■■■ ■■■ ■■■ ■■■ ■■■ ■■■ ■■■ ■■■
■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
```
{{out|output|text= when using the default size of the terminal width of 250:}}
(Shown at half size.)
■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■
■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■
■■■■■■■■■■■■■■■■■■■■■■■■■■■ ■■■■■■■■■■■■■■■■■■■■■■■■■■■ ■■■■■■■■■■■■■■■■■■■■■■■■■■■ ■■■■■■■■■■■■■■■■■■■■■■■■■■■
■■■■■■■■■ ■■■■■■■■■ ■■■■■■■■■ ■■■■■■■■■ ■■■■■■■■■ ■■■■■■■■■ ■■■■■■■■■ ■■■■■■■■■
■■■ ■■■ ■■■ ■■■ ■■■ ■■■ ■■■ ■■■ ■■■ ■■■ ■■■ ■■■ ■■■ ■■■ ■■■ ■■■
■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
```
## Ring
```ring
# Project : Cantor set
load "guilib.ring"
paint = null
new qapp
{
win1 = new qwidget() {
setwindowtitle("")
setgeometry(100,100,800,600)
label1 = new qlabel(win1) {
setgeometry(10,10,800,600)
settext("")
}
new qpushbutton(win1) {
setgeometry(150,500,100,30)
settext("draw")
setclickevent("draw()")
}
show()
}
exec()
}
func draw
p1 = new qpicture()
color = new qcolor() {
setrgb(0,0,255,255)
}
pen = new qpen() {
setcolor(color)
setwidth(10)
}
paint = new qpainter() {
begin(p1)
setpen(pen)
cantor(10,20,600)
endpaint()
}
label1 { setpicture(p1) show() }
return
func cantor(x,y,lens)
if lens >= 10
paint.drawline(x,y,x+lens,y)
y = y + 20
cantor(x,y,floor(lens/3))
cantor(x+floor(lens*2/3),y,floor(lens/3))
ok
```
Output image:
[https://www.dropbox.com/s/ap7c3301i0syh4e/CantorSet.jpg?dl=0 Cantor set]
## Ruby
This works by numbering the segments (starting with 0) in base 3. Print whitespace if this number contains the digit 1; a black square otherwise.
```ruby
lines = 5
(0..lines).each do |exp|
seg_size = 3**(lines-exp-1)
chars = (3**exp).times.map{ |n| n.digits(3).any?(1) ? " " : "█"}
puts chars.map{ |c| c * seg_size }.join
end
```
{{out}}
```txt
█████████████████████████████████████████████████████████████████████████████████
███████████████████████████ ███████████████████████████
█████████ █████████ █████████ █████████
███ ███ ███ ███ ███ ███ ███ ███
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
```
## Scala
===Imperative Programming (Q&D)===
```Scala
object CantorSetQD extends App {
val (width, height) = (81, 5)
val lines = Seq.fill[Array[Char]](height)(Array.fill[Char](width)('*'))
def cantor(start: Int, len: Int, index: Int) {
val seg = len / 3
println(start, len, index)
if (seg != 0) {
for (i <- index until height;
j <- (start + seg) until (start + seg * 2)) lines(i)(j) = ' '
cantor(start, seg, index + 1)
cantor(start + seg * 2, seg, index + 1)
}
}
cantor(0, width, 1)
lines.foreach(l => println(l.mkString))
}
```
{{Out}}See it in running in your browser by [https://scalafiddle.io/sf/QrqaHeu/0 (JavaScript)]
or by [https://scastie.scala-lang.org/4JTi1zXzRq6H4yUlAYNTSw Scastie (JVM)].
===Functional Programming (Recommended)===
```Scala
object CantorSetFP extends App {
val (width, height) = (81, 5)
def lines = (1 to height).map(_ => (0 until width).toSet)
def cantorSet(pre: Seq[Set[Int]], start: Int, len: Int, index: Int): Seq[Set[Int]] = {
val seg = len / 3
def cantorSet1(pre: Seq[Set[Int]], start: Int, index: Int): Seq[Set[Int]] = {
def elementsStuffing(pre: Set[Int], start: Int): Set[Int] =
pre -- ((start + seg) until (start + seg * 2))
for (n <- 0 until height)
yield if (index to height contains n) elementsStuffing(pre(n), start)
else pre(n)
}
if (seg == 0) pre
else {
def version0 = cantorSet1(pre, start, index)
def version1 = cantorSet(cantorSet1(pre, start, index), start, seg, index + 1)
cantorSet(version1, start + seg * 2, seg, index + 1)
}
}
def output: Seq[Set[Int]] = cantorSet(lines, 0, width, 1)
println(
output.map(l => (0 to width).map(pos => if (l contains pos) '*' else ' ').mkString)
.mkString("\n"))
}
```
{{Out}}See it in running in your browser by [https://scalafiddle.io/sf/szUjPWO/7 (JavaScript)]
or by [https://scastie.scala-lang.org/ZaNUtEOcStuBfJImOnEz5Q Scastie (JVM)].
## Sidef
{{trans|Perl 6}}
```ruby
func cantor (height) {
var width = 3**(height - 1)
var lines = height.of { "\N{FULL BLOCK}" * width }
func trim_middle_third (len, start, index) {
var seg = (len // 3) || return()
for i, j in ((index ..^ height) ~X (0 ..^ seg)) {
lines[i].replace!(Regex("^.{#{start + seg + j}}\\K."), ' ')
}
[0, 2*seg].each { |k|
trim_middle_third(seg, start + k, index + 1)
}
}
trim_middle_third(width, 0, 1)
return lines
}
cantor(5).each { .say }
```
{{out}}
```txt
█████████████████████████████████████████████████████████████████████████████████
███████████████████████████ ███████████████████████████
█████████ █████████ █████████ █████████
███ ███ ███ ███ ███ ███ ███ ███
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
```
## Smalltalk
{{works with|GNU Smalltalk}}
Smalltalk represents Intervals' start and stop values as Fraction, so precision is kept for quilte a while.
```Smalltalk
Object subclass: CantorSet [
| intervals |
CantorSet class >> new
[^self basicNew
initialize;
yourself]
initialize
[intervals := Array with: (CantorInterval
from: 0
to: 1)]
split
[intervals := intervals gather: [:each | each split]]
displayOn: aStream atScale: aNumber
[| current |
current := 0.
intervals do:
[:each |
(each start - current) * aNumber timesRepeat: [aStream space].
each length * aNumber timesRepeat: [aStream nextPut: $#].
current := each stop].
aStream nl]
]
Interval subclass: CantorInterval [
split
[| oneThird left right |
oneThird := self length / 3.
left := self class
from: start
to: start + oneThird.
right := self class
from: stop - oneThird
to: stop.
^Array
with: left
with: right]
start [^start]
stop [^stop]
length [^stop - start]
printOn: aStream
[aStream << ('%1[%2,%3]' % {self class name. start. stop})]
]
Object subclass: TestCantor [
TestCantor class >> iterations: anInteger
[| cantorset scale count |
scale := 3 raisedTo: anInteger. "Make smallest interval 1"
count := 0.
cantorset := CantorSet new.
[cantorset
displayOn: Transcript
atScale: scale.
count < anInteger] whileTrue:
[cantorset split.
count := count + 1]]
]
TestCantor iterations: 4.
```
Output:
```txt
#################################################################################
########################### ###########################
######### ######### ######### #########
### ### ### ### ### ### ### ###
# # # # # # # # # # # # # # # #
```
## Visual Basic .NET
{{trans|C#}}
```vbnet
Module Module1
Const WIDTH = 81
Const HEIGHT = 5
Dim lines(HEIGHT, WIDTH) As Char
Sub Init()
For i = 0 To HEIGHT - 1
For j = 0 To WIDTH - 1
lines(i, j) = "*"
Next
Next
End Sub
Sub Cantor(start As Integer, len As Integer, index As Integer)
Dim seg As Integer = len / 3
If seg = 0 Then
Return
End If
For i = index To HEIGHT - 1
For j = start + seg To start + seg * 2 - 1
lines(i, j) = " "
Next
Next
Cantor(start, seg, index + 1)
Cantor(start + seg * 2, seg, index + 1)
End Sub
Sub Main()
Init()
Cantor(0, WIDTH, 1)
For i = 0 To HEIGHT - 1
For j = 0 To WIDTH - 1
Console.Write(lines(i, j))
Next
Console.WriteLine()
Next
End Sub
End Module
```
{{out}}
```txt
*********************************************************************************
*************************** ***************************
********* ********* ********* *********
*** *** *** *** *** *** *** ***
* * * * * * * * * * * * * * * *
```
## zkl
```zkl
const WIDTH=81, HEIGHT=5;
var lines=HEIGHT.pump(List,List.createLong(WIDTH,"\U2588;").copy); // full block
fcn cantor(start,len,index){
(seg:=len/3) or return();
foreach i,j in ([index..HEIGHT-1], [start + seg .. start + seg*2 - 1]){
lines[i][j]=" ";
}
cantor(start, seg, index + 1);
cantor(start + seg*2, seg, index + 1);
}(0,WIDTH,1);
lines.pump(Console.println,"concat");
```
{{out}}
```txt
█████████████████████████████████████████████████████████████████████████████████
███████████████████████████ ███████████████████████████
█████████ █████████ █████████ █████████
███ ███ ███ ███ ███ ███ ███ ███
█ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
```