⚠️ 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.

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;
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;
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}}

```█████████████████████████████████████████████████████████████████████████████████
███████████████████████████                           ███████████████████████████
█████████         █████████                           █████████         █████████
███   ███         ███   ███                           ███   ███         ███   ███
█ █   █ █         █ █   █ █                           █ █   █ █         █ █   █ █
```

## 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&#64;` 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}}

```
█████████████████████████████████████████████████████████████████████████████████
███████████████████████████                           ███████████████████████████
█████████         █████████                           █████████         █████████
███   ███         ███   ███                           ███   ███         ███   ███
█ █   █ █         █ █   █ █                           █ █   █ █         █ █   █ █

```

## 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}}

```
*********************************************************************************
***************************                           ***************************
*********         *********                           *********         *********
***   ***         ***   ***                           ***   ***         ***   ***
* *   * *         * *   * *                           * *   * *         * *   * *

```

### 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}}

```█████████████████████████████████████████████████████████████████████████████████
███████████████████████████                           ███████████████████████████
█████████         █████████                           █████████         █████████
███   ███         ███   ███                           ███   ███         ███   ███
█ █   █ █         █ █   █ █                           █ █   █ █         █ █   █ █
```

### 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)

███████████████████████████
█████████         █████████
███   ███         ███   ███
█ █   █ █         █ █   █ █
```

=={{header|IS-BASIC}}== 100 PROGRAM "Cantor.bas" 110 GRAPHICS HIRES 2 120 SET PALETTE BLACK,WHITE 130 CALL CANTOR(28,500,1216,32) 140 DEF CANTOR(X,Y,L,HEIGHT) 150 IF L>3 THEN 160 PLOT X,Y;X+L,Y,X,Y+4;X+L,Y+4 170 CALL CANTOR(X,Y-HEIGHT,L/3,HEIGHT) 180 CALL CANTOR(X+2*L/3,Y-HEIGHT,L/3,HEIGHT) 190 END IF 200 END DEF

```

## 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

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

```
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}}

```*********************************************************************************
***************************                           ***************************
*********         *********                           *********         *********
***   ***         ***   ***                           ***   ***         ***   ***
* *   * *         * *   * *                           * *   * *         * *   * *
```

## JavaScript

```(() => {
'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}}

```█████████████████████████████████████████████████████████████████████████████████
███████████████████████████                           ███████████████████████████
█████████         █████████                           █████████         █████████
███   ███         ███   ███                           ███   ███         ███   ███
█ █   █ █         █ █   █ █                           █ █   █ █         █ █   █ █
```

### Dual representation

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)

███████████████████████████
█████████         █████████
███   ███         ███   ███
█ █   █ █         █ █   █ █
```

## 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}}

```
*********************************************************************************
***************************                           ***************************
*********         *********                           *********         *********
***   ***         ***   ***                           ***   ***         ***   ***
* *   * *         * *   * *                           * *   * *         * *   * *

```

## 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}}

```*********************************************************************************
***************************                           ***************************
*********         *********                           *********         *********
***   ***         ***   ***                           ***   ***         ***   ***
* *   * *         * *   * *                           * *   * *         * *   * *
```

```MODULE Cantor;

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;

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}}

```#################################################################################
###########################                           ###########################
#########         #########                           #########         #########
###   ###         ###   ###                           ###   ###         ###   ###
# #   # #         # #   # #                           # #   # #         # #   # #
```

## 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}}

```█████████████████████████████████████████████████████████████████████████████████
███████████████████████████                           ███████████████████████████
█████████         █████████                           █████████         █████████
███   ███         ███   ███                           ███   ███         ███   ███
█ █   █ █         █ █   █ █                           █ █   █ █         █ █   █ █
```

## 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}}

```
#################################################################################
###########################                           ###########################
#########         #########                           #########         #########
###   ###         ###   ###                           ###   ###         ###   ###
# #   # #         # #   # #                           # #   # #         # #   # #

```

## 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}}

```*********************************************************************************
***************************                           ***************************
*********         *********                           *********         *********
***   ***         ***   ***                           ***   ***         ***   ***
* *   * *         * *   * *                           * *   * *         * *   * *
```

### 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}}

```
█████████████████████████████████████████████████████████████████████████████████
███████████████████████████                           ███████████████████████████
█████████         █████████                           █████████         █████████
███   ███         ███   ███                           ███   ███         ███   ███
█ █   █ █         █ █   █ █                           █ █   █ █         █ █   █ █
```

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}}

```█████████████████████████████████████████████████████████████████████████████████
███████████████████████████                           ███████████████████████████
█████████         █████████                           █████████         █████████
███   ███         ███   ███                           ███   ███         ███   ███
█ █   █ █         █ █   █ █                           █ █   █ █         █ █   █ █
```

===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)

███████████████████████████
█████████         █████████
███   ███         ███   ███
█ █   █ █         █ █   █ █
```

## 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 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

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

█████████████████████████████████████████████████████████████████████████████████
███████████████████████████                           ███████████████████████████
█████████         █████████                           █████████         █████████
███   ███         ███   ███                           ███   ███         ███   ███
█ █   █ █         █ █   █ █                           █ █   █ █         █ █   █ █

```

```