Cantor set

From Rosetta Code
Task
Cantor set
You are encouraged to solve this task according to the task description, using any language you may know.
Task

Draw a Cantor set.


See details at this Wikipedia webpage:   Cantor set

11l[edit]

Translation of: 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(‘’))
Output:
*********************************************************************************
***************************                           ***************************
*********         *********                           *********         *********
***   ***         ***   ***                           ***   ***         ***   ***
* *   * *         * *   * *                           * *   * *         * *   * *

Action![edit]

PROC FillRect(INT x,y,w,h)
  INT i

  FOR i=y TO y+h-1
  DO
    Plot(x,i)
    DrawTo(x+w-1,i)
  OD
RETURN

PROC DrawCantor(INT x0,y0,h,level)
  INT x,y,i,j,w,w2,h2

  w=1
  FOR i=0 TO level-1
  DO w==*3 OD
  
  Color=1
  y=y0
  FOR i=0 TO level
  DO
    FillRect(x0,y,w,h)
    y==+h*2
  OD

  Color=0
  w2=1 h2=h*2
  FOR i=0 TO level-1
  DO
    x=w2 y=(level-i)*(h*2)
    WHILE x<w
    DO
      FillRect(x0+x,y0+y,w2,h2)
      x==+w2*2
    OD
    w2==*3
    h2==+h*2
  OD
RETURN

PROC Main()
  BYTE CH=$02FC,COLOR1=$02C5,COLOR2=$02C6

  Graphics(8+16)
  COLOR1=$0C
  COLOR2=$02

  DrawCantor(38,48,8,5)

  DO UNTIL CH#$FF OD
  CH=$FF
RETURN
Output:

Screenshot from Atari 8-bit computer

Ada[edit]

with Ada.Text_IO;

procedure Cantor_Set is

   subtype Level_Range is Integer range 1 .. 5;
   Image : array (Level_Range) of String (1 .. 81) := (others => (others => ' '));

   procedure Cantor (Level : Natural; Length : Natural; Start : Natural) is
   begin
      if Level in Level_Range then
         Image (Level) (Start .. Start + Length - 1) := (others => '*');
         Cantor (Level + 1, Length / 3, Start);
         Cantor (Level + 1, Length / 3, Start + 2 * Length / 3);
      end if;
   end Cantor;
begin
   Cantor (Level  => Level_Range'First,
           Length => 81,
           Start  => 1);

   for L in Level_Range loop
      Ada.Text_IO.Put_Line (Image (L));
   end loop;
end Cantor_Set;
Output:
*********************************************************************************
***************************                           ***************************
*********         *********                           *********         *********
***   ***         ***   ***                           ***   ***         ***   ***
* *   * *         * *   * *                           * *   * *         * *   * *

ALGOL 68[edit]

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
Output:
#################################################################################
###########################                           ###########################
#########         #########                           #########         #########
###   ###         ###   ###                           ###   ###         ###   ###
# #   # #         # #   # #                           # #   # #         # #   # #

ALGOL W[edit]

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.
Output:
#################################################################################
###########################                           ###########################
#########         #########                           #########         #########
###   ###         ###   ###                           ###   ###         ###   ###
# #   # #         # #   # #                           # #   # #         # #   # #

AppleScript[edit]

Using composable library functions whenever possible, for better productivity:

------------------------- CANTOR SET -----------------------

-- 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


---------------------------- TEST --------------------------
on run
    showCantor(5)
end run

-- showCantor :: Int -> String
on showCantor(n)
    unlines(map(my concat, ¬
        take(n, iterate(cantor, ¬
            {replicate(3 ^ (n - 1), "█")}))))
end showCantor


--------------------- GENERIC FUNCTIONS --------------------

-- 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
Output:
█████████████████████████████████████████████████████████████████████████████████
███████████████████████████                           ███████████████████████████
█████████         █████████                           █████████         █████████
███   ███         ███   ███                           ███   ███         ███   ███
█ █   █ █         █ █   █ █                           █ █   █ █         █ █   █ █

Arturo[edit]

width: 81
height: 5

lines: array.of: height repeat `*` width

cantor: function [start length idx].export:[lines][
    seg: length / 3
    if seg = 0 -> return null

    loop idx..dec height 'i [
        loop (start + seg).. dec start + 2 * seg 'j 
            -> set lines\[i] j ` `
    ]
    cantor start seg idx+1
    cantor start + 2 * seg seg idx+1
]

cantor 0 width 1

loop lines 'line 
    -> print join line
Output:
*********************************************************************************
***************************                           ***************************
*********         *********                           *********         *********
***   ***         ***   ***                           ***   ***         ***   ***
* *   * *         * *   * *                           * *   * *         * *   * *

AWK[edit]

# 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)
}
Output:
*********************************************************************************
***************************                           ***************************
*********         *********                           *********         *********
***   ***         ***   ***                           ***   ***         ***   ***
* *   * *         * *   * *                           * *   * *         * *   * *

BASIC[edit]

10 DEFINT A-Z
20 N = 4
30 W = 3^(N-1)
40 S = W
50 L$ = STRING$(W, "#")
60 PRINT L$
70 IF S = 1 THEN END
80 S = S\3
90 P = 1
100 IF P >= W-S GOTO 60
110 P = P+S
120 MID$(L$,P,S) = SPACE$(S)
130 P = P+S
140 GOTO 100
Output:
###########################
#########         #########
###   ###         ###   ###
# #   # #         # #   # #

BASIC256[edit]

Translation of: 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
Output:
Igual que la entrada de FreeBASIC.

BQN[edit]

Cantor ← {" •" ⊏˜ >⥊¨(¯1⊸⊏⊢¨¨⊢)1‿0‿1∧⌜⍟(↕𝕩)1}
Output:
   Cantor 5
┌─
╵"•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••
  •••••••••••••••••••••••••••                           •••••••••••••••••••••••••••
  •••••••••         •••••••••                           •••••••••         •••••••••
  •••   •••         •••   •••                           •••   •••         •••   •••
  • •   • •         • •   • •                           • •   • •         • •   • •"
                                                                                    ┘

C[edit]

Translation of: 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#[edit]

Translation of: 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();
            }
        }
    }
}
Output:
*********************************************************************************
***************************                           ***************************
*********         *********                           *********         *********
***   ***         ***   ***                           ***   ***         ***   ***
* *   * *         * *   * *                           * *   * *         * *   * *

C++[edit]

Translation of: 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;
}
Output:
*********************************************************************************
***************************                           ***************************
*********         *********                           *********         *********
***   ***         ***   ***                           ***   ***         ***   ***
* *   * *         * *   * *                           * *   * *         * *   * *

CLU[edit]

cantor = cluster is make
    rep = null
    ac = array[char]
    aac = array[array[char]]
    
    make = proc (width, height: int, ch: char) returns (string)
        lines: aac := aac$fill_copy(0, height, ac$fill(0, width, ch))
        cantor_step(lines, 0, width, 1)
        s: stream := stream$create_output()
        for line: ac in aac$elements(lines) do
            stream$putl(s, string$ac2s(line))
        end
        return(stream$get_contents(s))
    end make

    cantor_step = proc (lines: aac, start, len, index: int)
        seg: int := len / 3
        if seg = 0 then return end
        for i: int in int$from_to(index, aac$high(lines)) do
            for j: int in int$from_to(start+seg, start+seg*2-1) do
                lines[i][j] := ' '
            end
        end
        cantor_step(lines, start, seg, index+1)
        cantor_step(lines, start+seg*2, seg, index+1)
    end cantor_step
end cantor

start_up = proc ()
    po: stream := stream$primary_output()
    cs: string := cantor$make(81, 5, '*')
    stream$puts(po, cs)
end start_up
Output:
*********************************************************************************
***************************                           ***************************
*********         *********                           *********         *********
***   ***         ***   ***                           ***   ***         ***   ***
* *   * *         * *   * *                           * *   * *         * *   * *

COBOL[edit]

       IDENTIFICATION DIVISION.
       PROGRAM-ID. CANTOR.
       
       DATA DIVISION.
       WORKING-STORAGE SECTION.
       01 SETTINGS.
          03 NUM-LINES     PIC 9 VALUE 5.
          03 FILL-CHAR     PIC X VALUE '#'.
       01 VARIABLES.
          03 CUR-LINE.
             05 CHAR       PIC X OCCURS 81 TIMES.
          03 WIDTH         PIC 99.
          03 CUR-SIZE      PIC 99.
          03 POS           PIC 99.
          03 MAXPOS        PIC 99.
          03 NEXTPOS       PIC 99.
          03 I             PIC 99.
          
       PROCEDURE DIVISION.
       BEGIN.
           COMPUTE WIDTH = 3 ** (NUM-LINES - 1).
           PERFORM INIT.
           MOVE WIDTH TO CUR-SIZE.
           DISPLAY CUR-LINE.
           PERFORM DO-LINE UNTIL CUR-SIZE IS EQUAL TO 1.
           STOP RUN.
           
       INIT.
           PERFORM INIT-CHAR VARYING I FROM 1 BY 1
                UNTIL I IS GREATER THAN WIDTH.
       
       INIT-CHAR.
           MOVE FILL-CHAR TO CHAR(I).
           
       DO-LINE.
           DIVIDE 3 INTO CUR-SIZE.
           MOVE 1 TO POS.
           SUBTRACT CUR-SIZE FROM WIDTH GIVING MAXPOS.
           PERFORM BLANK-REGIONS UNTIL POS IS GREATER THAN MAXPOS.
           DISPLAY CUR-LINE.
       
       BLANK-REGIONS.
           ADD CUR-SIZE TO POS.
           PERFORM BLANK-CHAR CUR-SIZE TIMES.
           
       BLANK-CHAR.
           MOVE SPACE TO CHAR(POS).
           ADD 1 TO POS.
Output:
#################################################################################
###########################                           ###########################
#########         #########                           #########         #########
###   ###         ###   ###                           ###   ###         ###   ###
# #   # #         # #   # #                           # #   # #         # #   # #

D[edit]

Translation of: 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]);
    }
}
Output:
*********************************************************************************
***************************                           ***************************
*********         *********                           *********         *********
***   ***         ***   ***                           ***   ***         ***   ***
* *   * *         * *   * *                           * *   * *         * *   * *

Delphi[edit]

Translation of: Java
program Cantor_set;

{$APPTYPE CONSOLE}

const
  WIDTH: Integer = 81;
  HEIGHT: Integer = 5;

var
  Lines: TArray<TArray<Char>>;

procedure Init;
var
  i, j: Integer;
begin
  SetLength(lines, HEIGHT, WIDTH);
  for i := 0 to HEIGHT - 1 do
    for j := 0 to WIDTH - 1 do
      lines[i, j] := '*';
end;

procedure Cantor(start, len, index: Integer);
var
  seg, i, j: Integer;
begin
  seg := len div 3;
  if seg = 0 then
    Exit;
  for i := index to HEIGHT - 1 do
    for j := start + seg to start + seg * 2 - 1 do
      lines[i, j] := ' ';
  Cantor(start, seg, index + 1);
  Cantor(start + seg * 2, seg, index + 1);
end;

var
  i, j: Integer;

begin
  Init;
  Cantor(0, WIDTH, 1);
  for i := 0 to HEIGHT - 1 do
  begin
    for j := 0 to WIDTH - 1 do
      Write(lines[i, j]);
    Writeln;
  end;
  Readln;
end.
Output:

Same result of Java

Excel[edit]

LAMBDA[edit]

Binding names to the following lambda expressions in the Name Manager of the Excel WorkBook:

(See LAMBDA: The ultimate Excel worksheet function)

CANTOR
=LAMBDA(n,
    APPLYN(n)(
        LAMBDA(grid,
            APPENDROWS(grid)(
                CANTOROW(
                    LASTROW(grid)
                )
            )
        )
    )({0,1})
)


CANTOROW
=LAMBDA(xys,
    LET(
        nCols, COLUMNS(xys),

        IF(2 > nCols,
            xys,
            IF(3 < nCols,
                APPENDCOLS(
                    CANTORSLICES(TAKECOLS(2)(xys))
                )(
                    CANTOROW(DROPCOLS(2)(xys))
                ),
                CANTORSLICES(TAKECOLS(2)(xys))
            )
        )
    )
)


CANTORSLICES
=LAMBDA(ab,
    LET(
        a, INDEX(ab, 1),
        b, INDEX(ab, 2),
        third, (b - a) / 3,

        CHOOSE({1,2,3,4}, a, a + third, b - third, b)
    )
)


SHOWCANTOR
=LAMBDA(grid,
    LET(
        leaves, LASTROW(grid),
        leafWidth, INDEX(leaves, 1, 2) - INDEX(leaves, 1, 1),
        leafCount, 1 / leafWidth,

        SHOWCANTROWS(leafCount)(grid)
    )
)


SHOWCANTROWS
=LAMBDA(leafCount,
    LAMBDA(grid,
        LET(
            xs, FILTERP(
               LAMBDA(x, NOT(ISNA(x)))
            )(
                HEADCOL(grid)
            ),
            
            runLengths, LAMBDA(x, 
                CEILING.MATH(leafCount * x))(
                    SUBTRACT(TAILROW(xs))(INITROW(xs)
                )
            ),
            
            iCols, SEQUENCE(1, COLUMNS(runLengths)),
            
            CONCAT(
                REPT(
                    IF(ISEVEN(iCols), " ", "█"), 
                    runLengths
                )
            ) & IF(1 < ROWS(grid),
                CHAR(10) & SHOWCANTROWS(leafCount)(
                    TAILCOL(grid)
                ),
                ""
            )
        )
    )
)

and also assuming the following generic bindings in the Name Manager for the WorkBook:

APPENDCOLS
=LAMBDA(xs,
    LAMBDA(ys,
        LET(
            nx, COLUMNS(xs),
            ny, COLUMNS(ys),
            colIndexes, SEQUENCE(1, nx + ny),
            rowIndexes, SEQUENCE(MAX(ROWS(xs), ROWS(ys))),

            IFERROR(
                IF(nx < colIndexes,
                    INDEX(ys, rowIndexes, colIndexes - nx),
                    INDEX(xs, rowIndexes, colIndexes)
                ),
                NA()
            )
        )
    )
)


APPENDROWS
=LAMBDA(xs,
    LAMBDA(ys,
        LET(
            nx, ROWS(xs),
            rowIndexes, SEQUENCE(nx + ROWS(ys)),
            colIndexes, SEQUENCE(
                1,
                MAX(COLUMNS(xs), COLUMNS(ys))
            ),

            IFERROR(
                IF(rowIndexes <= nx,
                    INDEX(xs, rowIndexes, colIndexes),
                    INDEX(ys, rowIndexes - nx, colIndexes)
                ),
                NA()
            )
        )
    )
)


APPLYN
=LAMBDA(n,
    LAMBDA(f,
        LAMBDA(x,
            IF(0 < n,
                APPLYN(n - 1)(f)(
                    f(x)
                ),
                x
            )
        )
    )
)


DROPCOLS
=LAMBDA(n,
    LAMBDA(xs,
        INDEX(
            xs,
            SEQUENCE(ROWS(xs), 1),
            SEQUENCE(1, (COLUMNS(xs) - n), 1 + n, 1)
        )
    )
)


FILTERP
=LAMBDA(p,
    LAMBDA(xs,
        FILTER(xs, p(xs))
    )
)


HEADCOL
=LAMBDA(xs,
    LET(REM, "The first item of each column in xs",

        INDEX(xs, 1, SEQUENCE(1, COLUMNS(xs)))
    )
)


INITROW
=LAMBDA(xs,
    INDEX(
        xs,
        SEQUENCE(
            1,
            COLUMNS(xs) - 1,
            1, 1
        )
    )
)


LASTROW
=LAMBDA(xs,
    INDEX(
        xs,
        ROWS(xs),
        SEQUENCE(1, COLUMNS(xs), 1, 1)
    )
)


SUBTRACT
=LAMBDA(a,
    LAMBDA(b, a - b)
)


TAILCOL
=LAMBDA(cols,
    LET(REM, "The tail of each column in the grid.",

        INDEX(
            cols,
            SEQUENCE(ROWS(cols) - 1, 1, 2, 1),
            SEQUENCE(1, COLUMNS(cols))
        )
    )
)


TAILROW
=LAMBDA(xs,
    LET(REM,"The tail of each row in the grid",
        n, COLUMNS(xs) - 1,

        IF(0 < n,
            INDEX(
                xs,
                SEQUENCE(ROWS(xs), 1, 1, 1),
                SEQUENCE(1, n, 2, 1)
            ),
            NA()
        )
    )
)


TAKECOLS
=LAMBDA(n,
    LAMBDA(xs,
        INDEX(
            xs,
            SEQUENCE(ROWS(xs)),
            SEQUENCE(1, n)
        )
    )
)
Output:

As a string, with the format of the cell set to a mono-spaced font, and with Format > Cells > Alignment > Wrap text = True, to allow for the display of Excel's (platform - independent) CHAR(10) line breaks:

fx =SHOWCANTOR(CANTOR(1))
A B
1 SHOWCANTOR(CANTOR(0))
2 SHOWCANTOR(CANTOR(1))
███
█ █
3 SHOWCANTOR(CANTOR(2))
█████████
███   ███
█ █   █ █
4 SHOWCANTOR(CANTOR(3))
███████████████████████████
█████████         █████████
███   ███         ███   ███
█ █   █ █         █ █   █ █

The diagrams above are drawn from the array of underlying fractions defined by CANTOR(n).

(The expression in B2 below defines the values which populate the grid B2:Q5)

The enclosing application of the built-in IFNA function maps undefined numeric cells in that grid (with the Excel value #N/A) to empty strings, for a more readable display.

(The number format for the numeric cells is set to Fraction > Up to three digits.)

fx =IFNA(CANTOR(3), "")
A B C D E F G H I J K L M N O P Q
1
2 Unit range 0 1
3 Cantor 1 0 1/3 2/3 1
4 Cantor 2 0 1/9 2/9 1/3 2/3 7/9 8/9 1
5 Cantor 3 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

Factor[edit]

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
Output:
#################################################################################
###########################                           ###########################
#########         #########                           #########         #########
###   ###         ###   ###                           ###   ###         ###   ###
# #   # #         # #   # #                           # #   # #         # #   # #

Forth[edit]

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[edit]

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
Output:
█████████████████████████████████████████████████████████████████████████████████
███████████████████████████                           ███████████████████████████
█████████         █████████                           █████████         █████████
███   ███         ███   ███                           ███   ███         ███   ███
█ █   █ █         █ █   █ █                           █ █   █ █         █ █   █ █

Go[edit]

Translation of: 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[:]))
    }
}
Output:
*********************************************************************************
***************************                           ***************************
*********         *********                           *********         *********
***   ***         ***   ***                           ***   ***         ***   ***
* *   * *         * *   * *                           * *   * *         * *   * *

Groovy[edit]

Translation of: Java
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 = (int) (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++) {
                System.out.print(lines[i][j])
            }
            System.out.println()
        }
    }
}
Output:
*********************************************************************************
***************************                           ***************************
*********         *********                           *********         *********
***   ***         ***   ***                           ***   ***         ***   ***
* *   * *         * *   * *                           * *   * *         * *   * *

Haskell[edit]

Interval bars[edit]

Translation of: Python
(Functional version)
-------------------------- CANTOR ------------------------

cantor :: [(Bool, Int)] -> [(Bool, Int)]
cantor = concatMap go
  where
    go (bln, n)
      | bln && 1 < n =
          let m = quot n 3
           in [(True, m), (False, m), (True, m)]
      | otherwise = [(bln, n)]

--------------------------- TEST -------------------------
main :: IO ()
main = putStrLn $ cantorLines 5

------------------------- DISPLAY ------------------------
cantorLines :: Int -> String
cantorLines n =
  unlines $
    showCantor
      <$> take n (iterate cantor [(True, 3 ^ pred n)])

showCantor :: [(Bool, Int)] -> String
showCantor = concatMap $ uncurry (flip replicate . c)
  where
    c True = '*'
    c False = ' '
Output:
*********************************************************************************
***************************                           ***************************
*********         *********                           *********         *********
***   ***         ***   ***                           ***   ***         ***   ***
* *   * *         * *   * *                           * *   * *         * *   * *

Or, using strings for the model as well as the display:

-------------------------- CANTOR ------------------------

cantor :: [String] -> [String]
cantor = (go =<<)
  where
    go x
      | '█' == head x = [block, replicate m ' ', block]
      | otherwise = [x]
      where
        m = quot (length x) 3
        block = take m x
        

--------------------------- TEST -------------------------
main :: IO ()
main = putStrLn $ cantorLines 5


------------------------- DISPLAY ------------------------
cantorLines :: Int -> String
cantorLines =
  unlines . (concat <$>)
    . ( take
          <*> ( iterate cantor
                  . return
                  . flip replicate '█'
                  . (3 ^)
                  . pred
              )
      )
Output:
█████████████████████████████████████████████████████████████████████████████████
███████████████████████████                           ███████████████████████████
█████████         █████████                           █████████         █████████
███   ███         ███   ███                           ███   ███         ███   ███
█ █   █ █         █ █   █ █                           █ █   █ █         █ █   █ █

Dual representation[edit]

Intervals as fraction pairs, and intervals as graphic bars:

import Control.Monad (join)
import Data.Bifunctor (bimap)
import Data.List (intercalate, mapAccumL, maximumBy)
import Data.Ratio (Ratio, denominator, numerator, (%))

-------------------------- CANTOR ------------------------

cantor :: (Rational, Rational) -> [[(Rational, Rational)]]
cantor = iterate (go =<<) . pure
  where
    go (x, y) = [(x, x + r), (y - r, y)]
      where
        r = (y - x) / 3

--------------------------- TEST -------------------------

main :: IO ()
main =
  ( ( (>>)
        . putStrLn
        . unlines
        . fmap intervalRatios
    )
      <*> (putStrLn . intervalBars)
  )
    $ take 4 $ cantor (0, 1)

------------------------- DISPLAY ------------------------

intervalBars :: [[(Rational, Rational)]] -> String
intervalBars xs = unlines $ go (d % 1) <$> xs
  where
    d = maximum $ denominator . fst <$> last xs
    go w xs =
      concat . snd $
        mapAccumL
          ( \a (rx, ry) ->
              let (wy, wx) = (w * ry, w * rx)
               in ( wy,
                    replicate (floor (wx - a)) ' '
                      <> replicate (floor (wy - wx)) '█'
                  )
          )
          0
          xs

intervalRatios :: [(Rational, Rational)] -> String
intervalRatios =
  ('(' :) . (<> ")")
    . intercalate ") ("
    . fmap
      (uncurry ((<>) . (<> ", ")) . join bimap showRatio)

showRatio :: Rational -> String
showRatio = ((<>) . show . numerator) <*> (go . denominator)
  where
    go x
      | 1 /= x = '/' : show x
      | otherwise = []
Output:
(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)

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

IS-BASIC[edit]

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[edit]

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.

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[edit]

Translation of: 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();
        }
    }
}
Output:
*********************************************************************************
***************************                           ***************************
*********         *********                           *********         *********
***   ***         ***   ***                           ***   ***         ***   ***
* *   * *         * *   * *                           * *   * *         * *   * *

JavaScript[edit]

Cantor: (Bool, Int) pairs[edit]

Translation of: Python
(Functional version)
Translation of: Haskell
(() => {
    "use strict";

    // -------------- CANTOR BOOL-INT PAIRS --------------

    // cantor :: [(Bool, Int)] -> [(Bool, Int)]
    const cantor = xs => {
        const go = ([bln, n]) =>
            bln && 1 < n ? (() => {
                const x = Math.floor(n / 3);

                return [
                    [true, x],
                    [false, x],
                    [true, x]
                ];
            })() : [
                [bln, n]
            ];

        return xs.flatMap(go);
    };

    // ---------------------- TEST -----------------------
    // main :: IO ()
    const main = () =>
        cantorLines(5);


    // --------------------- DISPLAY ---------------------

    // cantorLines :: Int -> String
    const cantorLines = n =>
        take(n)(
            iterate(cantor)([
                [true, 3 ** (n - 1)]
            ])
        )
        .map(showCantor)
        .join("\n");


    // showCantor :: [(Bool, Int)] -> String
    const showCantor = xs =>
        xs.map(
            ([bln, n]) => (
                bln ? (
                    "*"
                ) : " "
            ).repeat(n)
        )
        .join("");

    // ---------------- GENERIC FUNCTIONS ----------------

    // iterate :: (a -> a) -> a -> Gen [a]
    const iterate = f =>
        // An infinite list of repeated
        // applications of f to x.
        function* (x) {
            let v = x;

            while (true) {
                yield v;
                v = f(v);
            }
        };


    // take :: Int -> [a] -> [a]
    // take :: Int -> String -> String
    const take = n =>
        // The first n elements of a list,
        // string of characters, or stream.
        xs => "GeneratorFunction" !== xs
        .constructor.constructor.name ? (
            xs.slice(0, n)
        ) : [].concat(...Array.from({
            length: n
        }, () => {
            const x = xs.next();

            return x.done ? [] : [x.value];
        }));

    // MAIN ---
    return main();
})();
Output:
*********************************************************************************
***************************                           ***************************
*********         *********                           *********         *********
***   ***         ***   ***                           ***   ***         ***   ***
* *   * *         * *   * *                           * *   * *         * *   * *

Cantor: Strings[edit]

Using strings for the model as well as the display:

Translation of: Haskell
(() => {
    "use strict";

    // ----------------- CANTOR STRINGS ------------------

    // cantor :: [String] -> [String]
    const cantor = xs => {
        const go = s => {
            const
                m = Math.floor(s.length / 3),
                blocks = take(m)(s);

            return "█" === s[0] ? (
                [blocks, " ".repeat(m), blocks]
            ) : [s];
        };

        return xs.flatMap(go);
    };

    // ---------------------- TEST -----------------------
    const main = () =>
        showCantor(5);


    // --------------------- DISPLAY ---------------------
    // showCantor :: Int -> String
    const showCantor = n =>
        take(n)(
            iterate(cantor)([
                "█".repeat(3 ** (n - 1))
            ])
        )
        .map(x => x.join(""))
        .join("\n");


    // ---------------- GENERIC FUNCTIONS ----------------

    // iterate :: (a -> a) -> a -> Gen [a]
    const iterate = f =>
        // An infinite list of repeated
        // applications of f to x.
        function* (x) {
            let v = x;

            while (true) {
                yield v;
                v = f(v);
            }
        };


    // take :: Int -> [a] -> [a]
    // take :: Int -> String -> String
    const take = n =>
        // The first n elements of a list,
        // string of characters, or stream.
        xs => "GeneratorFunction" !== xs
        .constructor.constructor.name ? (
            xs.slice(0, n)
        ) : [].concat(...Array.from({
            length: n
        }, () => {
            const x = xs.next();

            return x.done ? [] : [x.value];
        }));

    // MAIN ---
    return main();
})();
Output:
█████████████████████████████████████████████████████████████████████████████████
███████████████████████████                           ███████████████████████████
█████████         █████████                           █████████         █████████
███   ███         ███   ███                           ███   ███         ███   ███
█ █   █ █         █ █   █ █                           █ █   █ █         █ █   █ █

Cantor: Rational pairs[edit]

Translation of: Haskell
Translation of: Python


Cantor ternary intervals rendered both as lists of rational 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";

    // -------------- CANTOR RATIONAL PAIRS --------------

    // cantor :: [(Rational, Rational)] ->
    //           [(Rational, Rational)]
    const cantor = xs => {
        const go = ab => {
            const [r1, r2] = Array.from(ab).map(rational);
            const third = ratioDiv(ratioMinus(r2)(r1))(3);

            return [
                Tuple(r1)(ratioPlus(r1)(third)),
                Tuple(ratioMinus(r2)(third))(r2)
            ];
        };

        return xs.flatMap(go);
    };


    // ---------------------- TEST -----------------------
    // main :: IO ()
    const main = () => {
        const
            xs = take(4)(
                iterate(cantor)([Tuple(0)(1)])
            );

        return [
                `${unlines(xs.map(intervalRatios))}\n`,
                intervalBars(xs)
            ]
            .join("\n\n");
    };


    // --------------------- DISPLAY ---------------------

    // intervalRatios :: [(Rational, Rational)] -> String
    const intervalRatios = xs => {
        const go = ab =>
            Array.from(ab).map(
                compose(showRatio, rational)
            )
            .join(", ");

        return `(${xs.map(go).join(") (")})`;
    };

    // intervalBars :: [[(Rational, Rational)]] -> String
    const intervalBars = rs => {
        const go = w => xs =>
            snd(mapAccumL(
                a => ab => {
                    const [wx, wy] = Array.from(ab).map(
                        r => ratioMult(w)(
                            rational(r)
                        )
                    );

                    return Tuple(wy)(
                        replicateString(
                            floor(ratioMinus(wx)(a))
                        )(" ") + replicateString(
                            floor(ratioMinus(wy)(wx))
                        )("█")
                    );
                }
            )(0)(xs)).join("");
        const d = maximum(
            last(rs).map(x => fst(x).d)
        );

        return unlines(rs.map(
            go(Ratio(d)(1))
        ));
    };


    // ---------------- GENERIC FUNCTIONS ----------------

    // Ratio :: Integral a => a -> a -> Ratio a
    const Ratio = a => b => {
        const go = (x, y) =>
            0 !== y ? (() => {
                const d = gcd(x)(y);

                return {
                    type: "Ratio",
                    // numerator
                    "n": Math.trunc(x / d),
                    // denominator
                    "d": Math.trunc(y / d)
                };
            })() : undefined;

        return go(a * signum(b), abs(b));
    };


    // Tuple (,) :: a -> b -> (a, b)
    const Tuple = a =>
        b => ({
            type: "Tuple",
            "0": a,
            "1": b,
            length: 2
        });


    // abs :: Num -> Num
    const abs =
        // Absolute value of a given number
        // without the sign.
        x => 0 > x ? (
            -x
        ) : x;


    // approxRatio :: Float -> Float -> Ratio
    const approxRatio = eps =>
        n => {
            const
                gcde = (e, x, y) => {
                    const _gcd = (a, b) =>
                        b < e ? (
                            a
                        ) : _gcd(b, a % b);

                    return _gcd(Math.abs(x), Math.abs(y));
                },
                c = gcde(Boolean(eps) ? (
                    eps
                ) : (1 / 10000), 1, n);

            return Ratio(
                Math.floor(n / c)
            )(
                Math.floor(1 / c)
            );
        };


    // floor :: Num -> Int
    const floor = x => {
        const
            nr = (
                "Ratio" !== x.type ? (
                    properFraction
                ) : properFracRatio
            )(x),
            n = nr[0];

        return 0 > nr[1] ? n - 1 : n;
    };


    // fst :: (a, b) -> a
    const fst = ab =>
        // First member of a pair.
        ab[0];


    // gcd :: Integral a => a -> a -> a
    const gcd = x =>
        y => {
            const zero = x.constructor(0);
            const go = (a, b) =>
                zero === b ? (
                    a
                ) : go(b, a % b);

            return go(abs(x), abs(y));
        };


    // compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
    const compose = (...fs) =>
        // A function defined by the right-to-left
        // composition of all the functions in fs.
        fs.reduce(
            (f, g) => x => f(g(x)),
            x => x
        );


    // iterate :: (a -> a) -> a -> Gen [a]
    const iterate = f =>
        // An infinite list of repeated
        // applications of f to x.
        function* (x) {
            let v = x;

            while (true) {
                yield v;
                v = f(v);
            }
        };


    // last :: [a] -> a
    const last = xs =>
        // The last item of a list.
        0 < xs.length ? (
            xs.slice(-1)[0]
        ) : null;


    // lcm :: Int -> Int -> Int
    const lcm = x =>
        // The smallest positive integer divisible
        // without remainder by both x and y.
        y => (x === 0 || y === 0) ? (
            0
        ) : Math.abs(Math.floor(x / gcd(x)(y)) * y);


    // mapAccumL :: (acc -> x -> (acc, y)) ->
    // acc -> [x] -> (acc, [y])
    const mapAccumL = f =>
        // A tuple of an accumulation and a list
        // obtained by a combined map and fold,
        // with accumulation from left to right.
        acc => xs => [...xs].reduce(
            (a, x) => {
                const ab = f(a[0])(x);

                return [ab[0], a[1].concat(ab[1])];
            },
            [acc, []]
        );


    // maximum :: Ord a => [a] -> a
    const maximum = xs => (
        // The largest value in a non-empty list.
        ys => 0 < ys.length ? (
            ys.slice(1).reduce(
                (a, y) => y > a ? (
                    y
                ) : a, ys[0]
            )
        ) : undefined
    )(xs);


    // 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);
    };


    // quotRem :: Integral a => a -> a -> (a, a)
    const quotRem = m =>
        // The quotient, tupled with the remainder.
        n => Tuple(
            Math.trunc(m / n)
        )(
            m % n
        );


    // ratioDiv :: Rational -> Rational -> Rational
    const ratioDiv = n1 => n2 => {
        const [r1, r2] = [n1, n2].map(rational);

        return Ratio(r1.n * r2.d)(
            r1.d * r2.n
        );
    };


    // ratioMinus :: Rational -> Rational -> Rational
    const ratioMinus = n1 => n2 => {
        const [r1, r2] = [n1, n2].map(rational);
        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] = [n1, n2].map(rational);

        return Ratio(r1.n * r2.n)(
            r1.d * r2.d
        );
    };


    // ratioPlus :: Rational -> Rational -> Rational
    const ratioPlus = n1 =>
        n2 => {
            const [r1, r2] = [n1, n2].map(rational);
            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 : Number.isInteger(x) ? (
            Ratio(x)(1)
        ) : approxRatio(undefined)(x);


    // 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}`
            ) : ""
        );


    // signum :: Num -> Num
    const signum = n =>
        // | Sign of a number.
        n.constructor(
            0 > n ? (
                -1
            ) : (
                0 < n ? 1 : 0
            )
        );


    // snd :: (a, b) -> b
    const snd = ab =>
        // Second member of a pair.
        ab[1];


    // take :: Int -> [a] -> [a]
    // take :: Int -> String -> String
    const take = n =>
        // The first n elements of a list,
        // string of characters, or stream.
        xs => "GeneratorFunction" !== xs
        .constructor.constructor.name ? (
            xs.slice(0, n)
        ) : [].concat(...Array.from({
            length: n
        }, () => {
            const x = xs.next();

            return x.done ? [] : [x.value];
        }));


    // unlines :: [String] -> String
    const unlines = xs =>
        // A single string formed by the intercalation
        // of a list of strings with the newline character.
        xs.join("\n");


    // MAIN ---
    return main();
})();
Output:
(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)

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

jq[edit]

# cantor(width; height)
def cantor($w; $h):
  def init: [range(0; $h) | [range(0; $w) | "*"]];

  def cantor($start; $leng; $ix):
    ($leng/3|floor) as $seg
    | if $seg == 0 then .
      else reduce range($ix; $h) as $i (.;
             reduce range($start+$seg; $start + 2*$seg) as $j (.; .[$i][$j] = " "))
      | cantor($start; $seg; $ix+1)
      | cantor($start + 2*$seg; $seg; $ix+1)
    end ;
  init | cantor(0; $w; 1);
    
def pp: .[] | join("");
  
cantor($width; $height)
| pp
Output:

With the above in a file, cantor.jq, the following incantation yields the same output as shown e.g. under `awk`, `julia`, etc.

   jq -nr --argjson width 81 --argjson height 5 -f cantor.jq

Julia[edit]

Translation of: 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
Output:
#################################################################################
###########################                           ###########################
#########         #########                           #########         #########
###   ###         ###   ###                           ###   ###         ###   ###
# #   # #         # #   # #                           # #   # #         # #   # #

Kotlin[edit]

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[edit]

Translation of: 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
Output:
*********************************************************************************
***************************                           ***************************
*********         *********                           *********         *********
***   ***         ***   ***                           ***   ***         ***   ***
* *   * *         * *   * *                           * *   * *         * *   * *

Mathematica/Wolfram Language[edit]

Graphics[MeshPrimitives[CantorMesh[#],1]/.{x_}:>{x,-0.05#}&/@Range[5],ImageSize->600]
Output:

A graphic of a Cantor set is shown

Modula-2[edit]

Translation of: 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.

Nim[edit]

Translation of: Kotlin
import strutils

const
  Width = 81
  Height = 5

var lines: array[Height, string]
for line in lines.mitems: line = repeat('*', Width)

proc cantor(start, length, index: Natural) =
  let seg = length div 3
  if seg == 0: return
  for i in index..<Height:
    for j in (start + seg)..<(start + seg * 2):
      lines[i][j] = ' '
  cantor(start, seg, index + 1)
  cantor(start + seg * 2, seg, index + 1)

cantor(0, Width, 1)
for line in lines:
  echo line
Output:
*********************************************************************************
***************************                           ***************************
*********         *********                           *********         *********
***   ***         ***   ***                           ***   ***         ***   ***
* *   * *         * *   * *                           * *   * *         * *   * *

Objeck[edit]

Translation of: Java
class CantorSet {
  WIDTH : static : Int;
  HEIGHT : static : Int;
  lines : static : Char[,];
 
  function : Init() ~ Nil {
    WIDTH := 81;
    HEIGHT := 5;
    lines := Char->New[HEIGHT, WIDTH];
    
    each(i : HEIGHT) {
      each(j : WIDTH) {
        lines[i,j] := '*';
      };
    };
  }

  function : Cantor(start : Int, len : Int, index : Int) ~ Nil {
    seg : Int := len / 3;

    if(seg = 0) {
      return;
    };

    for(i := index; i < HEIGHT; i += 1;) {
      for(j := start + seg; j < start + seg * 2; j += 1;) {
        lines[i,j] := ' ';
      };
    };

    Cantor(start, seg, index + 1);
    Cantor(start + seg * 2, seg, index + 1);
  }

  function : Main(args : String[]) ~ Nil {
    Init();

    Cantor(0, WIDTH, 1);
    each(i : HEIGHT) {
      each(j : WIDTH) {
        lines[i,j]->Print();
      };
      ""->PrintLine();
    };
  }
}
Output:
*********************************************************************************
***************************                           ***************************
*********         *********                           *********         *********
***   ***         ***   ***                           ***   ***         ***   ***
* *   * *         * *   * *                           * *   * *         * *   * *

Perl[edit]

Translation of: Raku
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);
Output:
#################################################################################
###########################                           ###########################
#########         #########                           #########         #########
###   ###         ###   ###                           ###   ###         ###   ###
# #   # #         # #   # #                           # #   # #         # #   # #

regex version[edit]

#!/usr/bin/perl -l

use strict; # https://rosettacode.org/wiki/Cantor_set
use warnings;

$_ = '#' x 81;

1 while print, s/(#+)\1\1/ $1 . $1 =~ tr!#! !r . $1 /ge;
Output:
#################################################################################
###########################                           ###########################
#########         #########                           #########         #########
###   ###         ###   ###                           ###   ###         ###   ###
# #   # #         # #   # #                           # #   # #         # #   # #

Phix[edit]

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
Output:
#################################################################################
###########################                           ###########################
#########         #########                           #########         #########
###   ###         ###   ###                           ###   ###         ###   ###
# #   # #         # #   # #                           # #   # #         # #   # #

Phixmonti[edit]

include ..\Utilitys.pmt

5 >ps
3 tps 1 - power var w
"#" 1 get nip w repeat var line

ps> for
    3 swap 1 - power
    w over / int var step
    true >ps
    for var j
    	tps not if
            step for var k
            	line 32 j 1 - step * k + set var line
            endfor
        endif
        ps> not >ps
    endfor
    cps
    line ?
endfor

Other solution

include ..\Utilitys.pmt

5 >ps
3 tps 1 - power var w
"#" 1 get nip w repeat var line

( 2 ps> ) for
    line ?
    3 swap 1 - power
    w over / int var step
    2 swap 2 3 tolist for var j
        step for var k
            line 32 j 1 - step * k + set var line
        endfor
    endfor
endfor
line ?
Output:
#################################################################################
###########################                           ###########################
#########         #########                           #########         #########
###   ###         ###   ###                           ###   ###         ###   ###
# #   # #         # #   # #                           # #   # #         # #   # #

=== Press any key to exit ===

Processing[edit]

//Aamrun, 1st July 2022

void cantorSet(int x1,int y1,int x2,int y2,int strWt,int gap,int n){
    strokeWeight(strWt);
    line(x1,y1,x2,y2);
  if(n>0){
    cantorSet(x1,gap + y1,(2*x1+x2)/3,gap + (2*y1+y2)/3,strWt,gap,n-1);
    cantorSet((2*x2+x1)/3,gap + (2*y2+y1)/3,x2,gap + y2,strWt,gap,n-1);
  }
}

void setup(){
  size(1000,1000);
  cantorSet(100,10,900,10,1,10,5);
}

Python[edit]

Imperative[edit]

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])
Output:
*********************************************************************************
***************************                           ***************************
*********         *********                           *********         *********
***   ***         ***   ***                           ***   ***         ***   ***
* *   * *         * *   * *                           * *   * *         * *   * *

Functional[edit]

Separating (Bool, Int) model from String display:

Works with: Python version 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()
Output:
█████████████████████████████████████████████████████████████████████████████████
███████████████████████████                           ███████████████████████████
█████████         █████████                           █████████         █████████
███   ███         ███   ███                           ███   ███         ███   ███
█ █   █ █         █ █   █ █                           █ █   █ █         █ █   █ █

Or, using strings for both model and display:

Translation of: JavaScript
Translation of: Haskell
Works with: Python version 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()
Output:
█████████████████████████████████████████████████████████████████████████████████
███████████████████████████                           ███████████████████████████
█████████         █████████                           █████████         █████████
███   ███         ███   ███                           ███   ███         ███   ███
█ █   █ █         █ █   █ █                           █ █   █ █         █ █   █ █

Dual representations – fractional and graphic[edit]

Works with: Python version 3.7
'''A Cantor set generator, and two different
   representations of its output.
'''

from itertools import (islice, chain)
from fractions import Fraction
from functools import (reduce)


# ----------------------- CANTOR SET -----------------------

# 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)]

    return iterate(
        concatMap(go)
    )(
        [(0, 1)]
    )


# 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,
                (' ' * (x - a)) + ('█' * (y - x))
            )
        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))
    )


# 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 go


# 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()
Output:
(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) 

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

QB64[edit]

Translation of: FreeBASIC

Note: Other languages will need to zero out the a() array. In QB64 all arrays are initialized to zero at program start.

_Title "Cantor Set"

Dim Shared As Integer sw, sh, wide, high
sw = 800: sh = 200: wide = 729: high = 7
Dim Shared As Integer a(wide, high)

Screen _NewImage(sw, sh, 8)
Cls , 15: Color 0

Call calc(0, wide, 1)
Call CantorSet

Sleep
System

Sub calc (start As Integer, length As Integer, index As Integer)
    Dim As Integer i, j, newLength
    newLength = length \ 3
    If newLength = 0 Then Exit Sub
    For j = index To high - 1
        For i = start + newLength To start + newLength * 2 - 1
            a(i, j) = 1
        Next
    Next
    Call calc(start, newLength, index + 1)
    Call calc(start + newLength * 2, newLength, index + 1)
End Sub

Sub CantorSet
    Dim As Integer i, j, x, y
    For y = 0 To high - 1
        j = y + 1
        For x = 0 To wide - 1
            i = x + 34
            If a(x, y) = 0 Then Line (i, j * 24 - 5)-(i, j * 24 + 17)
        Next
    Next
End Sub

Quackery[edit]

Using an L-System[edit]

  [ $ "" swap witheach 
      [ nested quackery join ] ] is expand (   $ --> $ )
 
  [ $ "ABA" ]                    is A      (   $ --> $ )
 
  [ $ "BBB" ]                    is B      (   $ --> $ )
  
  [ char A = iff
      [ char q ] else space
    swap of echo$ ]              is draw   ( n c --> $ )
 
  81 $ "A"
  5 times
    [ dup witheach
        [ dip over draw ]
      cr
      i if
        [ expand
          dip [ 3 / ] ] ]
  2drop
Output:
qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq
qqqqqqqqqqqqqqqqqqqqqqqqqqq                           qqqqqqqqqqqqqqqqqqqqqqqqqqq
qqqqqqqqq         qqqqqqqqq                           qqqqqqqqq         qqqqqqqqq
qqq   qqq         qqq   qqq                           qqq   qqq         qqq   qqq
q q   q q         q q   q q                           q q   q q         q q   q q

R[edit]

Attribution-NonCommercial-ShareAlike 4.0 International, CC BY-NC-SA 4.0 to neonira@gmail.com

cantorSet <- function() {
  depth <- 6L
  cs <- vector('list', depth)
  cs[[1L]] <- c(0, 1)
  for(k in seq_len(depth)) {
    cs[[k + 1L]] <- unlist(sapply(seq_len(length(cs[[k]]) / 2L), function(j) {
      p <- cs[[k]][2L] / 3
      h <- 2L * (j - 1L)
      c(
        cs[[k]][h + 1L] + c(0, p),
        cs[[k]][h + 2L] - c(p, 0)
      )
    }, simplify = FALSE))
  }
  cs
}

cantorSetGraph <- function() {
  cs <- cantorSet()

  u <- unlist(cs)

  df <- data.frame(
    x_start = u[seq_along(u) %% 2L == 1L],
    x_end   = u[seq_along(u) %% 2L == 0L],
    depth   = unlist(lapply(cs, function(e) {
      l <- length(e)
      n <- 0
      while(l > 1) {
        n <- n + 1L
        l <- l / 2
      }
      rep(n, length(e) / 2)
    }))
  )

  require(ggplot2)
  g <- ggplot(df, aes_string(x = 'x_start', y = 'depth')) +
    geom_segment(aes_string(xend = 'x_end', yend = 'depth', size = 3)) +
    scale_y_continuous(trans = "reverse") +
    theme(
      axis.title = element_blank(),
      axis.line = element_blank(),
      axis.text = element_blank(),
      axis.ticks = element_blank(),
      legend.position = 'none',
      aspect.ratio = 1/5
    )

    list(graph = g, data = df, set = cs)
}
Output:

Currently, RosettaCode does not seem to accept image upload anymore. So, you will have to run the program under R or RStudio IDE to get the diagram result.

Racket[edit]

Translation of: 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)))
Output:
*********************************************************************************
***************************                           ***************************
*********         *********                           *********         *********
***   ***         ***   ***                           ***   ***         ***   ***
* *   * *         * *   * *                           * *   * *         * *   * *

Raku[edit]

(formerly Perl 6)

Translation of: 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);
Output:
█████████████████████████████████████████████████████████████████████████████████
███████████████████████████                           ███████████████████████████
█████████         █████████                           █████████         █████████
███   ███         ███   ███                           ███   ███         ███   ███
█ █   █ █         █ █   █ █                           █ █   █ █         █ █   █ █

REXX[edit]

/*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.

output   when using the default size of the terminal width of 100:

(Shown at half size.)

■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■
■■■■■■■■■■■■■■■■■■■■■■■■■■■                           ■■■■■■■■■■■■■■■■■■■■■■■■■■■
■■■■■■■■■         ■■■■■■■■■                           ■■■■■■■■■         ■■■■■■■■■
■■■   ■■■         ■■■   ■■■                           ■■■   ■■■         ■■■   ■■■
■ ■   ■ ■         ■ ■   ■ ■                           ■ ■   ■ ■         ■ ■   ■ ■
output   when using the default size of the terminal width of 250:

(Shown at half size.)

■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■
■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■                                                                                 ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■
■■■■■■■■■■■■■■■■■■■■■■■■■■■                           ■■■■■■■■■■■■■■■■■■■■■■■■■■■                                                                                 ■■■■■■■■■■■■■■■■■■■■■■■■■■■                           ■■■■■■■■■■■■■■■■■■■■■■■■■■■
■■■■■■■■■         ■■■■■■■■■                           ■■■■■■■■■         ■■■■■■■■■                                                                                 ■■■■■■■■■         ■■■■■■■■■                           ■■■■■■■■■         ■■■■■■■■■
■■■   ■■■         ■■■   ■■■                           ■■■   ■■■         ■■■   ■■■                                                                                 ■■■   ■■■         ■■■   ■■■                           ■■■   ■■■         ■■■   ■■■
■ ■   ■ ■         ■ ■   ■ ■                           ■ ■   ■ ■         ■ ■   ■ ■                                                                                 ■ ■   ■ ■         ■ ■   ■ ■                           ■ ■   ■ ■         ■ ■   ■ ■

Ring[edit]

# 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:

Cantor set

Ruby[edit]

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.

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
Output:
█████████████████████████████████████████████████████████████████████████████████
███████████████████████████                           ███████████████████████████
█████████         █████████                           █████████         █████████
███   ███         ███   ███                           ███   ███         ███   ███
█ █   █ █         █ █   █ █                           █ █   █ █         █ █   █ █

Rust[edit]

use convert_base::Convert;
use std::fmt;

struct CantorSet {
    cells: Vec<Vec<bool>>,
}
fn number_to_vec(n: usize) -> Vec<u32> {
    // for the conversion we need the digits in reverse order
    // i.e the least significant digit in the first element of the vector
    n.to_string()
        .chars()
        .rev()
        .map(|c| c.to_digit(10).unwrap())
        .collect()
}

impl CantorSet {
    fn new(lines: usize) -> CantorSet {
        // Convert from base 10- to base 3
        let mut base = Convert::new(10, 3);
        let mut cells: Vec<Vec<bool>> = vec![];

        for line in 0..lines {
            // calculate how many repeating sequence will be in the given line
            let segment_size = 3_usize.pow((lines - line - 1) as u32);
            let segment: Vec<bool> = (0..3_usize.pow(line as u32))
                .map(|n| {
                    let output = base.convert::<u32, u32>(&number_to_vec(n));
                    // return false in case the base 3 number contains at least one "1"
                    // otherwise return true
                    !output.contains(&1)
                })
                .collect();

            // copy the segment "segment_size" time
            let mut accum: Vec<bool> = Vec::with_capacity(segment.len() * segment_size);
            for c in segment.iter() {
                accum.extend(std::iter::repeat(*c).take(segment_size))
            }

            cells.push(accum);
        }

        CantorSet { cells }
    }
}

impl fmt::Display for CantorSet {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        for line in self.cells.iter() {
            for c in line {
                write!(f, "{}", if *c { "█" } else { " " })?
            }
            writeln!(f)?;
        }

        Ok(())
    }
}
fn main() {
    let cs = CantorSet::new(5);
    println!("Cantor set:");
    println!("{}", cs);
}
Output:
Cantor set:
█████████████████████████████████████████████████████████████████████████████████
███████████████████████████                           ███████████████████████████
█████████         █████████                           █████████         █████████
███   ███         ███   ███                           ███   ███         ███   ███
█ █   █ █         █ █   █ █                           █ █   █ █         █ █   █ █

Scala[edit]

Imperative Programming (Q&D)[edit]

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))
}
Output:
See it in running in your browser by (JavaScript)

or by Scastie (JVM).

Functional Programming (Recommended)[edit]

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"))
}
Output:
See it in running in your browser by (JavaScript)

or by Scastie (JVM).

Sidef[edit]

Translation of: Raku
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 }
Output:
█████████████████████████████████████████████████████████████████████████████████
███████████████████████████                           ███████████████████████████
█████████         █████████                           █████████         █████████
███   ███         ███   ███                           ███   ███         ███   ███
█ █   █ █         █ █   █ █                           █ █   █ █         █ █   █ █

Smalltalk[edit]

Works with: GNU Smalltalk

Smalltalk represents Intervals' start and stop values as Fraction, so precision is kept for quilte a while.

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:

#################################################################################
###########################                           ###########################
#########         #########                           #########         #########
###   ###         ###   ###                           ###   ###         ###   ###
# #   # #         # #   # #                           # #   # #         # #   # #

Visual Basic .NET[edit]

Translation of: C#
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
Output:
*********************************************************************************
***************************                           ***************************
*********         *********                           *********         *********
***   ***         ***   ***                           ***   ***         ***   ***
* *   * *         * *   * *                           * *   * *         * *   * *

Vlang[edit]

Translation of: Go
const (
    width = 81
    height = 5
)
 
fn cantor(mut lines [][]u8, start int, len int, index int) {
    seg := len / 3
    if seg == 0 {
        return
    }
    for i in index.. height {
        for j in start + seg..start + 2 * seg {
            lines[i][j] = ' '[0]
        }
    }
    cantor(mut lines, start, seg, index + 1)
    cantor(mut lines, start + seg * 2, seg, index + 1)
}
 
fn main() {
	mut lines := [][]u8{len:height, init: []u8{len:width, init:'*'[0]}}
    cantor(mut lines, 0, width, 1)
    for line in lines {
        println(line.bytestr())
    }
}
Output:
*********************************************************************************
***************************                           ***************************
*********         *********                           *********         *********
***   ***         ***   ***                           ***   ***         ***   ***
* *   * *         * *   * *                           * *   * *         * *   * *

Wren[edit]

Translation of: Kotlin
var width = 81
var height = 5

var lines = [[]] * height
for (i in 0...height) lines[i] = ["*"] * width

var cantor // recursive so need to declare variable first
cantor = Fn.new { |start, len, index|
    var seg = (len/3).floor
    if (seg == 0) return
    for (i in index...height) {
        for (j in (start+seg)...(start+seg*2)) lines[i][j] = " "
    }    
    cantor.call(start, seg, index + 1)
    cantor.call(start + seg*2, seg, index + 1)
}

cantor.call(0, width, 1)
for (i in 0...height) System.print(lines[i].join())
Output:
*********************************************************************************
***************************                           ***************************
*********         *********                           *********         *********
***   ***         ***   ***                           ***   ***         ***   ***
* *   * *         * *   * *                           * *   * *         * *   * *

XPL0[edit]

proc Cantor(N, LineSeg, Len);   \Delete middle third of LineSeg
int  N; char LineSeg; int Len, Third, I;
[if N>0 and Len>1 then
    [Third:= Len/3;
    for I:= Third, 2*Third-1 do LineSeg(I):= ^ ;
    Cantor(N-1, LineSeg, Third);
    Cantor(N-1, LineSeg+2*Third, Third);
    ];
];

char LineSeg, N;
[LineSeg:=
"#################################################################################
";
for N:= 0 to 4 do
    [Cantor(N, LineSeg, 81);
    Text(0, LineSeg);
    ];
]
Output:
#################################################################################
###########################                           ###########################
#########         #########                           #########         #########
###   ###         ###   ###                           ###   ###         ###   ###
# #   # #         # #   # #                           # #   # #         # #   # #

zkl[edit]

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");
Output:
█████████████████████████████████████████████████████████████████████████████████
███████████████████████████                           ███████████████████████████
█████████         █████████                           █████████         █████████
███   ███         ███   ███                           ███   ███         ███   ███
█ █   █ █         █ █   █ █                           █ █   █ █         █ █   █ █