Langton's ant
Langton's ant models an ant sitting on a plane of cells, all of which are white initially, facing in one of four directions. Each cell can either be black or white. The ant moves according to the color of the cell it is currently sitting in, with the following rules:
- If the cell is black, it changes to white and the ant turns left;
- If the cell is white, it changes to black and the ant turns right;
- The Ant then moves forward to the next cell, and repeat from step 1.
This rather simple ruleset leads to an initially chaotic movement pattern, and after about 10000 steps, a cycle appears where the ant moves steadily away from the starting location in a diagonal corridor about 10 pixels wide. Conceptually the ant can then travel to infinitely far away.
For this task, start the ant near the center of a 100 by 100 field of cells, which is about big enough to contain the initial chaotic part of the movement. Follow the movement rules for the ant, terminate when it moves out of the region, and show the cell colors it leaves behind.
The problem has received some analysis, for more details, please take a look at the Wikipedia article.
C
Requires ANSI terminal. <lang c>#include <stdio.h>
- include <stdlib.h>
- include <string.h>
- include <unistd.h>
int w = 0, h = 0; unsigned char *pix;
void refresh(int x, int y) { int i, j, k; printf("\033[H"); for (i = k = 0; i < h; putchar('\n'), i++) for (j = 0; j < w; j++, k++) putchar(pix[k] ? '#' : ' '); }
void walk() { int dx = 0, dy = 1, i, k; int x = w / 2, y = h / 2;
pix = calloc(1, w * h); printf("\033[H\033[J");
while (1) { i = (y * w + x); if (pix[i]) k = dx, dx = -dy, dy = k; else k = dy, dy = -dx, dx = k;
pix[i] = !pix[i]; printf("\033[%d;%dH%c", y + 1, x + 1, pix[i] ? '#' : ' ');
x += dx, y += dy;
k = 0; if (x < 0) { memmove(pix + 1, pix, w * h - 1); for (i = 0; i < w * h; i += w) pix[i] = 0; x++, k = 1; } else if (x >= w) { memmove(pix, pix + 1, w * h - 1); for (i = w-1; i < w * h; i += w) pix[i] = 0; x--, k = 1; }
if (y >= h) { memmove(pix, pix + w, w * (h - 1)); memset(pix + w * (h - 1), 0, w); y--, k = 1; } else if (y < 0) { memmove(pix + w, pix, w * (h - 1)); memset(pix, 0, w); y++, k = 1; } if (k) refresh(x, y); printf("\033[%d;%dH\033[31m@\033[m", y + 1, x + 1);
fflush(stdout); usleep(10000); } }
int main(int c, char **v) { if (c > 1) w = atoi(v[1]); if (c > 2) h = atoi(v[2]); if (w < 40) w = 40; if (h < 25) h = 25;
walk(); return 0; }</lang>
D
A basic textual version. <lang D>import std.stdio, std.algorithm, std.traits;
enum Direction { up, right, down, left } enum Turn : bool { left = false, right = true } enum Color : char { white = '.', black = '#' }
void main() {
enum width = 75, height = 52; enum nsteps = 12_000;
auto M = new Color[][](height, width); int x = width / 2; int y = height / 2; auto dir = Direction.up;
for (int i = 0; i < nsteps && x >= 0 && y >= 0 && x < width && y < height; i++) { immutable turn = M[y][x] == Color.black ? Turn.left : Turn.right; M[y][x] = M[y][x] == Color.black ? Color.white : Color.black;
immutable d = (4 + dir + (turn == Turn.right ? 1 : -1)) % 4; dir = [EnumMembers!Direction][d]; final switch(dir) { case Direction.up: y--; break; case Direction.right: x--; break; case Direction.down: y++; break; case Direction.left: x++; break; } }
foreach (row; M) writeln(cast(char[])row);
}</lang> Output:
........................................................................... ........................................................................... ........................................................................... ........................................................................... ..........................##..############..##............................. .........................##..#..........####..#............................ ........................#.##............##...###........................... ........................#....#..#.........#..#.#........................... ......................#.......###.........#.#.##..##....................... ......................###..##.##.....#.....#...#..#.###.................... ..................##..##.#..#.#...##.####.##..###..#.#..................... .................###...###.....#.#.###..##.#..##.###.#..................... ................#.#.#.###...#..####..#.#.#####...#.....#................... ................#...#.###.#.######.##.##..####.#...##.###.................. .................##.###.#####...#.##.##.##.#.#.##.#.###.#.................. ...............##.#....####..#.#...#...###.##.#...#.#...................... ..............##.....#.##.....##..#...##.##.........#..#................... .............#.##..##.###...#.....##..#..###.##.#.#...###.................. .............#...####.##..#....#..###...##.##...##..###..#................. ..............#.....#..###.##.#..##.####.#.#..#.#...#...###................ ............##..#..#.##.###......#..###.#..#....##.#..###..#............... ...........#...##.####..####.#####..##..##.#.##.#.....#...###.............. ..........#...#....#.#.#...##......##.#.#.###.#..#.#.#..###..#............. ..........#......#...####.####.......##...#.##..###.##..#...###............ ...........#....#....#..####..#.###########..##...#..#.#..###..#........... ...........##..#....##..#..#########..##..####.#......##..#...###.......... ..........#.####..##.#..#...###.###.##.##...##.#..##...#.#..###..#......... ..........#...##...###.###....#.#.##.#.##.######.#..#...##..#...###........ ...........#...##....#.##..#.#.....#####.#.#####.....#...#.#..###..#....... ...........#..#..#.##..#..#...#.#..##.#####.##.#.....#....##..#...###...... ...........##...##########...##.#####..#.####...#....#.....#.#..###..#..... ...............##.####.##...#..####...#..#...##...##.#......##..#...###.... .............#.#..#..#..#.#....#...#.##...##..#.#####........#.#..###..#... .............##..##..#..##.#.#.##.##....#.#.#.##..##..........##..#...###.. .............#.####..##.#.#.########.#....#..#.................#.#..###..#. .............#.##..#..#...##.##.......#...#..#..................##..#...### .............####.##...##..##..#......#..#..#....................#.#..##... ............###.#...#....##..##.......#...##......................##..#..## ............####.###.####....####..##.#............................#.#.#.#. ...........#..#.#.##.#..##....####..##..............................##.#### ..........#####.##.###.##....##....##................................#.##.# ..........####..#.##.#................................................####. ..........##.##.##.....................................................##.. ................##......................................................... ........#.####..##.#....................................................... ........###..###.#..#...................................................... .........#..#..#.##.#...................................................... ..........##......##....................................................... .................##........................................................ ........................................................................... ........................................................................... ...........................................................................
Icon and Unicon
<lang Icon>link graphics,printf
procedure main(A)
e := ( 0 < integer(\A[1])) | 100 # 100 or whole number from command line LangtonsAnt(e)
end
record antrec(x,y,nesw)
procedure LangtonsAnt(e)
size := sprintf("size=%d,%d",e,e) label := sprintf("Langton's Ant %dx%d [%d]",e,e,0) &window := open(label,"g","bg=white",size) | stop("Unable to open window")
ant := antrec(e/2,e/2,?4%4) board := list(e) every !board := list(e,"w") k := 0 repeat { k +:= 1 WAttrib("fg=red") DrawPoint(ant.x,ant.y) cell := board[ant.x,ant.y] if cell == "w" then { # white cell WAttrib("fg=black") ant.nesw := (ant.nesw + 1) % 4 # . turn right } else { # black cell WAttrib( "fg=white") ant.nesw := (ant.nesw + 3) % 4 # . turn left = 3 x right } board[ant.x,ant.y] := map(cell,"wb","bw") # flip colour DrawPoint(ant.x,ant.y) case ant.nesw of { # go 0: ant.y -:= 1 # . north 1: ant.x +:= 1 # . east 2: ant.y +:= 1 # . south 3: ant.x -:= 1 # . west } if 0 < ant.x <= e & 0 < ant.y <= e then next else break } printf("Langton's Ant exited the field after %d rounds.\n",k) label := sprintf("label=Langton's Ant %dx%d [%d]",e,e,k) WAttrib(label) WDone()
end</lang>
printf.icn provides formatting graphics.icn provides graphics support (WDone)
PicoLisp
This code pipes a PBM into ImageMagick's "display" to show the result: <lang PicoLisp>(de ant (Width Height X Y)
(let (Field (make (do Height (link (need Width)))) Dir 0) (until (or (le0 X) (le0 Y) (> X Width) (> Y Height)) (let Cell (nth Field X Y) (setq Dir (% (+ (if (car Cell) 1 3) Dir) 4)) (set Cell (not (car Cell))) (case Dir (0 (inc 'X)) (1 (inc 'Y)) (2 (dec 'X)) (3 (dec 'Y)) ) ) ) (prinl "P1") (prinl Width " " Height) (for Row Field (prinl (mapcar '[(X) (if X 1 0)] Row)) ) ) )
(out '(display -) (ant 100 100 50 50)) (bye) </lang>
Processing
Processing implementation, this uses two notable features of Processing, first of all, the animation is calculated with the draw() loop, second the drawing on the screen is also used to represent the actual state.
<lang processing>/*
* we use the following conventions: * directions 0: up, 1: right, 2: down: 3: left * * pixel white: true, black: false * * turn right: true, left: false * */
// number of iteration steps per frame // set this to 1 to see a slow animation of each // step or to 10 or 100 for a faster animation
final int STEP=100;
int x; int y; int direction;
void setup() {
// 100x100 is large enough to show the // corridor after about 10000 cycles size(100, 100, P2D);
background(#ffffff);
x=width/2; y=height/2;
direction=0;
}
int count=0;
void draw() {
for(int i=0;i<STEP;i++) { count++; boolean pix=get(x,y)!=-1; setBool(x,y,pix); turn(pix); move(); if(x<0||y<0||x>=width||y>=height) { println("finished"); noLoop(); break; } } if(count%1000==0) { println("iteration "+count); }
}
void move() {
switch(direction) { case 0: y--; break; case 1: x++; break; case 2: y++; break; case 3: x--; break; }
}
void turn(boolean rightleft) {
direction+=rightleft?1:-1; if(direction==-1) direction=3; if(direction==4) direction=0;
}
void setBool(int x, int y, boolean white) {
set(x,y,white?#ffffff:#000000);
}</lang>
Python
<lang python>width = 75 height = 52 nsteps = 12000
class Dir: up, right, down, left = range(4) class Turn: left, right = False, True class Color: white, black = '.', '#' M = [[Color.white] * width for _ in xrange(height)]
x = width // 2 y = height // 2 dir = Dir.up
i = 0 while i < nsteps and 0 <= x < width and 0 <= y < height:
turn = Turn.left if M[y][x] == Color.black else Turn.right M[y][x] = Color.white if M[y][x] == Color.black else Color.black
dir = (4 + dir + (1 if turn else -1)) % 4 dir = [Dir.up, Dir.right, Dir.down, Dir.left][dir] if dir == Dir.up: y -= 1 elif dir == Dir.right: x -= 1 elif dir == Dir.down: y += 1 elif dir == Dir.left: x += 1 else: assert False i += 1
print "\n".join("".join(row) for row in M)</lang> The output is the same as the basic D version.
Ruby
<lang ruby>class Ant
Directions = [:north, :east, :south, :west]
def initialize(plane, pos_x, pos_y) @plane = plane @position = Position.new(plane, pos_x, pos_y) @direction = :south end attr_reader :plane, :direction, :position
def run moves = 0 loop do begin if $DEBUG and moves % 100 == 0 system "clear" puts "%5d %s" % [moves, position] puts plane end moves += 1 move rescue OutOfBoundsException break end end moves end
def move plane.at(position).toggle_colour position.advance(direction) if plane.at(position).white? turn(:right) else turn(:left) end end
def turn(left_or_right) idx = Directions.index(direction) case left_or_right when :left then @direction = Directions[(idx - 1) % Directions.length] when :right then @direction = Directions[(idx + 1) % Directions.length] end end
end
class Plane
def initialize(x, y) @x = x @y = y @cells = Array.new(y) {Array.new(x) {Cell.new}} end attr_reader :x, :y
def at(position) @cells[position.y][position.x] end
def to_s @cells.inject("") do |output, row| column = row.inject("") {|col, cell| col + (cell.white? ? "." : "#")} output += column + "\n" end end
end
class Cell
def initialize @colour = :white end attr_reader :colour
def white? colour == :white end
def toggle_colour @colour = (white? ? :black : :white) end
end
class Position
def initialize(plane, x, y) @plane = plane @x = x @y = y check_bounds end attr_accessor :x, :y
def advance(direction) case direction when :north then @y -= 1 when :east then @x += 1 when :south then @y += 1 when :west then @x -= 1 end check_bounds end
def check_bounds unless (0 <= @x and @x < @plane.x) and (0 <= @y and @y < @plane.y) raise OutOfBoundsException, to_s end end
def to_s "(%d, %d)" % [x, y] end
end
class OutOfBoundsException < StandardError; end
- the simulation
ant = Ant.new(Plane.new(100, 100), 50, 50) moves = ant.run puts "out of bounds after #{moves} moves: #{ant.position}" puts ant.plane</lang>
output
out of bounds after 11669 moves: (26, -1) ..........................#.#....................................................................... ........................##.#.#...................................................................... .......................#.###.##..................................................................... ......................####.###.#.................................................................... ......................#####.#..##................................................................... .......................#...##.##.#.................................................................. ........................###...#..##................................................................. .........................#...##.##.#................................................................ ..........................###...#..##............................................................... ...........................#...##.##.#.............................................................. ............................###...#..##............................................................. .............................#...##.##.#............................................................ ..............................###...#..##........................................................... ...............................#...##.##.#.......................................................... ................................###...#..##......................................................... .................................#...##.##.#........................................................ ..................................###...#..##....................................................... ...................................#...##.##.#...................................................... ....................................###...#..##..................................................... .....................................#...##.##.#.................................................... ......................................###...#..##................................................... .......................................#...##.##.#.................................................. ........................................###...#..##................................................. .........................................#...##.##.#................................................ ..........................................###...#..##............................................... ...........................................#...##.##.#.............................................. ............................................###...#..##............................................. 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...........................................###....#...#.#......#.##.#............................... ...........................................###....#.##.....#.##..#.##............................... ............................................#....#...##.#.#.....##.................................. ............................................#.#......#.#####..#...#................................. ...........................................#...#####..........##.######............................. ...........................................###..##..#.##.#.#.#...##.#.##............................ .........................................##..#.#######.#...#..###....##.#........................... ........................................#..#..######.##...#..#.##...#...#........................... .......................................#....#.#.##.#..######.#######...#............................ .......................................#.####.##.#.####....##..##.#.##.#............................ ........................................#....####...#..#.######.##....###........................... ...........................................#...#.##.#.###.#..##..##...###........................... ..............................................#######....#..##.##.#.....#........................... ......................................####..##.##..####.##.##.##..#.....#........................... .....................................#....#.#...###.##.###....#.####....#........................... ....................................###.......###.#.#.#####....#.#......#........................... ....................................#.#...###.####.##.#...##.###.##.....#........................... ..........................................##.##..####....####.#.#.#.....#........................... .....................................#....#..##...###..###.....###......#........................... .....................................##...##.###.####..#......###...##..#........................... .....................................##.#.####.....#...#..#.##.###.##...#........................... ....................................####.##...##.####..#.#..#..#..###...#........................... ....................................#.##.###..#.#.##.#.#.....#.#.....#.#............................ ........................................#.#..#....##.##..#.#..###.##................................ ........................................##.#....#..#####.#....#....#..#.#........................... .......................................#.##.#..#....##.##.#..###......###........................... .....................................#.#...#..#..#..#..###...##..##....#............................ ....................................###.#.#####.######.###.#######.#.##............................. ....................................#.#.#....#####...##..#####.#####................................ ......................................#..##...#......#..#.##..###.###............................... ...................................####...#####.#########...#.#..................................... ..............................##....#..#.....###.#.#...#.###..###................................... .............................#..#..####.##...###.##...###.##.....##................................. ............................###....#.##.#.#####...#....#..#..##.###................................. ............................#.#####.#.#...##..##.....#....#...#..#.................................. ................................######.####..##.#...#..##..#.#.##................................... 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