Thursday, December 4, 2008

Cellular Automatons

I had a nice giggle at xkcd's bored guy stuck in an infinite desert, and remembered having read about Rule 110 and its universality. So during lunchtime I hacked up a universal universe simulator and scouted for pretty pictures.

Rule 30:

.................X.................
................XXX................
...............XX..X...............
..............XX.XXXX..............
.............XX..X...X.............
............XX.XXXX.XXX............
...........XX..X....X..X...........
..........XX.XXXX..XXXXXX..........
.........XX..X...XXX.....X.........
........XX.XXXX.XX..X...XXX........
.......XX..X....X.XXXX.XX..X.......
......XX.XXXX..XX.X....X.XXXX......
.....XX..X...XXX..XX..XX.X...X.....
....XX.XXXX.XX..XXX.XXX..XX.XXX....
...XX..X....X.XXX...X..XXX..X..X...
..XX.XXXX..XX.X..X.XXXXX..XXXXXXX..


Rule 110, not calculating anything:

.................X..
................XX..
...............XXX..
..............XX.X..
.............XXXXX..
............XX...X..
...........XXX..XX..
..........XX.X.XXX..
.........XXXXXXX.X..
........XX.....XXX..
.......XXX....XX.X..
......XX.X...XXXXX..
.....XXXXX..XX...X..
....XX...X.XXX..XX..
...XXX..XXXX.X.XXX..
..XX.X.XX..XXXXX.X..


And I was most surprised to see a zoomed-in look at a Sierpinski triangle with Rule 18:

.................X.................
................X.X................
...............X...X...............
..............X.X.X.X..............
.............X.......X.............
............X.X.....X.X............
...........X...X...X...X...........
..........X.X.X.X.X.X.X.X..........
.........X...............X.........
........X.X.............X.X........
.......X...X...........X...X.......
......X.X.X.X.........X.X.X.X......
.....X.......X.......X.......X.....
....X.X.....X.X.....X.X.....X.X....
...X...X...X...X...X...X...X...X...
..X.X.X.X.X.X.X.X.X.X.X.X.X.X.X.X..

1 comment:

  1. I shouldn't be surprised, but always am, by how these things remind me of Conway's Game of Life. Each line represents a generation of little cellular automata, breeding away. The "picture" is really a history of the colony (for want of a better word) where the GoL's history would be a right square prism of infinite width, marching tirelessly into the heavens.

    Actually, you know, I think someone rendered just that in OpenCroquet...

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