File:Byl loop animation.gif

Byl_loop_animation.gif (300 × 300 pixels, file size: 866 KB, MIME type: image/gif, looped, 250 frames, 25 s)

Summary

Description
English: Byl's loop: animation example
Date
Source Own work
Author Claudio Rocchini

Some notes

I used GIMP for gif creation.

I used the Byl's original paper (Self-Reproduction in small cellular automata), but the table II seems to miss the rule: 31523 -> 1.

Source Code

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <memory.h>
#include <algorithm>

/* (C)2017 Claudio Rocchini */

/* From:
   John Byl (1989), "Self-Reproduction in Small Cellular Automata", Physica D, 34: 295–299,
   doi:10.1016/0167-2789(89)90242-X
*/

struct by_rule2 { const char * i; const char o; };

const by_rule2 by_rule2s[]= {
	{ "00003", '1' }, { "00012", '2' }, { "00013", '1' }, { "00015", '2' }, { "00025", '5' },
	{ "00031", '5' }, { "00032", '3' }, { "00042", '2' }, { "0****", '0' },
	{ "10000", '0' }, { "10001", '0' }, { "10003", '3' }, { "10004", '0' }, { "10033", '0' },
	{ "10043", '1' }, { "10321", '3' }, { "11253", '1' }, { "12453", '3' }, { "1****", '4' },
	{ "20000", '0' }, { "20015", '5' }, { "20022", '0' }, { "20202", '0' }, { "20215", '5' },
	{ "20235", '3' }, { "20252", '5' }, { "2****", '2' },
	{ "30001", '0' }, { "30003", '0' }, { "30011", '0' }, { "30012", '1' }, { "30121", '1' },
	{ "30123", '1' }, { "31122", '1' }, { "31123", '1' }, { "31215", '1' }, { "31223", '1' },
	{ "31233", '1' }, { "31235", '5' }, { "31432", '1' }, { "31452", '5' },
	{ "31523", '1' }, /* Note: this rule is missing in the original paper (?) */
	{ "3****", '3' },
	{ "40003", '5' }, { "40043", '4' }, { "40212", '4' }, { "50222", '0' }, { "40232", '4' },
	{ "40242", '4' }, { "40252", '0' }, { "40325", '5' }, { "4****", '3' },
	{ "50022", '5' }, { "50032", '5' }, { "50212", '4' }, { "50322", '0' }, { "5****", '2' },
	{ "*****", 'x' }  /* Special end rule marker */
};

static const char byl_init2[4][4] = {	/* Initial configuration */
	{ '0','2','5','0' },
	{ '2','3','4','2' },
	{ '2','3','1','2' },
	{ '0','2','2','0' },
};

void byl_loop() {
	const int N = 50;	/* Grid size */
	char mat[N][N]; char ma2[N][N];
	int i, j;
	for (i = 0; i < N; ++i) for (j = 0; j < N; ++j) mat[i][j] = '0';
	for (i = 0; i < 4; ++i) for (j = 0; j < 4; ++j) mat[i+(N-4)/2][j+ (N - 4) / 2] = byl_init2[i][j];
	const int SS = 6;	/* Magnify factor */

	unsigned char * img = new unsigned char[SS*N*SS*N * 3];
	const uint8_t colors[8][3] = {	/* The palette */
		{0,0,0}, {255,0,0}, {0,224,0}, {0,0,255},
		{255,255,0}, {255,0,255}, {32,32,32}, {255,255,255}
	};

	for (int s = 0; s < 250; ++s) {
		memset(img, 32, SS*N*SS*N * 3);		/* Generate the image */
		for (i = 0; i < N; ++i) {
			for (j = 0; j < N; ++j) {
				const unsigned char * c = colors[mat[N - 1 - i][j] - '0'];
				for(int y=0; y<SS-1; ++y) for(int x=0; x<SS-1; ++x)
					memcpy(img + 3*(x+j*SS+(SS*N)*(y+i*SS)), c, 3);
			}
		}
		char name[256]; sprintf(name, "byl%03d.ppm", s);
		FILE * f2 = fopen(name, "wb");
		fprintf(f2, "P6\n%d %d\n255\n", N*SS, N*SS); fwrite(img, 1, SS*N*SS*N * 3, f2);
		fclose(f2);

		for (i = 0; i < N; ++i) for (j = 0; j < N; ++j) {
			char se[5];
			se[0] = mat[i][j];
			se[1] = i == 0     ? '0' : mat[i-1][j];
			se[2] = j == N - 1 ? '0' : mat[i][j + 1];
			se[3] = i == N - 1 ? '0' : mat[i+1][j];
			se[4] = j == 0     ? '0' : mat[i][j - 1];

			const by_rule2 * k = 0;
			for (k = by_rule2s; ; ++k) {
				if (k->i[0] != '*' && k->i[0] != se[0]) continue; /* bad rule header */
				char t[4];		/* The rule match also for circula shifs ... */
				memcpy(t, k->i + 1, 4);
				bool found = false;
				for(int q=0; q<4; ++q) {
					int l; for (l = 0; l < 4; ++l) if (t[l] != '*' && t[l] != se[l + 1]) break;
					if (l == 4) { found = true;  break; }
					char t1 = t[0]; t[0] = t[1]; t[1] = t[2]; t[2] = t[3]; t[3] = t1;
				}
				if (found) break;
			}
			ma2[i][j] = k->o;
		}
		for (i = 0; i < N; ++i) for (j = 0; j < N; ++j) mat[i][j] = ma2[i][j];	/* Swith the matrix */
	}
	delete[] img;
}

int main() {
	byl_loop();
    return 0;
}

Licensing

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w:en:Creative Commons
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