Conway’s game of Life is a type of cellular automata. It is simple enough to use on a monochrome display. The game is set on an infinite plane however computer implementations often use a toroidal universe due to memory and display limitations. A torus is simple to understand, roll a sheet of paper into a tube and this shows the idea in one dimension. Connecting the ends of the tube makes the x and y direction continual. A more advanced treatment can be seen with manifolds.

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or n-manifold for short, is a topological space with the property that each point has a neighborhood that is homeomorphic to the Euclidean space of dimension n.

## LIFE RULES

- Any live cell with fewer than two live neighbours dies, as if by underpopulation.
- Any live cell with two or three live neighbours lives on to the next generation.
- Any live cell with more than three live neighbours dies, as if by overpopulation.
- Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.

These rules, which compare the behavior of the automaton to real life, can be condensed into the following:

- Any live cell with two or three live neighbours survives.
- Any dead cell with three live neighbours becomes a live cell.
- All other live cells die in the next generation. Similarly, all other dead cells stay dead.

It should be noted that RAND is a pseudo random number. Random numbers are important in many areas but the designers neglected to address this problem. RAND simply returns a 0 or 1 to handle the rules of Life. This game and many others depend on good random numbers which has been a field of study of its own.

Following the rules it is not too hard to build a game of Life for your mainframe. Many mainframe machines were running the simulation which was a popular diversion from the day today drudgery.

## C VERSION

#include <stdio.h> #include <stdlib.h> #include <unistd.h> #define for_x for (int x = 0; x < w; x++) #define for_y for (int y = 0; y < h; y++) #define for_xy for_x for_y void show(void *u, int w, int h) { int (*univ)[w] = u; printf("\033[H"); for_y { for_x printf(univ[y][x] ? "\033[07m \033[m" : " "); printf("\033[E"); } fflush(stdout); } void evolve(void *u, int w, int h) { unsigned (*univ)[w] = u; unsigned new[h][w]; for_y for_x { int n = 0; for (int y1 = y - 1; y1 <= y + 1; y1++) for (int x1 = x - 1; x1 <= x + 1; x1++) if (univ[(y1 + h) % h][(x1 + w) % w]) n++; if (univ[y][x]) n--; new[y][x] = (n == 3 || (n == 2 && univ[y][x])); } for_y for_x univ[y][x] = new[y][x]; } void game(int w, int h) { unsigned univ[h][w]; for_xy univ[y][x] = rand() < RAND_MAX / 10 ? 1 : 0; while (1) { show(univ, w, h); evolve(univ, w, h); usleep(200000); } } int main(int c, char **v) { int w = 0, h = 0; if (c > 1) w = atoi(v[1]); if (c > 2) h = atoi(v[2]); if (w <= 0) w = 30; if (h <= 0) h = 30; game(w, h); }