In the late 1960s, the English mathematician John Conway began experimenting with a strange form of computer known as a cellular automaton. This device consists of a grid of squares that turn black or white depending on the color of the squares around them.
The computation proceeds in rounds. In each round, the automaton updates the color of each square based on the color of its neighbors according to a set of specified rules. The resulting pattern then becomes the starting point for the next round of computation and so on.
Conway found to his surprise that simple rules can produce remarkably complex behaviors. Some patterns even moved across the grid, rather like living things. Conway called his approach the Game of Life and others have since discovered patterns that perform calculations or are even capable of reproducing themselves completely.
That has raised all kinds of questions about how cellular automata can capture the behavior of living things and the way they grow. But while there has been much success in creating two-dimensional patterns, there has been less success in creating 3D shapes.
