Motivated by questions in mathematical logic and in part by work on simulation games by Ulam, among others, John Conway began doing experiments in 1968 with a variety of different two-dimensional cellular automaton rules. Conway's initial goal was to define an interesting and unpredictable cell automaton. As a result, in 1970 the mathematician John Conway introduced his aforementioned Life game, arguably the most popular automaton ever, and one of the simplest computational models ever proved to be a universal computer. It was viewed as a largely recreational topic, and little follow-up work was done outside of investigating the particularities of the Game of Life and a few related rules in the early 1970s.

Stephen Wolfram’s works in the 1980s contributed to putting the growing community of CA followers on the scientific map. In a series of papers, Wolfram extensively explored one-dimensional CA, providing the first qualitative taxonomy of their behavior and laying the groundwork for further research. A particular transition rule for one-dimensional CA, known as Rule 110, was conjectured to be universal by Wolfram. Some twenty years after the conjecture, Matthew Cook proved that Rule 110 is capable of universal computation. In 2002 Wolfram published a 1280-page text 'A New Kind Of Science', which extensively argues that the discoveries about cellular automata are not isolated facts but are robust and have significance for all disciplines of science.