Some small-scale structure is visible, but on a larger scale the pattern seems for all practical purposes random.

But even after all these steps there are no signs of overall regularity—and indeed even continuing for a million steps many aspects of the pattern obtained seem perfectly random according to standard mathematical and statistical tests.

It starts with all cells white, corresponding to a blank tape.

But all of these patterns in a sense have the same basic form in every direction. … In all cases the evolution starts from the same random initial condition, and is continued until it stabilizes.

And does it really apply to all of the various kinds of systems that we see in nature? … Indeed, almost all of the detailed applications ever made of the full Second Law have been concerned with just one specific area: the behavior of gases.

[No text on this page] The behavior of all 256 possible cellular automata with rules involving two colors and nearest neighbors.

[No text on this page] The behavior of all 256 possible cellular automata with rules involving two colors and nearest neighbors.

[No text on this page] Responses to a smaller version of the image from page 578 by cells sensitive to all 16 possible 2×2 blocks, as well as their repetitive 3×3 extensions.

Throughout all this, however, I had continued to investigate more basic questions, and by around 1985 I was beginning to realize that what I had seen before was just a hint of something still much more dramatic and fundamental. … But by 1986 I had realized that with a number of new ideas I had it would be possible to build a single coherent system for doing all kinds of technical computing. … And equipped with Mathematica I began to try all sorts of new experiments.

Doing this certainly required experience in all sorts of different areas of science. … And the fact that I had managed to make this work so many times in Mathematica was part of what gave me the confidence to try doing something similar in all sorts of areas of science. … But I had no idea just how important it would all ultimately turn out to be.