But in the development of this language I had seen rather clearly how just a few primitive operations that I had come up with could end up successfully covering a vast range of sophisticated computational tasks. So I thought that perhaps I could do something similar in natural science: that there might be some appropriate primitives that I could find that would successfully capture a vast range of natural phenomena.

Two sections from now I will discuss a rather striking potential example of this: if one looks at molluscs of various types, then it turns out that the range of pigmentation patterns on their shells corresponds remarkably closely with the range of patterns that are produced by simple randomly chosen programs based on cellular automata.

[Meaning in] molecular biology DNA sequences of organisms can be thought of as artifacts created by biological evolution, and current data suggests that they contain some long-range correlations not present in typical random sequences. … Note that the antibodies of the immune system are much like short random proteins—whose range of shapes must be sufficient to match any antigen.

Frequencies of [cellular automaton] classes The pie charts below show results for 1D totalistic cellular automata with k colors and range r .

When growth occurs at a slower rate, a wide range of polygonal and other shapes can be obtained, as illustrated in the main text.

Crushing [of solids] For a rather wide range of cases it appears that in crushed solids such as rocks the probability of a particular fragment having a diameter larger than r is given approximately by r -2.5 .

But also similar cells most likely receive inputs from regions with a range of different sizes on the retina—making even unfamiliar textures seem the same over at least a certain range of scales.

But the discovery in this book that a wide range of systems can generate randomness even with very simple initial conditions makes it seem considerably less surprising.

Distribution of chaotic behavior For iterated maps, unlike for discrete systems such as cellular automata, one can get continuous ranges of rules by varying parameters.

Experiences of modelling Over the course of the past 25 years I have constructed an immense number of models for a wide range of scientific, technical and business purposes.