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Phase transitions
The discrete transitions shown in cellular automata in this section are examples of general phenomena known in physics as phase transitions. … Boiling and melting are both examples of first-order transitions, as is the phenomenon shown in the cellular automaton in the main text.
The first picture shows the diffusion equation, which can be viewed as a limiting case of the continuous cellular automaton on page 156 .
The rule 30 cellular automaton provides a particularly clear and good example of intrinsic randomness generation.
As a very simple idealization of biological evolution, one can consider a sequence of cellular automaton programs in which each successive program is obtained from the previous one by a random mutation that adds or modifies a single element.
But which specific cellular automaton rule will any given mollusc use?
In an array of cells like in a cellular automaton each cell is always assigned some definite position.
For certainly a system like a typical cellular automaton does not—since for example its effective rules for evolution at different angles will usually be quite different.
As one example, the pictures on the facing page were all generated by starting from a single black cell and then applying very simple two-dimensional cellular automaton rules.
starting with a single black cell and then applying a simple two-dimensional cellular automaton rule 250 times.
Indeed, as it happens, every single one of the pictures on the facing page can for example be generated from very short cellular automaton programs.