Stanislaw Ulam also had an interest in the application of math to biology. One example that may have relevance is the subfield of cellular automata founded by von Neumann and Ulam. As an example of this class of problems imagine dividing a plane into a several small squares like a checkerboard with several objects placed in nearby squares. Then specify rules for the appearance of new objects or the disappearance of old objects in new squares depending on whether adjacent squares are occupied or not. With each application of the rules to all the squares, the pattern of occupied squares evolves with time. Depending on the initial configuration and the rules of growth, some computer generated cellular automata evolve into patterns of snowflakes or crystals and others seem to have an everchanging motion as if they are alive. In some cases, colonies of self replicating patterns expand to fill the available space like the growth of coral or bacteria in a petri dish.
Reference: Adventures of a mathematician, S. Ulam, 1991 edition.
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