The grid emerges by adding new lattice locations at positions for new cells. Cells change state as a function of the state of their neighbors and their own state. (It is simplified, because the lattice gets frustrated by nonlocal interaction via hormones and axons etc)
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The automaton rule of the whole CA is your DNA (of which all cells have a copy)
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What about epigenetic modification?
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I think if it as flash memory, i.e. mutable state, whereas the DNA is ROM. Differentiation of cells within an organism is epigenetic, I think. Epigenetic modification is very important within organisms, but not much for inheritance between generations of organisms.
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Recording of local state is going to be mostly epigenetic, for instance via methylation, folding or chemical switches elsewhere in the cell.
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Yes, afaik the sequence of amino acids remains mostly unaffected. But it is not the point: the gene is a largely immutable subroutine, its activation state is a local parameterization.
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I suspect that almost all interactions are local. They are so ubiquitous that we don't think about them: "of course neighboring muscle cells will share a chemical context". Also, local interactions will look more uniform. The non local interactions are sparse, but draw attention.
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