To build an intuition about how genes code for an organism, one may visualize that DNA is an operating system within each cell, which can only divide, differentiate, regulate or die. Individual genes can be thought of as rules for a cellular automaton on an emergent 3D lattice.
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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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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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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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