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    The examples given are surprisingly expressive. Very cool!

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      Very cool!

      First, in multiple dimensions there are no natural ways to insert a string into another string

      Arguably, this is exactly what hypergraph rewriting systems are. These are the systems that Stephen Wolphram, et al., are exploring as a model for basic physics: https://www.wolframphysics.org/

      However, the results are graphs with fractional dimensions, where dimensionality is measured as the asymptotic connectivity of the graph. So if you limit yourself to a fixed number of integers dimensions, then the original claim above is true.