Cellular Automata in Hyperbolic Space

[CARuler]

In hyperbolic space, it is possible for a moving replicator to replicate endlessly without interfering with itself.

yes, in fact there are now 2 examples of this behaviour
example1:

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B2aho/S1ho2a X X0a X1a

example2:

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B2ampx3m/S0a3c X3a X0 X1a

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edit:
i don't think all of these work as symmetries

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permute (OT)
rotate37 (minimum symmetry)
rotate37reflectx (reflect on hexagons only) might not work (MNW)
rotate37reflectp (reflect on heptagons only) MNW
rotate37reflect (isotropic)
rotate67 (psuedo symmetry)
rotate67reflectx MNW
rotate67reflectp MNW
rotate67reflect