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I wanted actually a toy model for 'diffusion' and it's actually derived from problem 23 of "advent of code 2022" which the significantly different 2D version of this. I think it could be even interpreted as a model for phase transitions. I intend to submit the sequence for a certain infinite starting string to oeis (usind decimal encoding for the sequence elements.
Thank you for trying! That seems not to work: dat={1,1,1,0,0,0}; dat /. rules; dat /. rules yields in the first and second iteration both times: {1,1,0,1,0,0}, while it should give {1,0,1,1,0,0} for the second round of rules.
