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(Less formal versions of the idea were also common in ancient Greek times.)
With r = 2 , it appears that if a solution exists, it must have length n + 4 or less.
(With size s coefficients it is for example known that the solutions must always be less than (14 s) 5 s .).
An area less than 2 inches square from inside the letter ρ on the extremely elaborate chi-rho page of the Book of Kells, an illuminated gospel manuscript created over a period of years at various monasteries, probably starting around 800 AD at the Irish monastery on the island of Iona, Scotland.
But I found that active research on what had been called cellular automata had more or less petered out (with the slight exception of a group at MIT at that time mainly concerned with building special-purpose hardware for 2D cellular automata).
The largest m less than 2 16 for which this is true is 65063, and the sequence generated in this case appears to be fairly random.
But few design principles emerged, and the technology for making chips with more elaborate and less uniform circuits developed rapidly.