Conway and Aperiodic Tilings

The uploaded paper is an expository tribute that asserts the key claims (planar: at most logarithmic growth due to commutativity; 3D quaquaversal: power-law growth) but does not supply proofs, instead pointing to earlier technical papers. The model’s solution gives a largely sound outline for the planar case and a plausible group-theoretic mechanism for the 3D case, but it relies on a critical, unproven assertion that “every word” in the generators occurs along substitution paths. Without justifying that surjectivity onto all words (or at least onto a free semigroup), the power-law lower bound is not fully established by the model’s text. Hence both are incomplete as presented here.