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Existing approaches either rely on hand-written algebraic rules (AM-Parser) or fail to generalize structurally (Transformer-based models). We present an alternative requiring no hand-written compositional rules, based on a neural cellular automaton (NCA) with a discrete bottleneck: all compositional rules are learned from data through local iteration. On the SLOG benchmark, the system achieves an overall accuracy of $67.3 \\pm 0.2\\%$ across 10 seeds (AM-Parser: $70.8 \\pm 4.3\\%$), with 11 of 17 structural generalization categories at $100\\%$ type-exact match, including three where AM-Parser scores $0$--$74\\%$. 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