A higher-order non-uniform cellular automata algorithm is introduced for translationally invariant Euclidean and hyperbolic lattices, demonstrated on the {5,4} lattice to generate subsystem symmetry-protected topological states and simulate directed percolation.
∞X k=0 ykrk(x) + ∞X k=n ykrk(x) + n−1X k=0 yk˜rk(x) # =x −iy−j
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Universal Design and Physical Applications of Non-Uniform Cellular Automata on Translationally Invariant Lattices
A higher-order non-uniform cellular automata algorithm is introduced for translationally invariant Euclidean and hyperbolic lattices, demonstrated on the {5,4} lattice to generate subsystem symmetry-protected topological states and simulate directed percolation.