3 citations · 8 across the 9 of their papers we have counts for
6 papers · 2 filters
Prevalence of Odometers in Cellular Automata
Ethan M. Coven, Marcus Pivato, Reem Yassawi +1
We consider a left permutive cellular automaton Phi, with no memory and positive anticipation, defined on the space of all doubly infinite sequences with entries from a finite alph…
Algebraic invariants for crystallographic defects in cellular automata
Marcus Pivato
Let L:= Z^D be the D-dimensional lattice and let A^L be the Cantor space of L-indexed configurations in some finite alphabet A, with the natural L-action by shifts. A `cellular aut…
Spectral domain boundaries in cellular automata
Marcus Pivato
Let L:=Z^D be a D-dimensional lattice. Let A^L be the Cantor space of L-indexed configurations in a finite alphabet A, with the natural L-action by shifts. A `cellular automaton' i…
Defect Particle Kinematics in One-Dimensional Cellular Automata
Marcus Pivato
Let A^Z be the Cantor space of bi-infinite sequences in a finite alphabet A, and let sigma be the shift map on A^Z. A `cellular automaton' is a continuous, sigma-commuting self-map…
Cellular Automata vs. Quasisturmian Shifts
Marcus Pivato
If L=Z^D and A is a finite set, then A^L is a compact space. A cellular automaton (CA) is a continuous transformation F:A^L--> A^L that commutes with all shift maps. A quasisturmia…
RealLife: the continuum limit of Larger Than Life cellular automata
Marcus Pivato
Let A:={0,1}. A `cellular automaton' (CA) is a shift-commuting transformation of A^{Z^D} determined by a local rule. Likewise, a `Euclidean automaton' is a shift-commuting transfor…