E Jen, Exact solvability and quasiperiodicity of one-dimensional cellular automata, Nonlinearity, 4(2):251, (1991)  Home/Search   Document Not in Database   Summary   Related Articles   Check

....s tending to infinity. Background. Study of the topology of the state transition graphs of cellular automata in finite geometries has been largely limited to numerical work. However, some analytical results concerning the set of temporal cycles have been obtained in a sequence of papers by Jen [23, 24, 25] for some large classes of rules, and for various rules with special characteristics e.g. 29] In addition, McIntosh [30] has collected a variety of mathematical techniques, which serve, for example, to count one time step preimages of small configurations. Published numerical work on ....

E Jen, Exact solvability and quasiperiodicity of one-dimensional cellular automata, Nonlinearity, 4(2):251, (1991)

.... 001 000 a 0 i : 0 0 0 1 0 0 1 0 Blocking pairs of sites together gives the algebra ffl 00 01 10 11 00 00 01 10 10 01 01 00 00 00 10 10 11 00 00 11 01 00 00 00 The subalgebras f00; 01g and f00; 10g form two domains on which the CA acts like Z 2 , and defects between them annihilate in pairs [8, 13, 17]. If it weren t for the product 10ffl01 = 11, the set f00; 01; 10g would form a subalgebra isomorphic to (with 00 = 0, 01 = 1, and 10 = 1 0 ) and 11 would not appear after the first time step. However, if we choose initial conditions with a single defect, and choose the phase of ....

E. Jen, "Exact solvability and quasiperiodicity of one-dimensional cellular automata." Nonlinearity 4 (1990) 251.

..... The difference in size between lattices in this set grows exponentially; we call such sets sparse . We chose the subset Nwc = f22; 46; 94; 190; 382; 766g. 2. Winding number = 0. The winding number is the rotation rate of spatial patterns on temporally periodic orbits of a finite lattice. [12] Since the nonattracted orbits in the vicinity are all temporally periodic, we initially hypothesized that the winding number might affect the statistics of vicinity convergence. Of the lattices with = 0 we chose the subset N 2 f20; 24; 36g. 3. Winding number = 1: N 2 f14; 31; 42g. In ....

E. Jen. Exact solvability and quasiperiodicity of one-dimensional cellular automata. Nonlinearity, 4:251, 1990.

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