Golden Mean Subshift Revised

摘要

The authors study subshifts of finite type on (0,1)z2 of the form where in afinite window there is always either one on no 1's present. The problem is converted to a tiling/covering problem on the (nZ)2 lattice and its shifts. In this set-up the authors consider the uniqueness of the equilibrium measure, density of 1's at equilibrium and the topological entropy. Further insight is achieved by realizing that the equilibrium measure is the ground state of an extremely simple probabilistic cellular automation. The study indicates critical behavior in this one parameter class of rules.