Tessellations with local transformations

摘要

Local transformations operating in a tessellated n-dimensional space are characterized by conditions of continuity and translation invariance. Nondeterministic as well as deterministic transformations are discussed. Populations of configurations which can be derived from an initial configuration using a nondeterministic transformation are considered and the analogy with linguistics is stressed. The Garden of Eden theorem plus compactness of the product topology is used to obtain the following: It a local transformation is a one-to-one function, it must also be onto and have a local inverse. Infinite as well as finite configurations are allowed in the domain of a local transformation.