Latticeet

Latticeet is a theoretical construct used to model multistate processes on regular lattices. It generalizes cellular automata by allowing a site’s next state to depend on its current state, its neighborhood, and an auxiliary potential that governs transitions. The term is used in mathematical and computational contexts within a fictional or speculative setting to describe pattern formation, phase transitions, and information flow on discrete grids.

In a typical latticeet model, the lattice is finite or infinite and may carry boundary conditions such as periodic or fixed edges. Each lattice site holds a state drawn from a finite alphabet. The local rule computes candidate transitions from the states of neighboring sites, then applies the potential or probabilistic rule to select the actual transition. Variants may incorporate energy-like quantities, stochastic update schemes, or asynchronous updating.

Key properties include symmetry under prescribed lattice groups, the emergence of attractor configurations, and the existence of phase-like regimes distinguished by order parameters. Analyses often employ combinatorial counting, Markov chains, or Monte Carlo sampling to study long-term behavior and complexity.

Applications are mostly theoretical: latticeets are used to explore how local interactions generate global patterns, to compare discrete models with continuum theories, and as teaching tools in courses on discrete dynamics, statistical mechanics, and complex systems. They also serve as a didactic bridge between cellular automata and lattice gas models.

See also: lattice, cellular automaton, percolation theory, spin model, lattice gas.