kvadratisen2

Kvadratisen2 is a hypothetical mathematical model used in discussions of two-dimensional discrete dynamical systems. It belongs to a family of square-grid, rule-based frameworks and is presented as a second-generation extension of a simpler kvadratisen concept, emphasizing local interactions on a lattice and multi-layer state evolution.

A kvadratisen2 configuration is defined on a finite square lattice. Each lattice site carries a state taken from a finite alphabet. Time advances in discrete steps, with a transition function that determines a cell’s next state from the current states of cells within a fixed neighborhood. The “2” in kvadratisen2 signals a second-order or two-layer variant, where updates may depend on both the present neighborhood and a representation of the previous time step, enabling memory effects or cross-layer coupling.

Common choices for the neighborhood include four-neighbor (von Neumann) and eight-neighbor (Moore) schemes, though other shapes and radii may be specified. The transition rules can be deterministic or probabilistic, producing complex spatiotemporal patterns from simple local interactions. Depending on the rules, kvadratisen2 systems can exhibit a range of behaviors from stable structures to propagating patterns and chaotic dynamics. They are used in thought experiments, educational demonstrations, and as toy models for exploring questions about computation, pattern formation, and tiling on grids.

Relation to related models includes cellular automata, lattice gas automata, and tiling systems. Kvadratisen2 provides a framework for analyzing how local rules give rise to global structure in a two-dimensional, multi-layer setting.