Plattice

Plattice is a term used in several disciplines to describe lattice-like structures that encode ordered relationships or spatial regularity. The exact meaning of plattice is not standardized, and its definition depends on context.

In mathematics, a planar plattice refers to a lattice embedded in the two-dimensional plane. It consists of all integer linear combinations of two linearly independent vectors a and b, yielding points of the form m a + n b with m and n integers. The geometry is governed by the parallelogram spanned by a and b, which serves as the fundamental region. Classic examples include square and hexagonal lattices, which model regular tilings and crystal-like arrangements in two dimensions.

In computer science, a plattice can denote a lattice-based data structure used to represent partially ordered information. The elements are arranged by a partial order, with defined join (least upper bound) and meet (greatest lower bound) operations. This structure supports fixed-point computations in static analysis and abstract interpretation, facilitating orderly combination and comparison of program states or facts. Variants are typically finite and designed to ensure monotonicity, which helps guarantee convergence of iterative analyses.

Across contexts, plattices emphasize the value of algebraic structure for organizing information, whether in space, symmetry, or data flow. They provide a formal framework for combining elements, comparing alternatives, and reasoning about hierarchical relationships. See also lattice theory, planar lattices, and abstract interpretation for related concepts.