LPpatterned

LPpatterned is a method in computational design that uses linear programming to generate repeatable patterns under predefined constraints. It treats a design space as a set of decision variables and seeks an arrangement that optimizes a chosen objective while satisfying structural rules. The approach is often applied to grid-based tilings, textiles, and digital art, where reproducibility and scalability are important.

In LPpatterned, the pattern is encoded as variables representing tile types or color values on a lattice. Constraints can enforce symmetry, density of elements, color balance, minimum spacing, or boundary conditions. An objective function, such as minimizing color variance or maximizing tiling efficiency, guides the solution toward aesthetically coherent results. The solution is exact for the linear program and can be computed efficiently for large grids using standard solvers.

Common domains for LPpatterned include textile fabrication, where families of motifs can be produced by adjusting parameters; architectural facades and interior surfaces where repeatable panels are desirable; and generative art, where designers explore parameter spaces to produce varied outputs.

Advantages of LPpatterned include reproducibility, fast parameter studies, and the ability to integrate multiple constraints. Limitations include potential restriction to linear relationships, which can limit some nonlinear aesthetic effects; dependence on solver performance; and the need for designers to translate subjective goals into formal constraints.

The concept grew from research in constraint-based design and optimization in the 2010s, with implementations in CAD and design automation tools. It is often complemented by nonlinear or heuristic methods to expand creative possibilities.