Polymetric brick wall patterns and two-dimensional substitutions

TL;DR

This paper introduces a rapid method for generating large polymetric brick wall patterns that meet structural and aesthetic constraints, overcoming the computational limitations of previous integer programming approaches.

Contribution

The paper presents an efficient, scalable technique for creating polymetric wall patterns, significantly reducing computation time compared to existing methods.

Findings

Method generates patterns of arbitrary size quickly

Supports complex structural and aesthetic constraints

Outperforms previous integer programming approaches

Abstract

Polymetric walls are walls built from bricks in more than one size. Architects and builders want to built polymetric walls that satisfy certain structural and aesthetical constraints. In a recent paper by de Jong, Vinduska, Hans and Post these problems are solved by integer programming techniques, which can be very time consuming for patterns consisting of more than 40 bricks. Here we give an extremely fast method, generating patterns of arbitrary size.