Motif Patterns and Coverings of Points with Unit Disks, Part I

TL;DR

This paper explores a lattice-constrained variation of a classic geometric problem, constructing packings of unit disks using motif patterns to analyze point coverings.

Contribution

It introduces a novel approach to packing problems by applying motif patterns within a lattice-constrained setting, extending previous work on dots and coins.

Findings

Constructed specific packings of unit disks on a square lattice.

Developed methods for covering points with motif patterns.

Provided insights into geometric arrangements on lattices.

Abstract

We consider a modification of Winkler's "dots and coins" problem, where we constrain the dots to lie on a square lattice in the plane. We construct packings of "coins" (closed unit disks) using motif patterns.