Spotlight Tiling

TL;DR

This paper introduces spotlight tiling, a dynamic covering method with elastic-sized tiles and order-dependent placement, analyzing their properties on rectangles and other regions to reveal elegant combinatorial results.

Contribution

It defines and explores the properties of spotlight tilings, a novel dynamic tiling concept with elastic tiles and order significance, expanding tiling theory.

Findings

Distribution of spotlight tilings by size on rectangles

Analysis of direction distribution of spotlights

Extensions to other regions suggest further combinatorial insights

Abstract

This article introduces spotlight tiling, a type of covering which is similar to tiling. The distinguishing aspects of spotlight tiling are that the "tiles" have elastic size, and that the order of placement is significant. Spotlight tilings are decompositions, or coverings, and can be considered dynamic as compared to typical static tiling methods. A thorough examination of spotlight tilings of rectangles is presented, including the distribution of such tilings according to size, and how the directions of the spotlights themselves are distributed. The spotlight tilings of several other regions are studied, and suggest that further analysis of spotlight tilings will continue to yield elegant results and enumerations.