Zhegalkin Zebra Motives Digital Recordings of Mirror Symmetry

TL;DR

This paper explores Zhegalkin zebra motives, a class of plane tilings by black and white polygons linked to ${ m f F}_2$-valued functions, revealing their geometric structure and potential for visualizing complex mathematical and physical concepts.

Contribution

It introduces a general theoretical framework for Zhegalkin zebra motives and provides initial explicit examples, paving the way for further detailed exploration.

Findings

Zhegalkin zebra motives form a rich geometric structure.

They serve as insightful visualizations for topics in physics and mathematics.

Initial examples demonstrate the potential of the theory.

Abstract

Zhegalkin zebra motives are tilings of the plane by black and white polygons representing certain ${\mathbb F}_2$-valued functions on ${\mathbb R}^2$. They exhibit a rich geometric structure and provide easy to draw insightful visualizations of many topics in the physics and mathematics literature. The present paper gives some pieces of a general theory and a few explicit examples. Many more examples will be shown in the forthcoming article "Zhegalkin zebra motives: algebra and geometry in black and white".