Representation of Geometric Objects by Color

TL;DR

This paper introduces a novel method of representing complex geometric objects and fractals using color-based actions, enabling visualization and analysis of high-dimensional shapes and infinite-volume fractals.

Contribution

It presents a new approach to representing high-dimensional and fractal geometries through color actions, expanding the scope of geometric visualization.

Findings

Representation of high-dimensional objects using color actions

Visualization of fractals like Cantor dust and Menger sponge

Proposal of a four-dimensional Menger sponge with infinite volume

Abstract

By introducing various actions involving color to geometrical objects, we represent a cube and simplex in four or fewer dimensions, the geometrical net of a cube and simplex in five or fewer dimensions, hyperprisms, truncated polytopes, stellated polytopes, and fractals such as Cantor dust and Menger sponge, and propose the "four-dimensional" Menger sponge whose volume is infinite.