An Optical Demonstration of Fractal Geometry

TL;DR

This paper presents an optical setup using a Sinai cube and colored light reflections to visually demonstrate and analyze fractal geometry, making the concept more accessible and intuitive.

Contribution

It introduces a novel optical demonstration of fractal geometry using a Sinai cube and ray tracing, combining aesthetic visuals with fractal analysis.

Findings

Images exhibit fractal scaling properties.

Ray tracing models match experimental images.

The demonstration enhances understanding of fractal dimensions.

Abstract

We have built a Sinai cube to illustrate and investigate the scaling properties that result by iterating chaotic trajectories into a well ordered system. We allow red, green and blue light to reflect off a mirrored sphere, which is contained in an otherwise, closed mirrored cube. The resulting images are modeled by ray tracing procedures and both sets of images undergo fractal analysis. We offer this as a novel demonstration of fractal geometry, utilizing the aesthetic appeal of these images to motivate an intuitive understanding of the resulting scaling plots and associated fractal dimensions.