"How to squash a mathematical tomato", Rubic's cube-like surfaces and their connection to reversible computation

TL;DR

This paper explores the connection between reversible computation processes and physical transformations on 2D surfaces, introducing fractal circle packings with potential applications in engineering modular surfaces.

Contribution

It introduces a novel geometric framework linking reversible computation to surface manipulations and discovers fractal circle packings with unique properties.

Findings

Reversible computation can be modeled as surface turning operations.

Discovered fractal circle packings with properties similar to the dragon curve.

Proposed applications in designing modular, kinetic surfaces.

Abstract

Here we show how reversible computation processes, like Margolus diffusion, can be envisioned as physical turning operations on a 2-dimensional rigid surface that is cut by a regular pattern of intersecting circles. We then briefly explore the design-space of these patterns, and report on the discovery of an interesting fractal subdivision of space by iterative circle packings. We devise two different ways for creating this fractal, both showing interesting properties, some resembling properties of the dragon curve. The patterns presented here can have interesting applications to the engineering of modular, kinetic, active surfaces.