Mixing, Twisty Puzzles and the Fractal Geometry of Piecewise Isometries

A piecewise isometry is a map that cuts and shuffles an object, for example, shuffling a deck of cards or scrambling a Rubik’s cube. The mixing properties of these maps are applicable to granular mixing and twisty puzzles (e.g. the Rubik’s cube). One remarkable property of piecewise isometries is that the mixing set typically has a complex fractal structure, and the fractal properties correlate with mixing performance. The idea of this project is to explore the mixing capabilities and fractal mixing sets associated with a range of piecewise isometries.

Martin Gossow

The University of Sydney

Martin Gossow is a third-year student at the University of Sydney, studying for a Bachelor in Science (Advanced), with majors in Mathematics and Data Science. Academically, Martin’s interests surround combinatorics, algebraic geometry/topology and fractal structures. He particularly enjoys finding links between seemingly unrelated areas of mathematics through unique ideas that highlight fundamental aspects of both topics. Outside of University, he attends Rubik’s Cube speedsolving competitions and tutors Year 12 in Extension Maths. Martin also enjoys music and creating visualisations to convey mathematical ideas to a wider audience.

You may be interested in

Thomas McCarthy McCann

Thomas McCarthy McCann

Nexus Between Randomised Numerical Linear Algebra and Big Time Series Data
Yong See Foo

Yong See Foo

A Comparison of Bayesian Inference Techniques for Sparse Factor Models
Thomas Vandenberg

Thomas Vandenberg

Bragg Edge Neutron Strain Tomography
Duong Thuy Dung Le

Duong Thuy Dung Le

Advanced Solution Techniques to Multi‐Component Optimisation Problems
Contact Us

We're not around right now. But you can send us an email and we'll get back to you, asap.

Not readable? Change text.