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.

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