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Particles move in beautiful patterns when they have ‘spatial memory’

A mathematical model of a particle that remembers its past so that it never travels the same path twice produces stunningly complex patterns

By Karmela Padavic-Callaghan

18 April 2024

Patterns produced by 'polygon billiards'

A beautiful and surprisingly complex pattern produced by ‘mathematical billiards’

Albers et al. PRL 2024

In a mathematical version of billiards, particles that avoid retracing their paths get trapped in intricate and hard-to-predict patterns – which might eventually help us understand the complex movement patterns of living organisms.

When searching for food, animals including ants and slime moulds leave chemical trails in their environment, which helps them avoid accidentally retracing their steps. This behaviour is not uncommon in biology, but when Maziyar Jalaal at the University of Amsterdam in the Netherlands and his colleagues modelled it…

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