World Cup football in fractal form

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To mark Germany's historic win over Brazil in the World Cup semifinal this week, Professor Lasse Rempe-Gillen created this beautiful image (above).

It shows the behaviour of a model that describes the phenomenon of phase-locking, something that can be seen in the synchronising flashes of fireflies or when a roaring stadium of football supporters gradually clap or stamp in unison.

The image is related to recent research and you can read more at the news story and at their related news story Maths, metronomes and fireflies.

The image below to celebrate Germany wnning the World Cup shows 4 curves, for Germany's 4 titles, at a single fixed point, for Götze's single goal.

Germany-Argentina fractal