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Prime Geometry: A New Way to Visualize Prime Numbers

This animation illustrates a deterministic geometric construction generated from the sequence of natural numbers. Each integer contributes one circular arc to a continuous trajectory. Prime numbers rotate the direction by 90° counterclockwise, while composite numbers rotate it by 90° clockwise.

The video shows the construction evolving step by step, making it possible to observe how simple local rules generate increasingly complex global geometric structures.

Transition from 3-branched to 5-branched spirals in the Rock-Paper-Scissors-Lizard-Spock equation on the sphere

Solution of a reaction-diffusion equation involving five chemicals, each of them dominating two others. There are two interaction parameters, which are equal at the beginning of the simulation. As one of them decreases to zero, spirals with 5 branches appear.

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