Modular Multiplication on a Circle

Multiply the positive integers by 3 (mod 10) to get the repeating sequence . This Demonstration connects the starting values to the ending values for a chosen modulus and multiplier .
With multipliers of 2, 3, and 6, cusped epicycloids develop—the cardioid, nephroid, and ranunculoid. Other patterns develop with other moduli and multipliers.

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References
[1] B. Polster. Times Tables, Mandelbrot and the Heart of Mathematics [Video]. (Nov 11, 2015) www.youtube.com/watch?v=qhbuKbxJsk8.
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