Modular Multiplication on a Circle
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 .
3,6,9,2,5,8,1,4,7,10,…
1,2,3,…
1k,2k,3k,…
k
With multipliers of 2, 3, and 6, cusped epicycloids develop—the cardioid, nephroid, and ranunculoid. Other patterns develop with other moduli and multipliers.