Iterated Cyclic Averaging of Points
Starting with a set of points in the complex plane (marked by red crosses: ×), iteratively form new points with where rescales and repositions the family . Even for random distributions of the initial , in the limit as , the points arrange themselves on smooth curves.
Contributed by: Michael Trott with permission of Springer (March 2011)
From: The Mathematica Guidebook for Numerics, second edition by Michael Trott (© Springer, 2008).
Open content licensed under CC BY-NC-SA
For a closedÃ¢ÂÂform solution of the corresponding twoÃ¢ÂÂterm recursions, see
K. Mas'lanka, J. Cisło, Order from Randomness.