Wolfram Demonstrations Project

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
From: The Mathematica Guidebook for Numerics, second edition by Michael Trott (© Springer, 2008).

For a closed-form solution of the corresponding two-term recursions, see

K. Mas'lanka, J. Cisło, Order from Randomness.

Contributed by: Michael Trott with permission of Springer

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Iterated Cyclic Averaging of Points