Researchers from Emory University, the University of Wisconsin Madison, Yale, and the Technical University of Darmstadt in Germany have discovered that partition numbers behave like fractals, possessing an infinitely-repeating structure.

The partition number P(N) of an integer N is the number of distinct ways in which N can be written as a sum of positive integers. For instance, 6 = 6, 5+1, 4+2, 4+1+1, 3+3, 3+2+1, 3+1+1+1, 2+2+2, 2+2+1+1, 2+1+1+1+1, and 1+1+1+1+1+1, so that P(6) = 11. P(N) grows very rapidly with N. For instance, P(100) = 190,569,292.

Partition numbers have captured the imagination of mathematicians since the time of

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