Odd Numbers
© 14 Feb 2012 Luther Tychonievich
Licensed under Creative Commons: CC BY-NC-ND 3.0
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We expect numbers to be boring, predictable. Not so.


I deal a lot with mathematics, which usually means manipulating symbols rather than messing with numbers. But I also keep my hand in the numbers world, and I am continually surprised by the strange things numbers do. Sometimes they are surprisingly beautiful. Today I want to share some of that beauty.

Complex numbers, like 2 + 3i, have two real numbers inside so they can be plotted on a plane. Take a real number p. For every complex number c make a pinpoint of light at cp + c, (cp + c)p + c, ((cp + c)p + c)p + c, (((cp + c)p + c)p + c)p + c, etc. Make each point a different color and animate the result for p between 1 and 3, then flip the real axis and animate back to 1, and you get this:

Why would certain areas get a lot more light than others? Why is there structure here at all, let alone beauty? I can work through the math that shows what happens and even (to a degree) how and under what conditions, but mathematics is not really equipped to answer why.

There is more beauty in the universe than anyone has time to discover in a lifetime.

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