Odd Numbers

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 `c`^{p} + `c`,
(`c`^{p} + `c`)^{p} + `c`,
((`c`^{p} + `c`)^{p} + `c`)^{p} + `c`,
(((`c`^{p} + `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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