I so thoroughly enjoyed James Tanton’s videos on new breakthroughs in partitions that I inspired to play around with my own patterns in the partitions. In particular, I’m pretty familiar with the dragon fractal but hadn’t seen the way you can generate it until Tanton showed the binary representation of the dragon fractal (in Video 4).
I started to play around with coloring bits of the partitions that appeared “self-similar.” I can see know how they are quite a bit more complex than the dragon fractal, and I see some intriguing patterns. I wonder if I play around long enough if I’ll recreate Euler’s method for generating the number of unordered partitions?
What’s gotten me hooked, I think, is that Ono’s work (Ono is the guy who came up with an explicit formula for the number of partitions of N) was inspired by visualization and partitions are so visualizable, and so I would like to see what the partition numbers look like to him. I don’t know anything about -adic spaces (or whatever they are called) but I do know some things about fractals and primes… I wonder if there is some representation that would allow me to see the fractal structure in the partition numbers.