Graduate Examples of fractal structure in prime partition numbers?

[Ventrella]

Regarding the recent discovery by Ken Ono and colleagues of the fractal structure of partition numbers for primes: a great lever of intuition would be to see a diagram, or any presentation of the numbers that reveals this fractal structure. Perhaps the fractal structure is somehow hidden in a long integer sequence? In this case, I assume it is still possible to reveal this fractal structure. Are there any known examples that I could see?

 

[willem2]

Googling for this, I can only find stuff from 2011. Of course it's a lot more recent than Euler.
The fractal structure is because there are structures stat are similar mod p, p^2, p^3 etc. The interesting stuff only seems to start at p=13, tough. A scale factor of 13 doesn't make for pretty pictures, I'm afraid. I found This lecture by Ken Ono, there are some examples starting at 50:00, but it's all numbers

 

[Ventrella]

Hi Willem2: Thanks for sharing that video - I understand the fractal structure better now. My interest in this topic is in regards to the art of visualizing patterns in large integers. I suspect that the patterns that Ono and colleagues have revealed could be visualized in a way that brings out the self-similarity - using one of many visualization techniques.

My fundamental interest is actually about finding patterns - not in a single partition number p(n) - but among the multiset of partitions themselves - which constitutes a larger dataset and which can be displayed in a 2D grid, using an ordering scheme such as the Dominance Order. I would be curious to learn if there are any correlations between the number p(n) and the patterns among the multiset of partitions themselves - and whether there are any insights to be gained from exploring the partitions of a large prime.

Also, I'm not sure what you mean when you say that a scale factor of 13 doesn't make for pretty pictures. There are many fractal patterns with a scale factor of 13 that are extremely interesting. Perhaps you were referring to the fact that p(13) is only 101, which doesn't offer much data for visual treatment.