Over the next few months I plan to offer substantial updates to this site and to release a new video. In the meantime, here is a quick update on 2017 developments.
The video circulated past senior people at Advanced Micro Devices, and they thought my efforts to find if pi ‘rolls double’ was an interesting computational effort and offered assistance in the form of powerful GPUs built for compute — and connections to the excellent Northeastern University Computer Architecture Research Laboratory (NUCAR).
AMD provided an 8 GPU supercomputer to NEU last Fall to compete in a supercomputing competition in Colorado, then to plot positions in the hexagon once it returned to NEU. The system is up and beautiful (photo)! However, the conversion of the fast cython code (developed by Perry Stoll, left) that ran on my Mac Pro 5.1s to run on the AMD/NEU system required rewriting / debugging and the addition new features such as ‘search’ have taken time. But testing is underway and plotting is not far off. Currently, a single GPU clocks is faster than my Mac Pro 5.1 server farm of 5 Xeon X5680s. The NEU code will reconcile the many threads – something I did by hand at great risk of error – and will be scalable should this become an even larger effort.
Kaustubh Shivdikar, pictured right, is part of the NUCAR team.
Once data come in I can revise my ‘numberscape’. That is, take a broad range of numbers, (say, 2.50000, 2.50001, 2.50002 …. 3.49999, 3.50000) raised to increasing powers to see how and when each rolls double. My early CPU generated data are very interesting and I will soon post the draft data once I figure out how best to display the thousand columns.
As for the theory side of things: While my friends at NUCAR have been working on computation, I’ve continued to contemplate the hexagon itself. Back when I first filled the hexagon I found (though it was already known) primes, aside from 2 and 3, come in two flavors, 1 mod 6 and 5 mod 6. Perhaps 1 mod 6 primes ‘spin’ one way, and 5 mod 6 primes spin the other. This offers a second way to fill the hexagon by switching direction of fill only when a different type of prime is encountered. So I have a Mac Pro heating a my office as 10 cores plot it this way. But even without a huge database, this path offers very interesting results I plan to soon share as a video.