Hey all. I stopped keeping up with this research a while ago since I couldn't keep up with the programming aspect, but I've been browsing sporadically. So, I broke off on my own efforts autistically looking for patterns that may be helpful. So far I've identified a couple of patterns within fibonacci sequences that might be relevant. Bare with me, this is extremely autistic…
Im working on an infograph at the moment, but for now here's a rundown of it.
The first (ones) digits in the numbers of a fib sequence make up a pattern of 60 numbers which repeats ad infinitum. Within this pattern there are subpatterns: every 5th and 10th number is a 5, every 15th a 0. Every 3rd number is even. The second half (#'s 31-60) is opposite the first half, i.e. the 1st and 31st add up to 10.
If you break the pattern of 60 into sets of 15 more patterns emerge, 1, 7, 9, 3 and 2, 4, 8, 6. As well as a helical sort of distribution throughout the set of 60 numbers.
For the time being that is all that needs to be said about the first digit pattern.
All digit columns subsequent of the first digit pattern also have patterns which they follow. Each pattern being 5 times larger than the pattern before it. The first digit pattern is 60 numbers long, the second digit pattern is 300. Every digit in a fibonacci sequence always has a repetitious pattern. And, these patterns appear to follow rules established by the first digit pattern.
If you break up any of the subsequent patterns into subsets Nx numbers long where x = the length of the previous pattern, you can establish at least one that I've proven thus far rule which dictates that pattern. The second (10's) digit pattern being 300 numbers long, and the previous pattern being 60, break this pattern up into 5 columns of 60 and the rule for this pattern becomes obvious. At first glance the numbers appear highly chaotic, but surprisingly follows a very simple rule. It follows the rule of "2, 4, 8, 6" in reverse. i.e. {6,8,4,2} the 1st + 6 = the 61st, the 4th + 2 = the 64th, ad infinitum.
The next (100's) digit follows the same rule, but this time the sequence is shifted two spaces so that it is {4, 2, 6, 8}
I'm going to cut myself off for now. If you guys find this interesting and relevant let me know and I will keep going.