by Doug Coulter » Sun Jun 12, 2011 9:51 am
VERY interesting. The last time I saw something like this I was investigating various schemes for pseudo-random vector generation, and plotting the results of a few vector components against one another. It turns out that most of the vector random number generators have accidental correlations when shown that way that look a lot like this (including the generator used for Black-Scholes analysis of market risks for option pricing). I was looking for a good generator for MLFN neural net training and perturbation, and I got pretty excited when most of the "best" algorithms had "these problems" of accidental correlations in various hyperplanes.
Of course, the reason I saw what I saw was that there was underlying structure in the PRN generators that only showed up under further analysis, and this did show up even in the ones from Knuth, Numerical recipes and others -- even some of the crypto PRN generators.
I would suppose the same would apply here, due to the underlying structure, or sub-structures in nuclei. This plot will bear some more analysis to tie that together.
Isn't the human ability to find patterns in things amazing? All the PRN's I found things like this in were highly "vetted" as producing completely uncorrelated numbers by the conventional techniques. But plot say, V1, V5, V11 as a 3d scatter plot (out of a longer vector) and here's these patterns and blobs....and most attempts to "fix" that and get a truly random, flat distribution by further shuffling simply changed the way it looked -- but not the non-random nature. I didn't get as far as trying a diode noise generator or a radioactive source, and probably I should -- we may be looking at a number theoretical issue there with the PRN's. With nuclei, it's probably due to underlying sub-structures, like the semi-classical idea that alphas are preformed in a larger nucleus before decay, or that ??? shell/magic number junk -- there's only so many ways to combine with a few integer (quantum number eigenvalues) or binary (say, spin) properties.
This deserves more looking at than I can do on a Sunday morning over the first cup of tea....
Posting as just me, not as the forum owner. Everything I say is "in my opinion" and YMMV -- which should go for everyone without saying.