hm, now I wonder what happens if you take 'any old function', add it to a reversed and shifted version of itself, and normalize. do you eventually get one of t

hm, now I wonder what happens if you take 'any old function', add it to a reversed and shifted version of itself, and normalize. do you eventually get one of these self-replicating functions, or are there functions that 'diverge' under this treatment? Taking a random array and giving it this treatment, I seem to get a gaussian distribution after just a few (say, 100) iterations on a 100-element sequence, shifted by 1/3 and then downsampled to be a 100-element sequence again). but of course this is a global and downsampled view, the function might be very craggy locally.