chuck@bunker.UUCP (Chuck Heaton) (08/27/84)
Hi. I wanted to thank all the responders to my 'Hoffstuff' question. I was glad to see it generated some discussion. Most appreciated were the nice definitions involving the 'golden ratio'. In my playing with the orginal Hoff. definition, I also played around with some generalizations of his: 1) h[0] = 0; h[k] = k - h[h[k-1]]; Namely: 2) h[k] = k - h[h[h[k-1]]] 3) h[k] = k - h[h[h[h[k-1]]]] . . . etc. Again,, it is the differences, g[n] = h[n] - h[n-1] (n>0) that I find most interesting. There is a commonality to the 'patterns' these produce. The way I was playing with all the above was to 'abbreviate' the sequences of '0's and '1's by replacing each occurence of n '1's surrounded by (lonely) '0's by the number 'n'. For example, 0101101011011.... becomes 12122.... . The original function g[] thus abbreviated produces only '1's and '2's and it is from these '1's and '2's that the patterns become more apparent. With 'higher level' g[]'s, the abbreviated sequence is made up of '1'...'n', where n = the 'nesting' level. Well, at least I find these amusing. Hopefully you will too. Thanks. Chuck Heaton