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Number Spiral - When You Chart a Number System, Patterns Emerge
- bayareaguy 18y ago12:45, restate my assumptions...
- pchristensen 18y agoI have no idea what this means, but it's got to be like heroin to number theorists.
- deleted 18y ago[deleted]
- jrp 18y agoHe mentions the also interesting Ulam spiral; http://en.wikipedia.org/wiki/Ulam_spiral http://en.wikipedia.org/wiki/Ulam_spiral If you like this kind of stuff, you might try to understand the following pattern (F_n is Fibonacci, F_0 = 0, F_1 = 1). F_n%2==0 whenever n%3==0. F_n%3==0 whenever n%4==0. F_n%4==0 whenever n%6==0. F_n%5==0 whenever n%5==0, etc.
- newt0311 18y agoThose are easily understood if you consider F_n mod k. Ex. F_n mod 2: 1, 1, 0 (as 1+ 1 = 2 == 0 in mod 2), 1, 1, 0, ... So on and so forth.
- ph0rque 18y agoWhen I grokked this for the first time, I had an idea for generating all the prime numbers: use a number spiral that "wraps" in n dimensions.
- cousin_it 18y agoA Russian blogger once described his dream of a music theory book with matrices of notes corresponding to chords in multidimensional time, e.g. the classic 3x3 magic square being the 2D-time counterpart to the major triad. Every perfect musical piece corresponded to a consonant n-dimensional hyperchord. PS: just checked the Lo Shu, sure enough it has 4 5 6 on the main diagonal, proportional to the tones of a major triad. Want some of his weed.
- IsaacSchlueter 18y agoI'm getting chills as I read this. I wish that I could vote it up more than once. To borrow a term from 4chan: MOAR!!
- river_styx 18y agoGenerally a bad idea to quote 4chan on Hacker News...
- celoyd 18y agoThey only provide a Windows binary for drawing them. If you want a start on doing it yourself, here's some postscript: http://basecase.org/code/numberspiral.ps http://basecase.org/code/numberspiral.ps .
- paulgb 18y agoSage code: plot = point2d((0,0)) for k in primes_first_n(500): r = sqrt(k) theta = sqrt(k) * 2*pi plot += point2d((r * cos(theta), r * sin(theta))) plot