Number Spiral - When You Chart a Number System, Patterns Emerge

[bdfh42]

http://www.numberspiral.com/index.html

[bayareaguy]

12:45, restate my assumptions...

[sachinag → bayareaguy]

Second best soundtrack I ever bought (Dead Presidents is numero uno).

[elai → bayareaguy]

I don't understand ?

[sachinag → elai]

It's a line from Pi, the movie. (Hence my soundtrack comment.)

[pchristensen]

I have no idea what this means, but it's got to be like heroin to number theorists.

[celoyd]

They 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 .

[paulgb → celoyd]

Sage 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

[jrp]

He mentions the also interesting 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 → jrp]

Those 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]

When 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 → ph0rque]

A 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]

I'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 → IsaacSchlueter]

Generally a bad idea to quote 4chan on Hacker News...