

Number Spiral - When You Chart a Number System, Patterns Emerge - bdfh42
http://www.numberspiral.com/index.html

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bayareaguy
12:45, restate my assumptions...

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elai
I don't understand ?

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

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

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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> .

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paulgb
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

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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.

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newt0311
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.

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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.

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cousin_it
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.

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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!!_

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

