- As part of a project to generate some computer art and to build a video game, it came to pass that I needed a way to convert whole numbers into graphic images. I do not mean drawing a picture of numerals, but to generate a graphic picture unique to the number with no numerals or text. It seems obvious that a number's prime factorization would be an important part of any algorithm designed to hash a number into a graphic image. I have settled on a system that I think may be of some interest to the list.

Originally I did a few interesting explorations of the system and wrote up all my results in a rather long paper, but I have shortened the paper to simply describe the algorithm and provide some examples. Most of the short paper are pictures of numbers and I have left out some interesting heuristic calculations, some short curious prime number sequences, and partitionings of the integers motivated by the algorithm which are probably of no interest to anyone. If you like this sort of thing have a look at the longer version. I do think the pictures are cool and I hope you enjoy the idea.

Along the way I think I invented a tres-cool fractal algorithm using prime numbers but my limited computing power kept me from making a really kick-butt graphic image of this prime number fractal picture. That fractal is discussed at the end of both versions.

You can have a look at the idea on a small site I built just for this purpose: https://home.comcast.net/~rwynar/. I will add an applet to generate these images soon, I just have to convert my little java code into applet form.

Of course all comments are welcome.

Roahn

[Non-text portions of this message have been removed] > Chris - I would enjoy seeing how your script outputs looked.

I'd wondered if you did that on purpose. Go to

> Is there anyway to send a sample on to me? In my algorithm

> the borders of the atoms get demagnified with the atoms which

> gives a slightly uneven appearance (that is...the borders at

> each recursive level are not all consistent.) However this

> effect is useful for tracking the recursion depth by eye, so

> I have not bothered to work that issue out. I am wondering

> if your script naturally handles this.

http://www.utm.edu/staff/caldwell/preprints/temp/

1to30 is just that, 1, 2, 3, ...

Then the flat primes p, pq, pqr, ... to 307

Then the same for the sharp.

Made by quick and sloppy Maple, exported, made smaller

with fireworks...

Hope I did these right, didn't check very carefully...

CC