WTF is this?

The images you see on this blog are output from various Ulam spiral generators I built in Flash, Python and most recently using Arduino. Generally, each dot in an image represents a number with integer 1 at center. In addition to writing algorithms to test each number for primality within a set I have discovered that an infinite number of calculations can be performed to create new designs and animation algorithms. The simplicity and speed of these algorithms make them an ideal fit for embedded systems graphics, scientific, mathematical and artistic explorations.

Friday, June 13, 2008

Visualizing Prime Numbers

This is the output from a Ulam spiral generator I built in Flash. The pattern is based on the Ulam spiral concept. I got the idea to play around with mapping prime numbers after reading a biography on Paul Erdos which talked about Stanislaw Ulam's now famous doodles. There's all kinds of patterns one can derive from this. Depending on how you draw out the pattern, you can indicate the interesting property where primes only fall on diagonals. But since that ground has been covered, I was hoping to discover the face of God, Elvis, or both.

Here I've colored each prime an independent color based on one of four directions the individual dot was plotted (the gray circles are composites, not primes). The cyan dots are also prime and are found at the end of each direction. Interestingly, there are no primes on the southeast quadrant between the red and green sections. There are similar prime DMZs, if you look. Apparently there isn't anything terribly profound about this pattern (some say), but I don't believe the naysayers. Hell, they just proved that 42 really is a significant number in the universe.

This blog contains many of the variants I have generated.

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