Wednesday, April 23, 2008

Greatest Common Divisor of 3 Numbers

I have taken the coprimes and gcd project from two to three numbers. The gcd of three numbers can be computed as gcd(a, b, c) = gcd(gcd(a, b), c). When I use my coprimes or gcd project functions to plot examples, they tend to make the results a regular, checkerboard-like plot. Here's a example with the third number set to 6.

I find this plot interesting because it takes the plot for coprimes, and forces a regular pattern into every six by six cell block.

Here's an example with the third number calculated, as row/col, rounded down to a whole number. It's interesting in that it appears the lower left is the basic coprimes pattern, which then fades out as it moves to upper right.

Here's a larger version of the same plot, with slightly different color assignments.

Tuesday, April 15, 2008


This is the first in a possible series of waterfall "masks".

Wednesday, April 9, 2008

Monday, April 7, 2008

Animated GCD Arc

This is the first animated GCD arc plot. It was captured during the animation, as you can see by the unconnected curve in the middle, which was in the process of moving from one grid cell to the adjacent one. Unless I change the parameters this image always starts out the same, because it's based on a sequence of formulas and the parameters. After that the animation process will change the image in a different way each time.