I created the coprimes project to see if I could uncover patterns or perhaps obliterate the perception of a pattern in modified coprime plots. I had seen the diagram on Wolfram's MathWorld of relatively prime numbers. This diagram plotted integer pairs in an X-Y grid, making coprime pairs black and non-coprimes white. I wanted to see if patterns emerged when the greatest common divisor (GCD) of integer pairs was tested for numbers other than one.
The program plots pairs of integers as cells within an X-Y grid, and colors them against a background if they share a greatest common divisor. I can define the GCDs to test for. If a GCD is not tested for, the cell color is the designated background color. I can test for one or many GCDs. I can also set the starting row and column to any integer pair, and vary the grid size.
Drawing Tool, Coprimes: The coprimes tool is based on the Euclidean algorithm to determine the greatest common divisor (GCD) of two integers. [4] I named this the coprimes project for brevity, though greatest common divisor project would have been more accurate.
Between 1951 and 1953, Ellsworth Kelly worked on Colors for a Large Wall, as well as Spectrum Colors Arranged by Chance. The first is a grid of 64 panels of flat colors. In the second, Kelly used a 38 by 38 grid, randomly distributing 18 colors, except half are black. Studies for the painting show a range of color schemes. [1] Ellsworth Kelly said, "I feel my paintings are fragments of the world and I'm simply digging them up and presenting them." [2] I see these plots as fragments of the world of numbers: Coprimes, Digital Drawings.
A reflection pattern with respect to the diagonal from 1,1 to n,n is obvious. Mapping colors to various GCDs reveals some grid patterns. It's possible to pick starting numbers and color mappings to obscure patterns. Still, some apparently non-random pattern usually emerges, though it often seems interrupted.
