Jeffrey Ventrella

A single curve carves out a self-similar shape that partially fills a golden triangle. The golden ratio is seen at many scales in the sub-triangles carved by the curve. This curve was generated from a recursive algorithm using integers of the 10th cyclotomic field, where pentagonal symmetry arises naturally (try to find the partial pentagrams). This algorithm extends a method for generating space-filling curves based on complex integers. The curve is generated as a line-drawing using custom JavaScript code. It is rendered to a canvas and saved as a file. I use an application to color-fill the two domains that the curve divides. More curves in this series are at: https://archive.org/details/fractal-curves