The simple mathematical concept of a pursuit curve can serve as the starting point for creating wonderfully intricate artistic designs.
Pursuit curves can arise in a variety of situations. Suppose, for instance, that four bugs are at the corners of a square. They start to crawl clockwise at a constant rate, each moving toward its neighbor. At any instant, they mark the corners of a square. As the bugs get closer to the original square’s center, the new square they define rotates and diminishes in size. In reaching the center, each bug travels on a logarithmic spiral with a length equal to the side of the original square. Superimposed snapshots of the bugs’ progress add up to an intriguing pattern.