String crossings [computer graphics

Abstract

When the author was about 10 years old, he completed a project which involved driving little brass nails into a piece of wood so that they were equally spaced around a circle, and then winding shiny metal wire between every pair of nails. The result was a shiny spider's web of wire-it was an algorithm for making an aesthetic visual piece. Years later, when he started to learn computer graphics, he programmed up these string art creations on vector storage tubes and plotters, mixing colors and changing line widths. Then recently, an artist friend (Dan Robbins) mentioned that he was planning a sculpture that involved a similar kind of design. Part of his sculpture involved placing objects at the intersections of pairs of strings. He wanted to plan part of the sculpture in advance and asked if there was a way to determine how many strings were necessary to get a desired number of intersections. The article starts with an answer to Dan's question. It also explores some other questions derived from these simple but elegant little string art patterns. These lovely little geometric patterns lead to numerical patterns every bit as graceful and aesthetically pleasing.