Accessibility and occlusion of biopolymers, ray tracing of radiating tubes, and the temperature of a tangle

Abstract

We introduce a measure of complexity, an energy, for any conformation of filaments. It is the occlusion, the portion hidden when viewed from an arbitrary exterior point. By inverting we get the exposure, a first approximation of the accessibility of the filaments. Assuming the filament is a source, we get the self-irradiation, which leads to both an interpretation as the temperature and a visualization technique: ray tracing as a virtual laboratory. There is a wide variety of applications, from enzyme action on and radiation damage of biopolymers, to the geometry of light bulb filaments. Energy minimization provides automatic detangling, resulting in symmetric and pleasing conformations.