Related Experiment Video
Updated: Jul 12, 2026

Generating Strictly Controlled Stimuli for Figure Recognition Experiments
Published on: March 18, 2019
Geometry, topology, and universality of random surfaces
Abstract:
Previous simulations of a self-avoiding, closed random surface with restricted topology (without handles) on a three-dimensional lattice have shown that its behavior on long length scales is consistent with that of a branched-polymer. It is shown analytically that such a surface with an unrestricted number of handles has a qualitatively different geometry and therefore is in a different universality class. The effect of a net external pressure is to suppress the handles and collapse the surface into a branched polymer-like configuration. Topology is thus shown to be a key factor in determining the universality class of the system.
Related Concept Videos
Quadric Surfaces
Oriented Surfaces
Parametric Surfaces
Theorems of Pappus and Guldinus
For finding the surface area, consider a differential line element that generates a ring with surface area dA when revolved.
Theorems of Pappus and Guldinus: Problem Solving
Tangent Planes to a Parametric Surface

