– Sometimes, Infinity is ed and Spherical –
Department – Mathematic (Graduate Student) –
Research Field – Geometric Topology (Pure Mathematics) –
How image was captured – Programmaically (for the black limit sets on white) w/ ray tracing (for the red spheres) –
Research Impact & Significance – I study very general abstract spaces which are three-dimensional, and a well-established problem in my subfield is that three dimensions is a lot; this makes my spaces hard to study. One partial solution is to consider lower-dimensional “parts” and to look at how these parts behave when acted on by some map or function. For natural reasons, the actions studied are often iterated ad infinitum, and the result of this infinite process is a collection of subparts/”images” referred to as the “limit set” for the map/function/action. As it happens, a lot of data about the original abstract space can be learned by studying its various limit sets, and for that reason, having (mathematically) “nice” visualizations of them is a huge perk! This particular picture has two “parts”: The “background component” consists of black circles on a white background (these circles are the limit set of this particular action) while the “foreground” consists of colored, textured spheres obtained by ray-tracing the limit set in a particular way. By way of ray tracing, the limit sets (which are 1-dimensional curves on a 2-dimensional plane) come to life in a way that sometimes aids in visualization.