Steve Trettel

MediumComputer generated using a custom-built shader material and THREEjs.
The ArtA parameterization of a tubular neighborhood of the trefoil knot, embedded in the 3-sphere. Viewed in 3 dimensional space via stereographic projection through a point on the knot, so that the negative space in the image is homeomorphic to the trefoil complement.
The MathKnot theory is the study of closed loops in 3-dimensional spaces, often in the 3-dimensional sphere. The trefoil knot is the simplest nontrivial knot, and the negative space surrounding the knot, known as the knot complement, is surprisingly ubiquitous in low dimensional topology.
CategoriesKnot Theory, Computer Graphics, Math Illustration, Stereographic Projection