Demos

GPU simulation of a quantum wavepacket captured by a potential well, solving the 2D Schrödinger equation

Schrodinger Double Slit

GPU simulation of the quantum double-slit experiment via the 2D time-dependent Schrödinger equation

Gravity Power Law

Orbital motion under a central force $F \sim r^n$ with adjustable power-law exponent

Rectangular Peg

Inscribed rectangles in smooth Jordan curves, related to self-intersections of a surface in four dimensions

Wave Eqn Double Slit

Classical wave equation double-slit experiment, showing diffraction and interference in real time

Wave Eqn Flash

2D wave equation with a localized initial pulse, demonstrating the failure of Huygens' principle in two dimensions

$Wave Eqn Refraction$ Featured

Wave Eqn Refraction

2D wave equation with spatially varying speed, demonstrating refraction and Snell's law

Whitehead S3

The Whitehead link in $S^3$, stereographically projected to $\mathbb{R}^3

Complex Exp

Graph of the complex exponential $e^z$ as a surface in $\mathbb{C}^2$, projected to three dimensions along a rotating axis

Complex Zn

Graphs of complex power functions $z^n$ projected from $\mathbb{C}^2$ to $\mathbb{R}^3$ with domain coloring

Geodesics Cylinder

Geodesics on a cylinder, appearing as helices that unwrap to straight lines

Hopf Tori

Tori swept out by Hopf fibers over circles of latitude on $S^2$, nested and stereographically projected

Nil Geodesic Spheres

Geodesic spheres in Nil geometry, distorted by the anisotropy of the Heisenberg group

Nil Geodesics Earth

Geodesics in Nil geometry with an earth texture on the geodesic sphere, showing helical twisting

Nil Geodesics Earth Animate

Expanding geodesic spheres in Nil geometry, animated to show increasing distortion at larger radii

Sol Geodesic Spheres

Geodesic spheres in Sol geometry, stretched by the exponential expansion and contraction

Sol Geodesics

Geodesics in Sol geometry, curving under the exponential stretching of this Thurston geometry

Square Torus

The flat torus obtained by identifying opposite sides of a square, with its intrinsic Euclidean metric

Torus Knots

Torus knots $(p,q)$ rendered as tubes winding $p$ times in one direction and $q$ times in the other

Fig8 Knot

The figure-eight knot, the simplest non-torus knot with four crossings

Fourier Series

Fourier series partial sums converging to target functions, showing trigonometric decomposition

Hopf Complement

Geodesics in the complement of a Hopf fiber in $S^3$, stereographically projected to $\mathbb{R}^3

Hopf Fibration

The Hopf fibration of $S^3$, showing families of linked great circles projected to $\mathbb{R}^3

Punctured Disk Geometrization

Hyperbolic metric on a punctured disk, showing the cusp that forms at the removed point

Seifert Fibration

Seifert fibration of a 3-manifold, showing regular and exceptional circle fibers

Code: Whitehead Double

Inside the Whitehead link complement in $\mathbb{H}^3$, with horosphere reflections creating a manifold double

Code: Whitehead Double Earth

Inside the Whitehead link complement in $\mathbb{H}^3$, with earth and Mars textures distinguishing the two sides

Code: 3torus Blackhole

Inside a 3-torus with a central wormhole, transitioning from $S^2 \times \mathbb{R}$ geometry to flat Euclidean

Swimmer

Low-Reynolds-number swimmer locomoting through cyclic shape changes, illustrating the scallop theorem

Code: 3torus Double

Inside a 3-torus manifold double connected by a wormhole, with earth and moon orbiting through the periodic space

Code: 3torus Double Earth

Inside a 3-torus manifold double with distinct sky textures on each side of the wormhole

Code: Auto Sum Earth Space

Connected sum of two Euclidean spaces joined by a wormhole with $S^2 \times \mathbb{R}$ throat geometry

Code: Wormhole

Raymarching through a wormhole connecting two Euclidean spaces, with $S^2 \times \mathbb{R}$ throat geometry