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Costa's Minimal Surface
Costa's minimal surface, a thrice-punctured torus with two catenoidal ends and a planar end
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Geodesics in Kerr Spacetime
Interactive visualization of particle and light paths around a spinning black hole, including a gravitational lensing renderer showing the photon ring and Doppler-beamed accretion disk.
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Rewriting My Website in Observable Notebook Kit
How I migrated this website from Idyll to Observable Notebook Kit
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Boy's Surface
Boy's surface, an immersion of the real projective plane in three-dimensional Euclidean space
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Denali Terrain
Interactive 3D terrain viewer for the Denali region built from scratch with WebGPU
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Visualizing Sloan Digital Sky Survey Data
Visualizing 3.3 million galaxies and quasars from the Sloan Digital Sky Survey
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Fluid Instability with Stable Fluids
Interactive fluid flow with the Stable Fluids method of Jos Stam.
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Hess-Smith Panel Method
Interactive demonstration of using the Hess-Smith panel method to compute the aerodynamic flow around an airfoil
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Multi-Scale Turing Patterns in WebGPU
Interactive multi-scale Turing patterns computed in WebGPU
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Strange Attractors in WebGPU
Strange attractors — chaotic dynamical systems whose trajectories trace out intricate fractal structures
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WebGPU Instanced Lines
GPU-accelerated line rendering for WebGPU
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Zoomable Multi-Layer Plots in Notebook Kit
Interactive mathematical plotting in Observable Notebook Kit
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Simulating the 2D Kuramoto-Sivashinsky Equation in WebGPU
The 2D Kuramoto-Sivashinsky equation, a chaotic PDE modeling pattern formation in combustion fronts and thin films.
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Wilcoxon Signed-Rank Test for Performance Testing
An interactive explainer of the Wilcoxon signed-rank test for comparing paired performance measurements.
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Perfectly Matched Layers for the Wave Equation
An explanation and WebGL implementation of Perfectly Matched Layers for absorbing boundary conditions in the scalar wave equation.
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Reflecting on Two Years of Yoga
A personal reflection on consistent yoga practice with attendance visualizations over two years.
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REGL in Observable Notebooks 2.0
Tips and tricks for instantiating and managing a REGL WebGL Canvas in Observable Notebooks 2.0.
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Hello, Observable Notebooks 2.0!
Kicking the tires of Observable's new notebook tooling!
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Clifford and de Jong Attractors
Clifford and de Jong strange attractors with interactive zooming.
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Chaotic Magnetic Pendulum
Interactive visualization of a magnetic pendulum demonstrating chaotic dynamics.
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Spring Training on the Treadmill
Quantifying treadmill efforts (to the point of injury).
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Speed Climbing World Record Progression
Plotting and extrapolating trends in competitive speed climbing
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Sliced Optimal Transport
Approximate pixel redistribution between images using sliced optimal transport.
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Series Acceleration with Shanks Transformation
The Shanks transformation for accelerating slowly-converging series, demonstrated on the arctangent formula for π.
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Cubic basis vs. Hermite interpolation
Visually compare cubic interpolation using different basis functions.
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Bicubic Texture Interpolation using Linear Filtering
Smooth bicubic texture filtering using the GPU's built-in bilinear interpolation.
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Knocking Down the Gates with our Friend Jacobi
Using Jacobi elliptic functions to solve an optimization problem about falling poles and large-amplitude pendulum dynamics.
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Night and Day
Visualizing Earth's solar terminator on a Mapbox map using NASA Black Marble imagery and WebGL shaders.
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Fast Generalized Winding Numbers in 2D
Fast generalized winding numbers in 2D for robust inside-outside queries on arbitrary polygons.
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HTML+CSS Periodic Three-Body Orbits
Animating periodic three-body orbits using pure CSS keyframe animations generated from Fourier decomposition.
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Lawson's Klein Bottle
Lawson's Klein bottle, a generalization of the Clifford torus in 4D space
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Computing π with the Bailey-Borwein-Plouffe Formula
Computing hexadecimal digits of π at arbitrary positions using the Bailey-Borwein-Plouffe formula.
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The Double Pendulum Map
Visualizing the phase space of simple and compound double pendulums, showing how chaos emerges from coupled nonlinear oscillations.
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Malkus Waterwheel
Interactive simulation of a chaotic mechanical system whose dynamics map to the Lorenz attractor.
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Selecting the Right Opacity for 2D Point Clouds
Deriving the formula for point opacity in large point cloud visualizations to maintain consistent visual density.
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Adaptive Contouring in Fragment Shaders
Adaptive contour rendering in fragment shaders using screen-space derivatives for smooth, resolution-independent contour lines.
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WebGPU Voronoi Diagrams using the Jump Flooding Algorithm
Computing Voronoi diagrams and distance fields on the GPU using the Jump Flooding Algorithm.
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Sphere Eversion
The Bednorz and Bednorz analytic sphere eversion, a continuous deformation turning a sphere inside out without creasing or tearing
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Transparency for 3D Surfaces
A comparison of three approaches to rendering transparent 3D surfaces in WebGPU, including a simple two-pass hack that draws gridlines and edges through solid geometry, weighted blended order-independent transparency, and depth peeling.
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Toiletpaperfullerenes and Charmin Nanotubes
Interactive 3D simulation of nanotube and fullerene structures that can be physically constructed from toilet paper tubes.
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3D Reaction-Diffusion
3D Gray-Scott reaction-diffusion with volumetric rendering.
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Visualizing Integers in Floating-Point
Interactive bit-level visualization of how IEEE-754 single-precision floats represent integers.
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Particle-Mesh Gravity in WebGPU
2D gravitational N-body simulation using the particle-mesh method.
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Periodic Planar Three-Body Orbits
Interactive catalog of periodic three-body orbits with topological classification via free group words.
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Multi-Scale Turing Pattern Gallery 2
Another gallery of multi-scale Turing patterns
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Multi-Scale Turing Pattern Gallery 1
A gallery of multi-scale Turing patterns
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Aligning 3D Scans
Automatically orienting 3D scans by computing principal axes from surface normals.
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Things I Learned the Hard Way Using React Native
A collection of lessons learned from eight months of React Native development - environment setup, Redux patterns, performance optimization, and cross-platform gotchas.
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A Series of Unfortunate Things I Programmed One Time
Reflections on a decade of programming projects and the search for meaning in complexity