Visual Lab
Interactive demos
Small mathematical visualizations and browser games. Some are related to my work or teaching; others are here because they were fun to make.
Math demos
Mathematical visualizations
Change the controls and watch each simulated system respond. The individual pages include a short explanation of what is being shown.
Game of Life on graphs
Run a Life-like cellular automaton on a toroidal grid, a random regular graph, an Erdős–Rényi graph, a preferential-attachment network, or a clustered network. Change the rule, seed a population, rewire edges as it runs, and follow it through three dimensions.
Cart–double-pendulum swing-up
Watch a cart drive two linked pendulums toward the unstable upright position, hand off to a balancing controller, or take over the actuator and attempt the swing-up yourself.
Game of Life through time
Draw an initial state on a flat grid, then watch Conway’s rule stack new generations along a vertical time axis. The count keeps going as old layers fall away; orbit the history to see still lifes become columns, oscillators become braids, and gliders carve paths.
Bifurcations in motion
Move a parameter through classical and generated one-dimensional systems. Read the bifurcation diagram, slope field, and phase line together; zoom into critical points for local normal forms, or sweep a fold back and forth to make hysteresis visible.
Flows on the circle
Watch a periodic vector field move points around the circle while its angular-velocity graph and cut-open lift update in step. Find fixed points, compare their stability, and see how rotation emerges when a stable–unstable pair disappears.
Bifurcations in the plane
Move a parameter through two-dimensional flows and watch the phase portrait, invariant branches, and Jacobian eigenvalues respond together. Launch trajectories, follow periodic orbits, and compare local and global bifurcations—including Hopf transitions and folds of cycles.
Nim as a graph
Play Nim against an optimal computer while the complete directed state graph tracks every move. Take counters on the board or navigate by clicking a neighboring node, then rotate the graph to see strategy as geometry.
Just for fun
Some games
These are small browser games built for play rather than mathematical demonstration. This seemed like the right place to share them.
Rune Garden
Survive an endless siege across five lanes. Defeat milestone bosses, choose Sun, Dew, Thorn, or Storm paths, then graft those seeds into branching guardians—or sell and replant.
Linewarden
Defend a three-pass siege lane with a leveling hero. Choose among 50 hostile contracts whose permanent bodies return strongest-first every wave, then balance each fixed payday against gear and relics as late-wave scaling turns catastrophic.
Bouncy Ball Blaster
Move around a twelve-sided 3D arena, hit roaming targets, collect power-ups, and launch bouncing balls that can splat and split. This is an arcade game, not a mathematical demo.
More later
I’ll add things here as I make them.
Some will be mathematical visualizations; others may be small games or experiments.