PULSE.

Polyomino exact cover. Watch backtracking search fill a rectangle with polyomino pieces, branching and pruning its way to every solution.

Polarization of light. Polarizing filters select oscillation direction by Malus's law. Insert a 45° filter between crossed polarizers and watch extinct light revive.

Lifelike cellular automata. Explore 262,144 birth/survival rules on one grid. Each rule string unlocks a completely different universe of emergent patterns.

Cusp catastrophe. Smooth parameter changes cause sudden jumps in equilibrium state. Hysteresis traces the geometry of discontinuous bifurcation.

Dyson Brownian motion of random matrix eigenvalues. Logarithmic repulsion and thermal noise produce the Wigner semicircle law and level-repulsion statistics.

Schottky group circle fractal. Four circles define Möbius transformations whose iteration nests circles within circles, converging on a Cantor-set limit.

Cascading failure on networks. One node falls, its load spills to neighbors, and collapse propagates. Scale-free networks are robust to random failure but fragile to targeted attack.

The Multibrot set. Smoothly vary the exponent d in z^d+c and watch the Mandelbrot set morph into (d-1)-fold symmetry.

Domain coloring of the Riemann zeta function. Non-trivial zeros align on the critical line, revealing deep number-theoretic structure.

Chaos control. Tiny parameter perturbations stabilize unstable periodic orbits hidden in the logistic map's chaos — the OGY method tames disorder into order.