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Gallery

Mathematical art from chaotic dynamical systems. Each image is a density plot of millions of iterations, rendered as luminous traces on dark backgrounds.

Lorenz Attractor — strange attractor density plot

Lorenz Attractor

The system that started chaos theory. Edward Lorenz discovered it in 1963 while modeling atmospheric convection — a deterministic system that never repeats, sensitive to initial conditions down to the 12th decimal place.

σ = 10, ρ = 28, β = 8/3
Clifford Attractor — strange attractor density plot

Clifford Attractor

A two-dimensional strange attractor discovered by Clifford Pickover. Four parameters generate an infinite variety of flowing, organic forms — from tight spirals to diffuse clouds — all from a pair of sine/cosine recurrences.

a = −1.4, b = 1.6, c = 1.0, d = 0.7
De Jong Attractor — strange attractor density plot

De Jong Attractor

Peter de Jong's iterated map produces intricate lacework from pure trigonometry. Tiny parameter shifts collapse structure into noise or unfold new symmetries — a sharp reminder that complex beauty lives at the edge of instability.

a = −2.24, b = 0.43, c = −0.65, d = −2.43
Hénon Map — strange attractor density plot

Hénon Map

Michel Hénon's 1976 map is one of the most studied discrete dynamical systems. Its fractal structure reveals self-similarity at every scale — zoom in anywhere and the same filamentary pattern reappears, infinitely nested.

a = 1.4, b = 0.3
Thomas' Attractor — strange attractor density plot

Thomas' Attractor

René Thomas designed this system to model particle motion with damped feedback. The result is an attractor with unusual three-fold symmetry — orbits wind through three interlinked lobes, producing dense, luminous knots.

b = 0.208186

The process

Each attractor is computed by iterating a simple recurrence relation millions of times. The images aren't photographs or simulations — they're histograms. Every pixel's brightness is proportional to how many times an orbit visited that region of phase space.

The coloring comes from mapping density to a hand-tuned color ramp. High-density regions glow hot; sparse regions fade to black. No post-processing, no filters — just mathematics and a careful choice of palette.