ERGODICA
Parameter-Space Explorer
GPU-accelerated exploration of attractors and complex dynamical systems, with live density accumulation and interactive orbit rendering.
Chaotic Attractors
Orbits and trajectory bundles folding through multi-dimensional phase space
Clifford attractor
A classic 2D discrete-time chaotic map where minor parameter changes fold the plane into intricate, nested loops.
x' = sin(a·y) + c·cos(a·x) y' = sin(b·x) + d·cos(b·y)Explore System →
Lorenz attractor
A continuous 3D system of differential equations famous for the butterfly effect and weather model chaos.
dx/dt = σ(y - x) dy/dt = x(ρ - z) - y dz/dt = x·y - β·zExplore System →
De Jong 3D
A 3D generalization of the Peter de Jong map that weaves complex, ribbon-like structures in three dimensions.
x' = sin(a·y) - cos(b·x) y' = sin(c·z) - cos(d·y) z' = sin(e·x) - cos(f·z)Explore System →
Loom
A 2D map with a tanh-saturated edge selvage and slow interior rotation — the structure weaves, turns, and never repeats identically.
s = tanh(e·r) x' = sin(a·y) − s·cos(b·x) + f·(x·cos(g) − y·sin(g)) y' = sin(c·x) − s·cos(d·y) + f·(x·sin(g) + y·cos(g))Explore System →
Complex Dynamics
Escape-time complex planes accumulated via high-resolution path density
Buddhabrot Explorer
A complex-plane fractal density accumulator where escaping Mandelbrot orbits splat their coordinates onto the canvas.
z_{n+1} = z_n^2 + c
Splat coordinates of escaping orbitsExplore System →Julia-brot Explorer
A complex-plane fractal density accumulator where escaping Julia orbits splat their coordinates onto the canvas.
z_{n+1} = z_n^2 + c
Splat coordinates of escaping orbitsExplore System →Newton Fractal
Basin-of-attraction map of Newton's root-finding method applied to z^n − 1 = 0. Each pixel is a starting point; its color encodes which root the orbit converges to and its brightness encodes convergence speed.
z_{n+1} = z_n - (z_n^n − 1) / (n · z_n^{n-1})Explore System →Newton's Fractal
Iterated root-finding optimization paths in the complex plane mapped by splatting density over convergence pathways.
z_{n+1} = z_n - f(z_n)/f'(z_n)
Visualizing root basin convergenceStochastic Flow Fields
Simplex-warped coordinate fields steering multi-million particle streams
Simplex Noise Flow Field
Millions of particles guided through vector flow fields generated by multi-octave coherent gradient noise. Creates turbulent streams.
v(p) = Noise(p * frequency) dx/dt = v(x)