ERGODICA
Ergodica Parameter-Space Explorer
Analyze the mathematical structures of complex dynamics, attractors, and cellular systems. Powered by direct GPU compute shaders, 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 →
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'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 convergenceRegistry Extension PendingStochastic 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)Registry Extension Pending