Craft continuous procedural color gradients using trigonometric wave functions or geometric harmony chords. Any palette synthesized here immediately drives all mathematical studios.
C(t) = a + b · cos(2π(c · t + d))
Click any swatch to copy its hex
Nested fields sampled from your active palette; the chord wheel below still drives Apply Chord
MATHEMATICAL FORMULAS & CHROMATIC SYNTHESIS
Start here: pick a system on the left, tune it or hit Mutate, then Capture. Palettes are made in Studio IV · Chromatic Lab and drive every visualizer. Everything auto-saves in this browser.
Deterministic nonlinear systems whose trajectories never repeat (aperiodic) yet remain confined to a complex fractal manifold in phase space. Slight changes to initial parameters (a, b, c, d) cause bifurcations between delicate silk filaments and dense topological knots.
Clifford, De Jong, Lorenz (σ, ρ, β), and Halvorsen 3D cyclic symmetry.
Botanical primordia pack most efficiently when successive elements diverge by the Golden Angle φ = 360°(1 − 1/φ) ≈ 137.50776°. Deviating by even 0.1° transforms Fibonacci spirals into radial spokes. Harmonographs model damped coupled pendulums.
r = c√n, θ = n · 137.50776° | Maurer Roses & Fourier Phasors.
Alan Turing's 1952 Reaction-Diffusion model describes how two chemical morphogens reacting and diffusing at unequal rates spontaneously self-organize into spots, stripes, and coral labyrinths. Ernst Chladni's equation maps acoustic standing-wave nodal lines.
cos(nπx)cos(mπy) - cos(mπx)cos(nπy) = 0
Popularized by shader pioneer Inigo Quilez, any smooth continuous artistic gradient can be compactly parameterized by four 3D vectors (a, b, c, d) driving a cosine wave for Red, Green, and Blue channels, avoiding muddy linear RGB transitions.
C(t) = a + b · cos(2π(c · t + d))