Fractal gallery
Every shape Spiralyst Lab can draw
27 fractal types — 14 in 2D, 13 in 3D — plus 4 scopes (audio visualizers): a third category of render type. Each is a live, parameter-driven system that reacts to your music. Hover any tile for motion; click for the math behind it.
Rendered straight from the app, not stock art.
2D fractals & spirals
Flowing spirals, phyllotaxis, recursive trees, the Apollonian gasket, Julia sets, and custom SVG fractals.
Archimedean
The classic arithmetic spiral — arms spaced a constant distance apart. Even, clockwork winding; the most 'engineered' of the spirals.
2D · spinLogarithmic
The growth spiral of nautilus shells and galaxies — each turn scales by a fixed ratio, so it looks self-similar at every zoom.
2D · spinFermat
A parabolic spiral winding symmetrically both ways from the center, weaving a tight rosette of interleaved arms.
2D · spinHyperbolic
An inverse spiral (r = a/θ) rushing in from infinity toward a central asymptote — dense at the rim, vanishing at the core.
2D · spinPhyllotaxis
The sunflower-seed pattern — points placed at the golden angle (137.5°) so florets pack with no gaps. Nature's optimal spiral.
2D · spinRose (coiled)
A rose curve wound outward into a coil — petals (k) multiplied by a growing radius give a layered, blooming spiral.
2D · spinMulti-arm
Several logarithmic spirals sharing a center, evenly rotated — a pinwheel / galaxy-arm motif.
2D · spinFractal phyllotaxis
Phyllotaxis within phyllotaxis — each seed of an outer golden-angle pattern carries its own miniature spiral cluster.
2D · spinFractal rose
A recursive rose: each petal tip sprouts a smaller rose, branching into a self-similar floral fractal.
2D · spinPythagoras tree
The classic recursive tree of squares — each square spawns two scaled children at a branch angle, growing a fractal canopy.
2D · branch angle 0.35↔1.20Recursive log spiral
Logarithmic spirals branching off logarithmic spirals — an organic, fern-like recursive curl.
2D · spinApollonian gasket
A packing of mutually tangent circles, each gap filled by ever-smaller circles (Descartes' theorem) — a foam of infinite detail.
2D · spinSVG Fractal
Any shape (here a 5-point star) with its edges recursively replaced by a fractal rule (Koch, Césàro, Lévy-C…) — vector fractal stamping.
2D · spinJulia set
The escape-time fractal for z²+c at a fixed c — frozen swirls and dendrites; the connected cousin of the Mandelbrot set.
2D · spin3D fractals
Ray-marched worlds — the Mandelbulb and Mandelbox, Menger sponge, quaternion Julia sets, KIFS symmetry solids, and triply-periodic minimal surfaces.
Mandelbulb
The iconic 3D Mandelbrot analogue — a spherical-coordinate power map. Organic, bulbous, cauliflower-like surface detail.
3D · orbitMandelbox
A box-fold + sphere-fold iteration — a space-filling fractal of nested boxes and corridors; architectural and infinite.
3D · orbitMenger sponge
The 3D Cantor set — a cube recursively drilled with square holes on every face. Pure geometric lattice.
3D · orbitQuaternion Julia
A 4D Julia set sliced into 3D — smooth, liquid-metal lobes; sweep the slice (w) to morph the cross-section.
3D · orbitKIFS tetra
Kaleidoscopic IFS folded to tetrahedral symmetry — crystalline, snowflake-like 3D structure.
3D · orbitKIFS octa
Kaleidoscopic IFS with octahedral folding — eight-fold symmetric mineral growth.
3D · orbitKIFS cube
Kaleidoscopic IFS on a cubic lattice — boxy, circuit-like recursive scaffolding.
3D · orbitPseudo-Kleinian
An inversion-fold fractal evoking Kleinian limit sets — sparse, spread-out organic webbing across space.
3D · orbitSierpinski tetrahedron
The 3D Sierpiński gasket — a tetrahedron recursively subdivided into four; optionally twisted.
3D · orbitApollonian 3D
3D sphere-inversion packing — bubbles within bubbles filling space; the volumetric Apollonian gasket.
3D · orbitTPMS Schwarz P
A triply-periodic minimal surface (Schwarz Primitive) — a smooth, soap-film lattice partitioning space into two channels.
3D · orbitTPMS Gyroid
The gyroid minimal surface — a chiral, channel-weaving membrane found in butterfly wings and 3D-printing infill.
3D · orbitHybrid (Bulb↔Box)
A continuous blend between Mandelbulb and Mandelbox — dial the mix to morph from organic bulb to faceted box.
3D · orbitScopes — audio visualizers
A third category of render type. Instead of reacting to the sound, scopes draw the sound — the waveform, the stereo image, the frequency content, or the mathematical curve audio could be made to dance. See the Scopes feature page for the full walkthrough.
Oscilloscope
A true software oscilloscope of the captured audio — the raw waveform plotted as height against time. The most direct picture of a sound there is.
Scope · audioLissajous (X-Y)
A real vectorscope plotting the left audio channel against the right — a mono signal collapses to a diagonal, a wide stereo mix blooms into a cloud.
Scope · audioSpectrum
A frequency-bar (or curve) analyzer drawing the sound's energy at each pitch — bass left, treble right. Reuses the existing FFT.
Scope · audioHarmonograph
A mathematical recreation of the Victorian pendulum-drawing machine — a single damped sinusoid per axis. Pure math at draw time; every slider audio-bindable.
Scope · audioPick a shape. Add your sound.
Every type here reacts to audio, runs fullscreen, and exports to video, image, or vector.
Get Spiralyst Lab — $24.99/yr