Fractal gallery

Every shape Spiralyst Lab can draw

33 render types in four families: 27 fractals (14 in 2D, 13 in 3D), 4 scopes that draw the sound itself, and 2 3D flows that send tens of thousands of particles through real fluid mathematics. 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. See the 2D fractals feature page for the full walkthrough.

Archimedean

The classic arithmetic spiral — arms spaced a constant distance apart. Even, clockwork winding; the most 'engineered' of the spirals.

2D · spin

Logarithmic

The growth spiral of nautilus shells and galaxies — each turn scales by a fixed ratio, so it looks self-similar at every zoom.

2D · spin

Fermat

A parabolic spiral winding symmetrically both ways from the center, weaving a tight rosette of interleaved arms.

2D · spin

Hyperbolic

An inverse spiral (r = a/θ) rushing in from infinity toward a central asymptote — dense at the rim, vanishing at the core.

2D · spin

Phyllotaxis

The sunflower-seed pattern — points placed at the golden angle (137.5°) so florets pack with no gaps. Nature's optimal spiral.

2D · spin

Rose (coiled)

A rose curve wound outward into a coil — petals (k) multiplied by a growing radius give a layered, blooming spiral.

2D · spin

Multi-arm

Several logarithmic spirals sharing a center, evenly rotated — a pinwheel / galaxy-arm motif.

2D · spin

Fractal phyllotaxis

Phyllotaxis within phyllotaxis — each seed of an outer golden-angle pattern carries its own miniature spiral cluster.

2D · spin

Fractal rose

A recursive rose: each petal tip sprouts a smaller rose, branching into a self-similar floral fractal.

2D · spin

Pythagoras 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↔1.20

Recursive log spiral

Logarithmic spirals branching off logarithmic spirals — an organic, fern-like recursive curl.

2D · spin

Apollonian gasket

A packing of mutually tangent circles, each gap filled by ever-smaller circles (Descartes' theorem) — a foam of infinite detail.

2D · spin

SVG 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 · spin

Julia set

The escape-time fractal for z²+c at a fixed c — frozen swirls and dendrites; the connected cousin of the Mandelbrot set.

2D · spin

3D fractals

Ray-marched worlds — the Mandelbulb and Mandelbox, Menger sponge, quaternion Julia sets, KIFS symmetry solids, and triply-periodic minimal surfaces. See the 3D fractals feature page for the full walkthrough.

Mandelbulb

The iconic 3D Mandelbrot analogue — a spherical-coordinate power map. Organic, bulbous, cauliflower-like surface detail.

3D · orbit

Mandelbox

A box-fold + sphere-fold iteration — a space-filling fractal of nested boxes and corridors; architectural and infinite.

3D · orbit

Menger sponge

The 3D Cantor set — a cube recursively drilled with square holes on every face. Pure geometric lattice.

3D · orbit

Quaternion Julia

A 4D Julia set sliced into 3D — smooth, liquid-metal lobes; sweep the slice (w) to morph the cross-section.

3D · orbit

KIFS tetra

Kaleidoscopic IFS folded to tetrahedral symmetry — crystalline, snowflake-like 3D structure.

3D · orbit

KIFS octa

Kaleidoscopic IFS with octahedral folding — eight-fold symmetric mineral growth.

3D · orbit

KIFS cube

Kaleidoscopic IFS on a cubic lattice — boxy, circuit-like recursive scaffolding.

3D · orbit

Pseudo-Kleinian

An inversion-fold fractal evoking Kleinian limit sets — sparse, spread-out organic webbing across space.

3D · orbit

Sierpinski tetrahedron

The 3D Sierpiński gasket — a tetrahedron recursively subdivided into four; optionally twisted.

3D · orbit

Apollonian 3D

3D sphere-inversion packing — bubbles within bubbles filling space; the volumetric Apollonian gasket.

3D · orbit

TPMS Schwarz P

A triply-periodic minimal surface (Schwarz Primitive) — a smooth, soap-film lattice partitioning space into two channels.

3D · orbit

TPMS Gyroid

The gyroid minimal surface — a chiral, channel-weaving membrane found in butterfly wings and 3D-printing infill.

3D · orbit

Hybrid (Bulb↔Box)

A continuous blend between Mandelbulb and Mandelbox — dial the mix to morph from organic bulb to faceted box.

3D · orbit

Scopes — 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 · audio

Lissajous (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 · audio

Spectrum

A frequency-bar (or curve) analyzer drawing the sound's energy at each pitch — bass left, treble right. Reuses the existing FFT.

Scope · audio

Harmonograph

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 · audio

3D Flows — fluid motion

A fourth category of render type. Fractals are shapes; flows are motion. Each scene starts from the mathematics of how a fluid moves and sends up to 60,000 glowing particles through it in full 3D, on the same orbit camera as the fractals. See the 3D Flows feature page for the full walkthrough.

The Navier–Stokes vortex: a bright yellow jet rising from the axis above a wide spinning disc of particles shading from green at the centre through blue to violet at the rim.

Navier–Stokes vortex

A vortex from the frontier of mathematics — the shape of a fluid that spins itself up to infinite speed in finite time, beside two exact whirlpools that help explain it.

Flow · particles
The waterfall coloured by speed: a pale blue river reaching the lip, the falling sheet warming from violet to orange, and a violet pool sweeping away below with faint mist arcs.

Waterfall

A waterfall, solved rather than drawn. The river draws down toward the lip, the sheet thins as it falls, and the hydraulic jump where it lands is computed from the flow itself.

Flow · particles

Pick a shape. Add your sound.

Every type here reacts to audio, runs fullscreen, and exports to video, image, or vector.

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