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DE safety factor · lower = safer (no overshoot) but slower
0 = fog at camera · 1 = legacy · 3 = far horizon
Quaternion c = (a, b, c, d) drag to rotate
Fractal Power · Lyapunov
2.0 = classic · 3.0 = two bulbs · 4.0 = three-lobed star · fractional values morph between · for Newton this is the integer degree n
0 = pure Mandelbrot · ±0.5667 = canonical Phoenix · negative p inverts the feedback dragon
A = x-axis ratio · B = y-axis ratio · max 16 chars · also accepts r/l
Chaos Game
Fraction of the way each point jumps toward a random vertex. Around 0.5 fills the polygon; lower values open fractal gaps.
Formula Sandbox GLSL
A custom formula controls this fractal's iteration step.
Write the body of customIter(z, c); return next z as vec2. Available: cmul, cdiv, cpow, cexp, clog, csin, ccos, csqrt, cabs. Avoid unbounded loops (while(true) / for(;;)). GLSL can't time them out, so they may freeze the GPU; reload the tab to recover.
3D DE Sandbox GLSL
A custom formula controls this fractal's surface shape.
Write a body for float DE(vec3 p) returning distance to nearest surface. Default: Mandelbulb power 8. Variables in scope: p. Bounded loops are fine; avoid unbounded ones (while(true)). They can freeze the GPU, so reload the tab if it hangs.
Buddhabrot
Details
More samples = finer nebula detail (slower). v6.0.8: cap raised 4M → 10M for serious print-quality density work; cancel via the render pill if a high-sample run gets long.
Higher = remove fast-escaping boundary noise
Sample Bounding Box
Attractor Parameters
How the attractor's shape shifts as you adjust its coefficients.
These coefficients define the attractor's equations, and their labels change with the attractor type. Small changes near the defaults keep the shape recognizable; large ones can collapse or transform it.
Initial Conditions
Flame Studio 100 vars
Pre-Affine x′=ax+by+e
abe
cdf
▶Post-Affineoff
abe
cdf
Variations
palette sample
▶Xaos Matrixcross weights
Row=from, Col=to. 1=normal, 0=never
Render
Symmetry
↓ Import .flame (Apophysis/Fractorium) · drop or click
Render Quality
WebGPU: not initialized (toggle to enable)
Higher = more detail at deep zooms (slower).
Higher smooths boundary edges.
2× / 3× multiply render time (4× / 9× the pixels).
Shape Controls
Concentric rings or depth levels.
Rotational fold count
Lissajous Frequencies
Superformula (Gielis)
Spirograph
0 = derive from layer count · 0.1..0.9 = explicit ratio
0 = pure circle · 0.6 = canonical spirograph · >1 = looped petals
0 derives n from m+1; set n yourself for an asymmetric (m,n) pair
Truchet
0 = all type B · 0.5 = balanced (legacy) · 1 = all type A
Islamic Star {n/k}
0 = auto ⌊n/3⌋ (legacy) · 2 = pentagram-like · 3 = star · 4 = denser
Metatron's Cube
Fruit of Life
The densest way to pack spheres in 3D.
3D = the densest 3D sphere-packing nucleus (1 center + 12 cuboctahedron vertices). Buckminster Fuller called this the "Vector Equilibrium". The 2D figure is its hexagonal projection.
Egg of Life
Eight spheres touching at a shared center point.
3D = 8 spheres at cube vertices, all touching at the body-center (Drunvalo Melchizedek's canonical 3D Egg).
Flower of Life
Nineteen spheres stacked in one tightly packed layer.
3D = the canonical 19-sphere figure as a single hex-close-packed layer; rotation reveals the lattice structure.
Fibonacci Lattice / Sphere
Points spread evenly across a sphere's surface.
3D = N points on the unit sphere via golden-angle spiral. Used in cosmology, ML embedding init, and irradiation modeling for its near-uniform spherical distribution.
Phyllotaxis (sphere)
The same spiral spread as the Fibonacci sphere, with an adjustable angle.
3D = same construction as Fibonacci sphere, but tunable: 137.508° = uniform · 137.4° / 137.6° = visible parastichy bands. Phyllotaxis panel above controls angle + dot size.
Vesica Piscis
Off = nested rosette of S.layers pairs (decorative)
Hyperbolic {p,q}
Need 1/p + 1/q < 1/2. {7,3}, {6,4}, {8,3}, {5,4} all work.
Shifts the pattern between a solid interior and a torn, fractal edge.
μ ≈ 1.5+0.5i = quasi-Fuchsian interior (default). 1.91+0.05i = near the real-axis Apollonian cusp. 2+0i = Apollonian cusp. 0+2i = degenerate vertical cusp. Below the discreteness boundary the limit set tears apart.
Polyhedron Display
Off = wireframe (default). On = depth-sorted faces with Z-fade.
4D Projection
Two ways to flatten a 4D shape into 3D · pick whichever reads more clearly for this shape.
Schlegel = the classic nested "cube-in-cube" edge graph (flattens one cell to a frame) · Stereographic = round pole-projection from the 4-sphere. Simple convex polytopes open in Schlegel; the dense 120/600-cell and star polytopes open in stereographic. (Also reachable via ?schlegel.)
Modulates auto-rotation through the xw / zw planes when geometry animation is on.
Torus Knot (p, q)
How many times the knot winds around the tube before it closes.
p comes from the Layers slider · (2,3) = trefoil · (2,5) = cinquefoil · (3,4)/(3,5) = denser knots · gcd(p,q)>1 yields a torus link
Quasicrystal
Symmetry with no repeating tile, the same idea as a Penrose tiling.
A custom shader formula controls this pattern's shape.
GLSL ES 3.00 · return a vec2. Available: z (vec2 input), cmul(a,b), cdiv(a,b), u_N (int), u_rot, u_tau (vec2). The formula is checked before it reaches the shader, and it needs WebGL2 (there is no CPU fallback).
Colors show the complex function's phase and magnitude directly.
Phase plot of f:ℂ→ℂ. Hue = arg f(z), brightness = log|f(z)|. Zeros are black rosettes; poles white rosettes; essential singularities Picard-chaotic. Degree applies to zn − 1 and Blaschke; rotation feeds Möbius/Blaschke. SSAA smooths branch cuts at N²× cost. Auto-rotate animates the function-parameter rotation (Möbius / Blaschke a-points). 3D lift renders a height-mapped Riemann surface; drag to rotate, height = log1p|f(z)|. Reference: Wegert 2012.
Composite Polyhedron
Renders two named solids simultaneously.
Gray-Scott Parameters
Feed and kill rates shape spots, stripes, or other reaction-diffusion textures.
Controls that keep the pattern inside its stable, lifelike range.
μ = preferred density · σ = growth width · R = kernel size. Lenia lives in a narrow band; these ranges stay inside it.
Gierer–Meinhardt Decay
Balances spot versus stripe patterns in the reaction-diffusion simulation.
Activator (μₐ) / inhibitor (μₕ) decay, the spot-vs-stripe balance. Gierer–Meinhardt lives in a narrow band near these defaults: lower μₐ → bolder blobs, higher μₕ → finer texture.
Spectre Monotile
0 = the straight-edged Tile(1,1) · higher = more strongly curved edges, which still fit their neighbours
Mandala
Offsetting alternate bands is what makes the pattern interlock rather than align.
Alternates with the motif above, position by position. An odd count leaves one seam.
A heavy outer border around fine inner bands is most of what reads as intricate.
Radial ties running inward to the next band. 0 leaves the gap open.
Blends each element toward its cardinal color: white east, yellow south, red west, green north. Applies to every band.
L-System Preset
Axiom
Rules one per line: X = production
Turtle: F/G draw forward · +/− turn · [/] push/pop. Try axiom F, rule F=F[+F]F[-F]F, angle 25.7° for a tree.
Stroke & Fill
Set either to 0 for a fill-only silhouette
Solid: one unbroken stroke.
Dash tuning
Scales the preset above. Gap at 0 renders solid.
Slides the dash along the path to register marks against vertices. Keyframeable in Motion Studio.
Round: each mark ends in a semicircle. Extends every mark by half the line weight at both ends.
Round: corners are arcs. Softest, and the safest at heavy line weights.
Off: draw strokes only.
This pattern draws strokes only, so fill has no effect on it.
Nonzero: any region the path winds around is filled. Overlaps read as one solid body.
How overlapping fills combine. Multiply turns overlap into structure.
Luminous bloom · 0 disables
Off: hide the concentric-circle and spoke overlay.
Picks which property of an element controls its color.
Which property of an element picks its color. Its warp, repeat, and phase live in Color Mapping below; the generator parameters live in Field Generators.
Mirror
N-fold reflective symmetry · 1 = off
Rotation & Recording
Time-evolution playback
Drag the iteration slider to scrub · ⏸ pause / ▶ play · ⏭ steps one when paused · ⏮ resets to seed
Palette
Gradient Editor
α 1.00
Import
Color Tuning
Step 2 of the color chain. This panel holds Palette, Palette Repeats and Offset; the step's Warp, Repeat and Phase controls are in Color Mapping.
Cycles color offset automatically
Coloring Algorithm
Smooth: continuous gradient across iteration count (no banding). Fast and visually clean.
Color Mapping
Steps 3 to 5 of the color chain: Warp, Repeat, Phase. Palette Repeats and Offset are step 2 in Color Tuning. The Source stage, the generator parameters, is shared with Opacity Field.
Field Generators
Shared settings for the generators used elsewhere in this panel.
Parameters for the Banded, Noise, and Gradient generators. Each one applies wherever that generator is selected, in Color Mapping or Opacity Field.
Color rings and transparency rings can now have different periods.
Opacity Field
Varies transparency across the image. Stroke applies everywhere; Fill applies to filled geometry only.
Stroke
Shared by both halves. Only Power, Exponential and Gain read it.
Fill
Post-FX
Bloom
TonemapACES
Vignette
Film Grain
Chroma Shift
LUT (.cube)—
Drop a .cube file here, or click to browse.
Seed
Each seed deterministically picks a starting view · same number reproduces the same image · share the URL or the seed to share the view.
Layer Studio
Editing Layer 1
100%
%
%
×
°
Data Seed
Real-world data can drive several parameters at once instead of a fixed seed.
Drive renderer parameters from real-world data: date/time, sun & moon position, pasted text, image / audio files. Each source feeds multiple knobs (palette, iteration, rotation, …) for richer output than a plain integer seed. Everything is computed locally; nothing leaves your browser.
No data fetched.
Construction
Actions
Gallery
No saved works yet
Bookmarks
Motion Studio
Templates
The first keyframe is the animation start. Duration and easing apply to the transition into each following keyframe.
Easing Curve
0.0 / 0.0s
Export
Export Artwork
Renders at the current view · Post-FX applies to all raster exports
Screen & web · up to 4K
Format
PNG
Lossless · best quality
WebP
Compressed · smaller file
JPEG
Compressed · universal
TIFF
16-bit · archival · print
GIF
Still image · 256 colors
Resolution
Match canvas
860 px
2048 px
4K
Custom…
Custom size (100–16384 px)
× px
Gallery prints · DPI, tiling, up to 32K
Sizing Mode
Pixel
Physical · DPI
Output Size
4K
8K
16K
24K
32K
Custom…
Custom size (512–32768 px)
× px
Preset
8×10″
11×14″
16×20″
24×36″
36×48″
A4
A3
A2
A1
A0
12×12″
24×24″
Phone Pro Max
4K UHD
8K UHD
Custom…
Custom dimensions (0.5–200)
×
DPI
72
150
200
300
400
600
Supersample
1× (Direct)
2× (Lanczos)
3× (Lanczos)
Render at the target resolution.
Fractal Compose (non-square only)
Letterbox
Extend
Render the fractal at the inscribed square; pad with bg color. What you composed on screen is what hangs on the wall.
Pixels: 4800 × 6000 · Aspect 4:5
3D Projection
Perspective
Equirectangular (2:1)
Format
PNG
Lossless · DPI · metadata
TIFF
16-bit · archival
EXR
Half-float · VFX intermediate
Post-FX Preview
Renders tiled · pHYs DPI stamped · State URL embedded in PNG tEXt
Output Size
Preset
Full color strokes and fills
Clean <path> elements · raster-field patterns export as PNG instead
Rendering…
Catalog
Gallery
Your gallery is empty
Compose a piece you love. Then press Save in the right panel (Output tab) to keep it here.