Fractal Tools
Draw recursive geometry, space-filling curves, mathematical sets and exportable generative artwork locally in your browser.
Popular tools
IFS Renderer and Explorer
IFS Renderer workspace with an editable transform table, deterministic live rendering, Barnsley fern presets and SVG, PNG or JSON export.
Mandelbrot Power Morph Explorer
A specialized Fractal Studio mode for morphing Mandelbrot or Julia powers with live preview, animation export and reproducible JSON.
Draw a Dendrite Fractal
Draw a branching dendrite with configurable recursive angles, ratios, colors and export formats.
Draw a Canopy Fractal
Generate an asymmetric recursive canopy tree using controlled branch geometry.
Draw a Flowsnake Fractal
Render a Gosper flowsnake curve from its exact L-system replacement rules.
Draw a Hilbert Fractal
Draw a continuous Hilbert space-filling curve from recursive L-system instructions.
Draw a Heighway Fractal
Generate the classic Heighway dragon curve using deterministic folding rules.
Draw a Koch Fractal
Generate the Koch snowflake curve with accurate recursive segment replacement.
Draw a Sierpinski Fractal
Render a Sierpinski triangle curve from validated recursive geometry.
Draw a Cantor Fractal
Visualize recursive Cantor-set interval removal as a layered drawing.
Draw a Pythagoras Fractal
Build a Pythagoras tree from recursively rotated and scaled squares.
Mandelbrot Set Generator
Explore and render the Mandelbrot set with smooth coloring, deep zoom, panning and supersampling.
Escape-Time Sets
Coloring & Styling
Burning Ship Fractal Generator
Explore the Burning Ship set using absolute complex components and smooth escape coloring.
Fractal Palette Generator
Build interpolated palettes for compatible fractals.
Apply Gradient to Fractal
Create a reusable gradient for fractal rendering.
Smooth Escape-Time Coloring
Preview palettes for continuous iteration coloring.
Histogram Fractal Coloring
Prepare palettes for histogram-equalized coloring.
Magnet Fractal Generator
Render a rational Magnet fractal with configurable plane position and color palette.
Distance Estimation Coloring
Design gradients for distance-estimated boundaries.
Orbit Trap Coloring
Create palettes for orbit-trap coloring workflows.
Interior Fractal Coloring
Style fractal interior regions independently.
Fractal Palette Remapper
Remap fractal colors into a custom gradient.
Fractal Background and Edge Styler
Coordinate background, boundary and gradient colors.
Analysis & Measurement
Newton Fractal Generator
Visualize Newton-method convergence basins for complex polynomial roots.
Estimate Fractal Dimension
Estimate dimension from occupied boxes across multiple grid scales.
Box-Counting Dimension Calculator
Calculate a log-log box-counting regression from image pixels.
Fractal Complexity Analyzer
Report boundary-to-area structural complexity.
Fractal Convergence Analyzer
Measure escape iteration behavior across a complex-plane sample.
Draw a Peano Fractal
Render a Peano-style space-filling curve with safe complexity limits.
Draw a Dust Fractal
Visualize a two-dimensional Cantor dust construction with recursive intervals.
Fractal Self-Similarity Analyzer
Measure multiscale occupancy as evidence of self-similarity.
Fractal Iteration Analyzer
Analyze generated or uploaded fractal structure across scales.
Fractal Area Estimator
Estimate occupied fractal area from decoded pixels.
Fractal Perimeter Estimator
Estimate boundary length using pixel-neighborhood transitions.
Advanced Complex Fractals
Custom Escape-Time Fractal
Build a controlled power-and-coefficient escape-time formula without unsafe code execution.
Complex Function Fractal Explorer
Explore sine, cosine and exponential complex functions through an interactive escape-time renderer.
Nova Fractal Generator
Generate Nova fractals from relaxed Newton iteration with a complex perturbation.
Phoenix Fractal Generator
Render the Phoenix recurrence using the previous complex iteration state.
L-Systems, IFS & Recursive Geometry
L-System Fractal Generator
Build and render classic Lindenmayer systems with safe turtle commands.
Custom L-System Designer
Define axioms, production rules, angles and recursion depth.
Barnsley Fern Generator
Generate a Barnsley fern from weighted affine transformations.
IFS Fractal Generator
Render weighted iterated function systems locally.
Custom IFS Editor
Edit affine coefficients and weights for a custom IFS.
Sierpinski Chaos Game
Construct a Sierpinski triangle using midpoint sampling.
Fractal Tree L-System Generator
Grow a branching tree from an L-system grammar.
Plant Fractal Generator
Create botanical forms using bracketed turtle states.
Chaos Game Generator
Plot reproducible chaos-game point sets.
Dragon Curve L-System Generator
Render the Dragon curve using L-system substitution.
Recursive Polygon Fractal Generator
Place scaled child polygons recursively on vertices.
Recursive Shape Fractal Generator
Explore reusable recursive shape geometry and SVG export.
Flames & Density Fractals
Fractal Flame Generator
Render density-weighted flames from affine transforms.
Random Fractal Flame Generator
Create reproducible seeded random flame transforms.
Fractal Flame Variation Explorer
Explore seven nonlinear flame variations.
Apophysis-style Flame Generator
Design Apophysis-inspired weighted fractal flames.
Density Plot Fractal Generator
Accumulate orbit samples into logarithmic density plots.
Buddhabrot Generator
Generate an actual escaped-orbit Buddhabrot density image.
Nebulabrot Generator
Create a multichannel Nebulabrot orbit-density image.
Symmetric Flame Generator
Generate rotationally symmetric density flames.
IFS Flame Generator
Combine IFS transforms and nonlinear flame variations.
Orbit Trap Fractal Generator
Render orbit-driven generative density forms.
Zoom, Parameters & Animation
Fractal Color Cycling
Generate palettes for animated color cycling.
Fractal Zoom Explorer
Explore escape-time fractals with reproducible zoom and center settings.
Deep Zoom Mandelbrot Explorer
Explore Mandelbrot detail up to the safe precision limit of browser numbers.
Julia Parameter Explorer
Explore Julia sets by changing their real and imaginary constants.
Mandelbrot–Julia Relationship Explorer
Move through Mandelbrot space and update the corresponding Julia set live.
Create Fractal Zoom Animation
Create an eased fractal zoom as a numbered PNG sequence.
Create Fractal Color Animation
Create a palette-cycling fractal frame sequence.
Fractal Keyframe Animator
Interpolate reproducible fractal settings between animation keyframes.
Tricorn Fractal Generator
Render the antiholomorphic Tricorn set using conjugated complex iterations.
Biomorph Fractal Generator
Create biomorph forms with component-based complex escape testing.
Fractal Parameter Sweep Generator
Generate a contact sheet across zoom and power parameters.
Animate Fractal Parameters
Generate reproducible parameter-transition frame sequences.
Create Fractal Morph Animation
Morph fractal power parameters across real rendered frames.
3D Fractals & GPU Rendering
Mandelbulb Generator
Ray-march a Mandelbulb using a WebGL2 distance estimator.
Mandelbox Generator
Ray-march a folded Mandelbox with WebGL2 and CPU fallback.
3D Julia Fractal Generator
Render a three-dimensional Julia-style distance field.
Fractal Ray Marcher
Preview distance-estimated fractal surfaces using WebGL2 ray marching.
Quaternion Julia Generator
Render a quaternion-inspired Julia surface preview.
3D IFS Fractal Generator
Render a three-dimensional IFS-inspired fractal surface.
Procedural Textures & Export
Fractal Noise Texture Generator
Generate seeded fBM, ridged, turbulence and warped textures.
Fractal Terrain Heightmap Generator
Generate a deterministic grayscale terrain heightmap.
Seamless Fractal Texture Generator
Create a tileable deterministic procedural texture.
Fractal SVG Exporter
Prepare compatible fractal artwork for scalable export workflows.
Fractal Studio
Curves & L-Systems
Draw a Morton Fractal
Create a Morton-order space-filling Z curve with bounded iteration depth.
Draw Heighway Twins Fractal
Render two mirrored Heighway dragon curves in one balanced composition.
Draw a Triangle Dragon Fractal
Draw a triangular dragon curve from repeated angular substitutions.
Draw a Moore Fractal
Render a closed Moore space-filling curve using paired recursive symbols.
Draw a Levy Fractal
Generate the Levy C curve through repeated 45-degree substitutions.
Trees & Recursive Geometry
Draw a V-Fractal
Create a recursive V-shaped branching fractal with adjustable angle and branch ratio.
Draw a Frosty Fractal
Create a crisp frost-like recursive curve with configurable styling.
Draw a T-Square Fractal
Generate the recursive T-square construction with filled or outlined geometry.
Draw a Hausdorff Fractal
Visualize recursively scaled cross geometry associated with Hausdorff constructions.
Recursive Sets & Flakes
Draw a Triflake Fractal
Create a recursive three-sided flake with vector and raster export.
Draw a Pentaflake Fractal
Create a recursive five-sided flake with configurable fill and stroke styling.
Draw a Hexaflake Fractal
Create a recursive six-sided hexaflake at a safe bounded depth.
Draw a Multiflake Fractal
Generate a many-sided recursive flake with shared geometry controls.