fracgenSmall shape. Infinite possibility.
Turn a simple line into a fractal. Draw, repeat, and make it yours.
A little inspiration
Start with a shape. Take it somewhere new.
A world of fractals
Explore familiar classics and find a new favorite.
No matching fractals. Try another name or choose all families.
About the 32 included fractals
- Mandelbrot set
- Square a complex number, add its starting point, and find the boundary between escape and stability. Reference
- Julia set
- Explore the filled quadratic Julia set for c = −0.8 + 0.156i. Reference
- Douady rabbit
- A quadratic Julia set with three connected lobes, using the period-three rabbit parameter. Reference
- Burning Ship
- Taking absolute values before squaring creates a jagged, ship-like escape boundary. Reference
- Tricorn
- Complex conjugation turns the Mandelbrot rule into a three-cornered parameter set. Reference
- Cubic Multibrot
- Cube instead of square: z becomes z³ + c, creating a two-lobed parameter set. Reference
- Newton basins
- Color starting points by the cube root of one reached by Newton’s method. Reference
- Koch snowflake
- Replace each triangle edge with four smaller edges to grow a snowflake. Reference
- Koch curve
- A single line sprouts a triangular bump, then every new edge repeats the rule. Reference
- Minkowski curve
- Eight right-angle segments replace every line segment, forming a winding square-grid curve. Reference
- Quadratic Koch island
- Apply the eight-segment square-grid Koch rule around a closed square. Reference
- Heighway dragon
- Repeated right-angle paper folds unfold into the interlocking dragon curve. Reference
- Lévy C curve
- Replace each segment with two sides of an isosceles right triangle. Reference
- Hilbert curve
- Four rotated copies weave a continuous path through an increasingly fine square grid. Reference
- Peano curve
- A continuous path snakes through nine smaller squares at each refinement. Reference
- Gosper curve
- Seven smaller curves wind across a hexagonal grid to form the flowsnake. Reference
- Sierpiński arrowhead
- A continuous triangular path approaches the Sierpiński gasket as it repeats. Reference
- Terdragon
- Three segments with 120-degree turns fold into a triangular dragon curve. Reference
- Moore curve
- Four connected Hilbert curves form a closed loop that fills a square in the limit. Reference
- Sierpiński triangle
- Remove the middle triangle, then repeat inside each of the three remaining triangles. Reference
- Sierpiński carpet
- Divide a square into nine parts and repeatedly remove the middle one. Reference
- Cantor set
- Remove the middle third of every interval. Each row shows the next construction step. Reference
- Cantor dust
- Keep the four corner squares: the two-dimensional product of the Cantor set. Reference
- Vicsek fractal
- Keep a square’s center and four corners, then repeat this five-square pattern. Reference
- T-square
- Add half-size squares at every corner, keeping all earlier squares in the growing union. Reference
- H-tree
- Attach a half-size H at each of the four endpoints of the previous H. Reference
- Pythagoras tree
- Build two smaller squares on a right triangle above every parent square. Reference
- Pentaflake
- Five small pentagons surround a reversed central pentagon, repeating at the golden-ratio scale. Reference
- Hexaflake
- Replace a hexagon with six corner hexagons and one center hexagon, each one-third size. Reference
- Binary fractal tree
- Every branch splits into two shorter branches at fixed angles. Reference
- Barnsley fern
- Four weighted affine transformations scatter points into a fern, using the original fern coefficients. Reference
- L-system plant
- A branching rewrite rule grows a plant with repeated stems and paired shoots. Reference
A growing collection of named constructions. Fractals have infinitely many variations, so no finite library includes them all.
Your shape, on repeat.
FracGen is a free fractal generator for curious minds. Start with a line, bend it into a simple pattern, and replace every segment with a smaller copy. A small triangle becomes a Koch snowflake. A few square steps become an intricate crystal.
Explore Mandelbrot and Julia sets, Sierpiński patterns, space-filling curves, and branching trees in the library. Zoom into the details or watch a pattern build, then save a still image or an animation.
Do I need to know any math?
No. Start with a preset or drag the points in the editor. Your fractal updates as you move. Each library example has a short explanation.
Can I save a fractal animation?
Yes. Choose a smooth or step-by-step zoom and a length from 1 to 30 seconds, then export a looping GIF or MP4 video. Zooms move at a steady speed, so a longer animation travels deeper. MP4 requires a browser with video encoding support. Custom line drawings also export as SVG, and all designs export as PNG.
Can I edit a library fractal?
Yes. Open any fractal in the library and choose Open in studio. Line-based ones, like the Koch curve and Lévy C curve, become points you can drag. The rest keep their own rule and use the studio's detail, color, zoom, animation, and download controls.
Are my drawings uploaded anywhere?
No. Drawing, fractal generation, and exports happen in your browser. No account is needed. Download your design before leaving the page.
How deep can I zoom?
Zooms keep a steady speed, so a longer animation goes deeper. The studio redraws fractals at each zoom level, revealing new detail, until a practical limit set by the construction and numerical precision. The animation settings show how deep the current design goes and when it reaches that limit.