Loading page
About this tool
Interactive real-time fractal generator exploring Mandelbrot, Julia sets, Koch Snowflake, Sierpinski Triangle, and Barnsley Fern with deep zoom controls.
The Fractal Generator draws five classic fractals in real time — the Mandelbrot set, a Julia set, the Sierpinski triangle, the Koch snowflake and the Barnsley fern — and shows the generating rule beside each one. It uses the method that actually defines each shape: escape-time iteration of z → z² + c for the Mandelbrot and Julia sets, the chaos game for Sierpinski, recursive middle-third replacement for Koch, and the four affine transformations of the Barnsley iterated function system. It is built for students and teachers who need to see how a single iteration depth changes the picture.
Open Fractal Generator on AltFTool — it loads instantly in your browser.
Choose one of the five buttons under Fractal Type — Mandelbrot Set, Julia Set, Sierpinski Triangle, Koch Snowflake or Barnsley Fern — and the card below names that fractal's formula, such as zₙ₊₁ = zₙ² + c.
Drag Iteration Depth anywhere between 20 and 150, pick Teal, Fire or Neon under Color Palette, and use Zoom In and Zoom Out to move the Zoom Depth readout between 0.5x and 100x.
The 480x360 canvas redraws immediately on every change, and its image label reports the fractal, zoom, palette and iteration depth; Reset in the header returns to the Mandelbrot Set at depth 60, 1x zoom and the Teal palette.
Each fractal is labelled with its generating formula and a one-line description, so the image and the maths stay connected.
Escape-time sets and iterated function systems are both included, which makes the difference between the two construction methods obvious.
Iteration depth controls escape iterations, chaos-game point counts and recursion levels alike, so a single control shows convergence across all five.
Five: the Mandelbrot set, a Julia set, the Sierpinski triangle, the Koch snowflake and the Barnsley fern. The Julia set uses the fixed constant C = -0.7 + 0.27015i, a value that sits just outside the Mandelbrot set and gives the familiar dendritic shape.
It runs from 20 to 150 and means something slightly different per fractal: for Mandelbrot and Julia it is the escape-iteration cap, for Sierpinski and the fern it multiplies the number of plotted points (150 and 200 points per unit respectively), and for Koch it sets the recursion level.
By repeatedly applying one of four affine transformations chosen at random with fixed probabilities — roughly 1% for the stem map, 85% for the main frond, and the remainder split between the two side leaflets. Each application produces one point, and the fern shape emerges from millions of them, never from a drawn outline.
Recursion is capped at a small number of levels so the render stays instant — past that point each extra generation quadruples the segment count for detail thinner than a pixel on the 480x360 canvas. Mathematically the boundary is infinite in length while enclosing a finite area.