Math

Fractal Generator

Details

How to use Fractal Generator

What the tool does, how to run it, and what to expect from the result.

How to generate a fractal image

Choose a fractal. Mandelbrot and Julia are escape-time sets rendered pixel by pixel, so they give you iteration, zoom, and base hue controls. Sierpinski and Koch are recursive constructions, so they give you depth and a single color instead.

If a zoomed Mandelbrot looks like a featureless blob, raise the iterations rather than the zoom. The blackness means points have not yet escaped within the budget you gave them.

  • Pick Mandelbrot, Julia, Sierpinski, or Koch.
  • For Mandelbrot or Julia, set iterations (up to 500), zoom (0.5x to 40x), and the base hue.
  • For Sierpinski or Koch, set the recursion depth (0 to 8) and the color.
  • Raise iterations whenever a deeper zoom turns black.
  • Press Download PNG to save the 640 x 640 canvas.
Tips

Getting a better result out of Fractal Generator

Specific settings and thresholds, not general advice.

  • Mandelbrot and Julia are escape-time fractals: every one of the 640 x 640 pixels is iterated through z = z^2 + c until it escapes a radius of 2 or hits the iteration cap. The color you see encodes how many iterations that took, which is why raising iterations reveals filaments that were solid black before.
  • The iteration slider tops out at 500. Zoom in far and 120 iterations is not enough: the boundary detail collapses into a black blob because points that would eventually escape have not yet done so. Push iterations up before you blame the zoom.
  • The Julia set here uses the fixed constant c = -0.7 + 0.27015i, which is the classic dendrite-like Julia. Changing c is what produces the whole family of Julia shapes, and this tool does not expose it.
  • Sierpinski and Koch are recursive constructions, not escape-time sets, so they use recursion depth (0 to 8) rather than iterations. Depth 8 for Sierpinski means 3^8 = 6561 triangles; Koch at depth 8 means 4^8 = 65,536 segments per side. That is why the cap is 8.
  • The canvas is a fixed 640 x 640, and Download PNG saves exactly that. There is no way to render at a higher resolution for print.
Limits

What Fractal Generator does not do

The honest boundary, so you do not lose time finding it yourself.

  • Fixed 640 x 640 output. No resolution control and no higher-resolution export.
  • The view is centred and fixed. Zoom scales about the centre; you cannot pan to an arbitrary point of the Mandelbrot set.
  • The Julia constant c is hardcoded at -0.7 + 0.27015i and cannot be changed.
  • Coloring is a single hue-rotation scheme. There is no palette editor, no smooth (continuous) coloring, and no orbit traps.
At a glance

Who Fractal Generator is for

A quick way to understand who this helps, what it solves, and where it connects next.

Best fit

Anyone rendering fractal art.

Ideal for

Using the fractal generator without installing anything or signing up.

FAQ

Common questions

Short answers for the questions people usually have before trying a utility like this.

Why does the Mandelbrot go black and featureless when I zoom in?

You have run out of iterations. Deep in the set's boundary, points take many more iterations to escape, and any point that has not escaped by the cap is painted as interior black. Raise the iterations slider toward 500 and the structure comes back. This is the single most common misunderstanding about zooming into fractals.

What is the difference between the Mandelbrot and the Julia set?

Both iterate z = z^2 + c. For the Mandelbrot, c is the pixel's coordinate and z starts at 0. For a Julia set, c is a fixed constant and z starts at the pixel's coordinate. So there is one Mandelbrot set, and a different Julia set for every value of c. The Mandelbrot is effectively a map of which c values give connected Julia sets.

Why can I only zoom to 40x?

Because the math runs in double-precision floating point, and beyond a certain zoom the pixel spacing falls below what a double can represent, so the image degrades into blocky artefacts. Deep zooms into the Mandelbrot need arbitrary-precision arithmetic and perturbation techniques, which are far heavier than a per-pixel loop on the main thread.

Why is the recursion depth capped at 8?

Because the work grows exponentially. Sierpinski triples its triangle count each level (3^8 = 6561 at depth 8) and Koch quadruples its segments (4^8 = 65,536 per side). Depth 12 would be thousands of times more work for detail finer than a pixel.

Can I use the download as wallpaper or print it?

The PNG is exactly 640 x 640, which is fine for a small web image but too small for a phone wallpaper at native resolution, and well short of print. There is no higher-resolution export.

What does the base hue slider actually do?

It rotates the starting point of the color ramp. The hue for each pixel is the base hue plus 300 degrees times the fraction of the iteration budget the point survived, so moving the base hue shifts the whole banding pattern around the color wheel without changing the underlying math.

Recommendations

You Might Also Like

Nearby tools from the catalog that fit the same job or workflow.

Cleanor app

Do it all on your device

Cleanor puts these tools in one app: compress and convert images, video, and audio, work with PDFs, and scan text right on your device. Plus free up storage and clear inbox clutter with Email Cleaner. Start with a free trial.

  • iPhone
  • Android
  • Macsoon
  • Windowssoon