Fractal Generator Online - Mandelbrot, Julia Set & Zoom Explorer

How the Fractal Generator Works

This tool uses the escape-time algorithm. Each pixel is mapped to a complex number, then an iteration is run until the point either escapes beyond the chosen radius or reaches the iteration limit. Points that do not escape are colored as part of the set; escaped points are colored by how quickly they escaped.

Assumptions: this is an educational renderer, not arbitrary-precision math software. Very deep zooms eventually hit JavaScript floating-point precision limits.

Controls Explained

• View width: the width of the visible complex-plane window. Lower values zoom in.
• Iterations: maximum steps before a point is treated as bounded. Increase it for deep zooms and sharper boundaries.
• Escape radius: distance from the origin where a point is considered escaped. The usual Mandelbrot test can use radius 2; larger values are useful for smooth coloring and related fractals.
• Julia c: the fixed complex parameter used only for Julia sets. Small changes can radically change the image.
• Palette: affects only coloring, not the underlying mathematical set.

About Fractals and Complex Dynamics

Fractals are shapes with detail at many scales. The Mandelbrot set is one of the most recognizable examples because the simple rule z = z^2 + c produces a boundary with endlessly nested structure. The Julia set uses the same family of functions, but instead of varying c for each pixel, it fixes c and varies the starting point.

This page is designed for exploration: start with a preset, zoom into boundary regions, raise the iteration count when details become soft, and download images for notes, classroom slides, or personal artwork. All rendering is client-side, so your settings are not uploaded.

Good experiments to try

• Compare Mandelbrot and Julia with the same Julia c value.
• Zoom into the Mandelbrot boundary and increase iterations from 350 to 900.
• Switch palettes after rendering to see how coloring changes perception without changing the math.
• Use Burning Ship, then zoom near its lower edge to find vertical structures and miniature copies.

References & Further Reading

• Mandelbrot set - definition and escape criterion
• Mandelbrot Set - Wolfram MathWorld
• Julia set - complex dynamics background
• Burning Ship fractal - iteration formula

External links open in a new tab. Starlight Tools is not affiliated with those sites.

Fractal Generator FAQ

What fractals can I generate?

You can render Mandelbrot, Julia, Burning Ship, and Tricorn fractals. Each uses a related escape-time iteration in the complex plane.

What equation does the Mandelbrot set use?

For each complex point c, the Mandelbrot set starts with z = 0 and repeatedly applies z = z^2 + c. If the sequence remains bounded, the point is considered part of the set.

How is a Julia set different?

A Julia set keeps c fixed and uses each pixel as the starting z value. Try changing the Julia real and imaginary fields to see how much the shape changes.

Why does deep zooming get blurry or slow?

Deep zooms need more iterations and eventually exceed normal JavaScript floating-point precision. Raise iterations for modest zooms; for extreme zooms, arbitrary-precision renderers are better.

Can I download the image?

Yes. Use Download PNG to save the current canvas image. The image is generated in your browser.

Are my settings private?

Yes. Rendering, config export, and PNG download run locally. The share link stores settings in the URL hash, which you control.