What is the Mandelbrot set?

The Mandelbrot set is the set of complex numbers c for which the sequence z(n+1) = z(n)² + c does not diverge when iterated from z=0. Points inside the set are colored black; points outside are colored by how quickly they escape to infinity.

A Julia set uses the same iteration formula z(n+1) = z(n)² + c but holds c fixed and varies the starting point z. Every point on the complex plane either escapes or remains bounded, producing a fractal boundary. Different values of c produce wildly different shapes.

Why does increasing iterations improve quality?

Higher iteration counts give points more chances to escape before being classified as 'inside' the set. At deep zoom levels, low iteration counts misclassify many points, creating false solid regions. More iterations reveal fine boundary detail at the cost of rendering time.

How do I zoom in smoothly?

Scroll your mouse wheel over the canvas to zoom toward the cursor position. Click and drag to pan. Use the Reset View button to return to the starting coordinates centered on the full Mandelbrot set.

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Fractal Generator

Interactive Mandelbrot and Julia set fractal explorer with pan, zoom, and color palettes.

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Sobre esta ferramenta

The Fractal Generator renders the Mandelbrot set and Julia sets directly in your browser using an HTML5 Canvas. Drag to pan across the complex plane and scroll to zoom into infinite levels of detail, revealing the self-similar structure of these famous mathematical objects. Five color palettes — Classic, Fire, Ocean, Grayscale, and Neon — map iteration counts to vivid color gradients. An iteration depth slider controls quality: lower values render faster, while higher values reveal sharper detail at deep zoom levels. Switch between the Mandelbrot set and Julia sets (with adjustable C parameter) with one click. Use the Reset button to return to the default view.

Como usar

1 The Mandelbrot set renders automatically when the page loads.
2 Scroll to zoom in or out; drag to pan.
3 Select a color palette from the palette buttons.
4 Adjust the iteration slider to trade speed for detail.
5 Click Julia Set and drag the C point to explore Julia sets.
6 Click Reset View to return to the default view.

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