Fractal Explorer - Online Mandelbrot Set Renderer
A fractal is a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole. This tool renders three classic fractals in real-time using HTML5 Canvas.
What is the Mandelbrot Set?
The Mandelbrot Set is one of the most famous fractals, discovered by Benoit Mandelbrot in 1980. It is defined by the iterative complex equation z ← z² + c, where both z and c are complex numbers. Points c for which the iteration remains bounded belong to the set. Its boundary exhibits infinitely intricate detail at every scale.
Julia Sets vs Mandelbrot
Julia Sets use the same iteration formula but with a key difference: the Mandelbrot set fixes z₀=0 and varies c, while Julia sets fix c and vary z₀. Thus the Mandelbrot set can be seen as a "catalog" of all possible Julia sets.
Tips for Exploring
- Click to zoom: Click anywhere to zoom in on that point
- Drag to select: Drag a rectangle to zoom to that area
- Scroll to zoom: Use scroll wheel for smooth zooming
- Higher iterations: More iterations reveal finer detail but take longer
FAQ
What is a fractal?
A fractal is a geometric shape that exhibits self-similarity at different scales. Mathematically, fractals have fractional dimensions. Visually, they display infinitely nested complex structures.
Why is the Mandelbrot set black?
The black interior represents points where the iteration remains bounded. The colored exterior shows the speed of divergence. The black region contains infinitely fine detail that reveals more fractal structures when zoomed.
What is the Burning Ship fractal?
The Burning Ship is a variation of the Mandelbrot set where the absolute value of each component is taken at each iteration step. It produces a unique shape resembling a burning ship.
Are fractals used in real life?
Yes! Fractals are used in computer graphics (terrain, clouds, textures), astronomy (galaxy distribution), biology (plant growth, blood vessels), and finance (market analysis).