Mandelbrot & Julia Explorer
Explore the Mandelbrot and Julia fractals in your browser. Click to zoom, tune iterations and the Julia constant, switch palettes, and export a PNG.
click to zoom in · 1.0× · 384×384 px
The Mandelbrot set
The Mandelbrot set is the set of complex numbers c for which the iteration z → z² + c (starting at z = 0) stays bounded forever. Points that never escape are drawn dark; points that escape are coloured by how fast they fly to infinity. Studied by Benoit Mandelbrot in 1980, its boundary is infinitely detailed — you can zoom forever and keep finding new structure.
Julia sets & the connection
A Julia set uses the same iteration, but c is a fixed constant and the starting z is the pixel. Each value of c gives a completely different Julia set. The deep link: a Julia set is connected exactly when its c lies inside the Mandelbrot set — so the Mandelbrot set is a “map” of all Julia sets. Slide the Julia constant near the Mandelbrot boundary to watch the shape transform.
How to explore
- Click the canvas to recenter on that point and zoom in 2×. Keep clicking to dive into the boundary.
- Max iterations controls detail: deeper zooms need more iterations to resolve fine filaments, at a linear cost in render time.
- Reset view returns to the full set; switching fractal type also resets the framing.
- Palettes use smooth (continuous) iteration colouring, so there is no harsh banding between bands.
About the rendering
Each pixel is computed with the escape-time algorithm and a smooth-colouring formula μ = n + 1 − log₂(log|z|) that turns the integer iteration count into a continuous value for gradient-free shading. Everything runs client-side on a 64-bit float, so extreme zooms eventually hit floating-point precision limits — the image turns blocky once you pass roughly 10¹³ magnification. The exported PNG captures exactly what you see.