Labs / Mathematics
Mandelbrot Explorer
Every colored pixel asks the same question: starting from zero, does repeatedly applying z → z² + c stay bounded, or race off to infinity? Click to dive into the fractal boundary, box-drag to frame a region, and glide your pointer around to see the Julia set that belongs to the point c beneath it.
center —zoom 1.0×n —
What to try
- Zoom into a fjord along the black boundary. Do the shapes ever stop repeating, or keep going forever?
- Drag the pointer just inside the black set versus far outside it. How does the Julia set's shape change?
- Zoom deep, then raise the max iterations. Why does new detail suddenly appear where there was only flat color?
- Hunt for a tiny black "mini-Mandelbrot" far from the main body. How much do you have to magnify to find one?
- Watch the cursor's iteration count as you approach the boundary. Why does it climb toward your max just before a point turns black?