Plot fractals from the iteration z → z² + c. Change the complex parameter c and see connected sets or dust. All work runs in your browser.
Julia sets come from iterating z → z² + c for a fixed complex number c. For each pixel you start at some z and count how many steps until the orbit escapes (or cap at max iterations). The count decides the color.
If c lies inside the Mandelbrot set, the Julia set is usually one connected shape. If c is outside, you get a dust of points. On the boundary you get the most detailed fractals.
Start with z₀ = pixel position. Then z₁ = z₀² + c, z₂ = z₁² + c, and so on. If |z| exceeds 2, the orbit escapes to infinity. Pixels that never escape (up to the iteration limit) form the filled Julia set; the boundary is the Julia set itself.
