Julia set study
Back to visual explanationsFollow one point.
Square a complex number, add c, then repeat. The yellow path shows the orbit of one starting point.
zn+1 = zn² + c
Orbit · 0 iterationsLive mathematics
Why does this form a fractal?
For each pixel, z starts at its position in the complex plane. We repeatedly calculate z² + c. Points that stay bounded appear dark; others are coloured by their escape time. The yellow orbit is one example, not the boundary of the set. A finite iteration limit approximates the infinite mathematical set.