Escape-time coloring of the Julia set for f(z) = z² + c. Each pixel's color encodes how quickly the orbit escapes to infinity.
c = -0.7269 + 0.1889i
Re(c): -0.727
Im(c): 0.189
Max Iter: 100
Zoom: 1.0
Color: Fire
About Julia Sets
The Julia set for a complex parameter c is defined as the boundary between initial points z₀ whose orbits z→z²+c remain bounded and those that escape to infinity. For each pixel, we iterate z←z²+c starting from z₀=pixel position. If |z|>2 after n iterations, the orbit escapes; n becomes the color. Connected Julia sets occur when c lies inside the Mandelbrot set. The smooth coloring uses fractional escape count: n + 1 − log₂(log|z|) giving smooth gradients instead of hard bands.