JULIA SETS — COMPLEX DYNAMICS
f_c(z) = z² + c · Escape time · Smooth coloring · Mandelbrot picker
Re(c)
-0.745
Im(c)
0.113
Max iterations
120
Zoom
1.0
Coloring
Ultraviolet
Fire
Ice
Galaxy
Mode
Escape time (smooth)
Filled Julia set
Orbit trap
c = -0.745 + 0.113i
Click Mandelbrot to pick c
The
Julia set
J_c = boundary of points that don't escape under iteration z→z²+c.
Connected ⟺ c ∈ Mandelbrot set (Böttcher).
Click the Mandelbrot strip
to pick c and watch the Julia set morph.
Each c gives a unique fractal; the Mandelbrot set encodes all Julia sets via the Douady-Hubbard uniformization.
Animate c path
Re-render