Fractal Series — Image Pack

The Mandelbrot set and its companion Julia sets live in the complex plane at the edge of order and chaos. For each complex number c, iterate z → z² + c starting from z = 0: if the sequence stays bounded, c belongs to the Mandelbrot set; otherwise, the escape speed colors the surrounding fractal boundary. Julia sets fix c and vary the starting point, producing connected dust, dendrites, or solid regions depending on where c lies. Both reveal infinite self-similar detail at every zoom level — you can keep magnifying forever and the structure keeps renewing itself. Every image in this collection is computed at high iteration depth with smooth-iteration coloring, so the gradients you see correspond exactly to how fast each point escapes.

z_{n+1} = z_n² + c, escape when |z| ≥ 2