What happens to a Julia set when its c moves outside the Mandelbrot set? Points far from the set escape in the first few ticks and are drawn orange; points closer to the boundary escape later and come out pink, purple, then dark indigo.
Try this Choose Julia Spirals, then set julia-real to 0.3 and julia-imag to 0 and press Reset (both are read only at setup). c = 0.3 lies just outside the Mandelbrot set, whose rightmost point is 0.25, so the Julia set is dust with no interior. Every point escapes, bounded-points ends at 0, and the run stops at tick 52.
About this model Where it ends up
The Mandelbrot set and the Julia sets, named for Benoit Mandelbrot and Gaston Julia, come from the same recurrence, z → z² + c. For the Mandelbrot set each point of the plane is c and z starts at 0. For a Julia set each point is the starting z and every orbit shares one c. Once |z| exceeds 2 the orbit is certain to diverge, so the point is outside the set.
Each of the 121 × 81 patches is one point, spanning view-width across and centered on center-real + center-imag·i, and stores its own z, c and iteration count. Each tick every patch still computing applies z → z² + c once, all at once. A point whose |z| passes 2 is marked escaped and colored by how early it escaped; a point that reaches max-iterations without escaping is marked bounded. fractal-kind, the view and the Julia constant are read only at setup; max-iterations is read every tick.
The presets show the full Mandelbrot set, a 17.5× zoom on Seahorse Valley (the cleft between the main cardioid and the period-2 bulb), and two Julia sets, c = −0.8 + 0.156i and the Douady rabbit at c = −0.123 + 0.745i. max-iterations tops out at 80, which limits how deep a zoom can resolve.
