Quartic iteration
z(n+1) = z(n)^4 + c
One step has the effect of four squarings: the argument is multiplied by four, so a point near the boundary can split four ways. Try c = 0. The recurrence becomes zₙ₊₁ = zₙ⁴, simply a fourth-power map. From z₀ = 0.5 + 0i, the values shrink toward zero and remain bounded; from z₀ = 1.5 + 0i, they grow rapidly and escape. As in the quadratic case, |zₙ| signals escape: once it passes a fixed threshold (about 2 for this quartic), the orbit must diverge. The fourth power hastens the outward flight; it also speeds the angular splitting that creates the four-fold shape.
FractalPark holds c fixed across the image and varies the starting point z₀ from pixel to pixel—the usual Julia-family setup.
