Halley Lace A Rosette

Halley's method applied to f(z) = (z^4 - 1)(z^4 + 16) = z^8 + 15z^4 - 16, framed on the whole object. The eight roots lie on two rings, radius 1 at the compass points and radius 2 at the diagonals. Halley's iteration is a rational map of degree 2n - 1 where Newton's is degree n, so the boundary grows chains of scalloped bubbles instead of feathered filaments. Each root owns one hue, turquoise and azure on the inner ring, violet and rose on the outer.