Z7 Log Lockets

Newton's method applied to f(z) = z^7 - z^3 + Log(1 + z^2) on the principal branch. The logarithm rewrites the polynomial, turning the triple root at the origin into a double root and turning the roots at +/- i into branch points instead. All nine free critical points land on roots, so there is no attracting cycle and no void, and the lockets are rosettes around the poles of the Newton map. The window sits on the real axis between the conjugate poles 0.604411 +/- 0.119110i.