Ouroboros

The Burning Ship map z -> (|Re z| + i|Im z|)^2 + c iterated over the parameter plane, sampled through the Moebius inversion c = 1/w. Under the inversion c = 0 is interior and c = infinity is exterior, so the far field floods with hull and the boundary closes into a ring around the origin. The distance estimate is transferred exactly as d_w = d_c / (|c|(|c| + d_c)) rather than by the naive chain rule, and the mid-field is engraved by equipotential bands of the smooth count.