The Lit Interior

The Burning Ship map z -> (|Re z| + i|Im z|)^2 + c iterated over the parameter plane, framed at c = -1.7532 - 0.0168i with half-width 0.0140 on the hull of the flagship island. The lit cells are the periodic interior components, a period-3 hold with a chain of period 6, 9, 12, 15, 18 and 24 lamps rising along the deck. The rest of the interior is aperiodic under a search to period 4000, so it is shaded by the orbit's Lyapunov exponent instead.