  The class of fighting fish is a recently introduced model of branching
surfaces generalizing parallelogram polyominoes. We can alternatively see them
as gluings of cells, walks on the square lattice confined to the quadrant or
shuffle of Dyck words. With these different points of view, we introduce a
natural extension of fighting fish that we call \emph{generalized fighting
fish}. We show that generalized fighting fish are exactly the Mullin codes of
rooted planar maps endowed with their unique rightmost depth-first search
spanning tree, also known as Lehman-Lenormand code. In particular, this
correspondence gives a bijection between fighting fish and nonseparable rooted
planar maps, enriching the garden of bijections between classes of objects
enumerated by the sequence $\frac{2}{(n+1)(2n+1)} \binom{3n}{n}$.
