Lattice Animals with self-avoiding perimeters

[Jonathan Post]

Furher following up on Frank T. Adams-Watters's comment about holes in
A057730, note that a sufficently large polyomino (with self-avoiding
loop perimeter)

(1) May have multiple disjoint holes;
(2) Holes in polyominoes may contain within them multiple polyominoes;
(3) which themselves may have holes, etc.

Thus there is a tree-structure inherent in Frank Adams-Watters
insightful question.  That is, a homomorphism from elements of the set
of polyominoes with holes with polyominoes...  into the set of trees,
and thus from elements of the set of sets of disjoint polyominoes with
holes with polyominoes... to the set of forests.

I can't recall the reference, but there is known to be on Earth a
continent with a lake with an island with a lake with an island.