Note if any point is contained in some smaller version of the whole, then any point is contained in arbitrarily smaller versions of the whole.
It isn't possible to unambiguously communicate in a picture whether or not a few specific points are included in the fractal. The pictures are interpreted as what is intuitively simplest. To make matters less ambiguous, all the fractals here contain all points arbitrarily close to points in them. (They are topologically closed. See also BP1239.)
The left hand side of this is a stronger condition than the left hand side of BP1116.
Tiled by pair of fractals including itself such that both tile the other vs. tiled by pair of fractals including itself such that the other tiles itself.
Proofs still needed that all the examples on the left hand side cannot fit on the right hand side as well, and that EX9881 cannot fit on the left hand side as well.
CROSSREFS
The left hand side implies the left hand side of BP1116.
The right hand side does not imply the right hand side of BP1116. (EX9881 is meant to be a counterexample.)