  We show that products of sufficiently thick Cantor sets generate trees in the
plane with constant distance between adjacent vertices. Moreover, we prove that
the set of choices for this distance has non-empty interior. We allow our trees
to be countably infinite, which further distinguishes this work from previous
results on patterns in fractal sets. This builds on the authors' previous work
on graphs and distance sets of products of Cantor sets of sufficient Newhouse
thickness.

Classical Analysis and ODEs