You actually do not have to remove any axioms from Peano arithmetic to prove that a model of PA with such a 'bleem' exists. It is a straightforward consequence of the compactness theorem: just enrich PA with a new constant c and an infinite series of axioms 'c != N' for every numeral N.
For any finite set of these new axioms a model exists (just set c to a large enough number), therefore by the compactness theorem there exists a model which satisfies all our new axioms.
I wonder why the depth fail shadow rendering algorithm had been explicitly excluded from the open source release. It's been around for years now, after all.
See also http://en.wikipedia.org/wiki/Non-standard_model_of_arithmeti...