But as my office-mate mentioned about the Singularity, Godel plays a role.
A finite self-organizing system isn't going to be complete. Anything physical in our universe is going to be finite in construction and finite in the number of operations it can perform. Any finite mathematical construct which is trying to show new things can't be complete; there will be propositions within the system, really true or really false, which cannot be proven true or false from within the system. You can add more propositions, and create a larger construct, and face the same problem again. And again. But because time is also finite, the number of new propositions it can add is finite. The system will always be finite, and incomplete.
Notice something odd here. The best possible system organized in this universe, whether Omega or Singularity, is incomplete, which means that something exists which does not exist within that system. This means there are different kinds of existence, one of which--existence as an instance--can be found in our Omega/Singularity at the end of the universe (the highest form of whatever-it-is) and another of which need not.
A bottom-up tower isn't going to reach completeness.