12/05/2011, 07:58 PM

That's a very weird looking sexp!

Does this mean we're going to have to clarify uniqueness based on the infinite list of fix points?

Already, by looking at the new sexp it doesn't seem as fitting as the one based off of the primary fix point. But I don't know how you'd express this aesthetic requirement in mathematical notation. Perhaps merely because the derivative goes to zero at integers?

And, I wonder if we'll see more erratic behaviour across a third fix point or a fourth! Is it likely that they'll get more erratic as we get further from the primary fixpoint? Or will it be more chaotic, as to which ones look nice and which ones don't?

Very very interesting.

Does this mean we're going to have to clarify uniqueness based on the infinite list of fix points?

Already, by looking at the new sexp it doesn't seem as fitting as the one based off of the primary fix point. But I don't know how you'd express this aesthetic requirement in mathematical notation. Perhaps merely because the derivative goes to zero at integers?

And, I wonder if we'll see more erratic behaviour across a third fix point or a fourth! Is it likely that they'll get more erratic as we get further from the primary fixpoint? Or will it be more chaotic, as to which ones look nice and which ones don't?

Very very interesting.