08/30/2007, 11:20 PM

While the sine wave idea makes sense from the standpoint of creating a simple and infinitely differentiable function, it doesn't seem to fit the idea of continuous iteration. If continuous iteration is to be considered, the sine wave idea doesn't fit. Given a value near the infinite limit, how would the function "know" which direction to go for a small fractional iteration? Is it on the upswing or the downswing?

On the other hand, perhaps this is a situation where complex outputs are actually desirable? By having a spiral that hits the real plane only at the integer tetrations, we can embed information in the output that would "tell" the function where it is, and hence where to go next.

Just an idea...

On the other hand, perhaps this is a situation where complex outputs are actually desirable? By having a spiral that hits the real plane only at the integer tetrations, we can embed information in the output that would "tell" the function where it is, and hence where to go next.

Just an idea...

~ Jay Daniel Fox