Negmandels of Early 2011

I am starting to wonder if anyone else in the world has explored this view of the generalized mandelbrot formula much. A while back I did try to add an example image to wikipedia but unfortunately it did not stick. As anyone who's tried to contribute to Wikipedia will know, it can be incredibly hard to convince the deletionists that things are notable and worth keeping.

I can understand though why negmandel is not readily accepted as notable by pure-math oriented people because the main generator for detail is not really there in the mathematics. It is rather born from the limitations of the common digital implementation of complex power (and it's reliance upon complex logarithm). Indeed, these 'branch cuts' that negmandel is so intensely covered with, can be viewed as just an artifact of the implementation -a very low level artifact- but thus of little theoretical interest.

I still think that there is something to learn from negmandel, quite apart from the gorgeous images that it is capable of producing. The adaptation of complex log into a number system that does not naturally support the representation of multivalues (nor any kind of infinity, particularly) is the folding of an infinite number of values into a fixed range. This is quite reminiscent of what a modulo function does.

It can be thought of similarly to a modulo on the phase component of a complex number. It has the effect of converting an infinite number of input values into a single finite value. Computers necessarily do this kind of range-optimization a lot, and I think there are aspects of mind that use this same type of reduction in order to make concepts more tractable. Clearly it makes quite a mess of structures that may have existed in the full 'multivalued' result of the formula. I am very interested to explore exactly what kind of mess it makes, and what traces remain of the original structures.

There are truly endless amounts of detail to explore in the negative fractional exponent mandelbrot fractal, the following are some of the shots I've taken on recent trips.