Here is another fractal, still using the 3rd equation with f(t)=1. However I switch z and c. Looks to have an infinite line of complexity. Don’t have much computing power (no double precision graphics card) Really want to zoom in.
The equations that I posted, the first two can be made into fractals. I don’t have a double precision graphics card, so it takes a long time to calculate. The first one was the infinite area fractal I posted before. This one is from the second equation. I do someday want to create better resolution and more images of these. Maybe some of these people still trying to calculate the deepest of the Mandelbrot Set might spend some of there calculation time on something new.
As you might noticed there seems to be some complexity at integer values near zero.
Here are three equations I came up with. Not that anyone reads this post, or would ever take me seriously as a mathematician. I am no doctor. I do not have a masters. However, I thought I’d post anyway. I could show the derivation of these equations, they are actually interesting results. I think this could turn into an entire new area of mathematics. That relates to many other branches. These equations may even help solve the Riemann Hypothesis. I also have intuition that it maybe the key to show that there are multiple solution to Einstein’s equations, possibly even infinite. The last equation in this pdf, is a formula with a double integral that I think could give the Nth derivative, the Nth integral, fractional derivatives, and possible give light to the possibility of complex derivative and complex integration (Not the variables, the actual calculus). This will likely not be taken seriously. I will likely not receive anything for this. This is likely to be read by nearly no one. I am surprised that this and the number space I posted, hasn’t been derived yet. I wouldn’t be surprised if this was purposely hidden. Anyway below is a small pdf, with equations, that I haven’t really proved, nor do I really know how to. However if the process in mathematics is taken to a likely course of action, I feel it is enough to be important. If by some small rare chance anyone sees this to be important, and want to contact, email email@example.com. I have been trying to somehow make this page useful and have come to realize it is far too much work to do in one lifetime, and there is no point in trying without anyone else.
Here is the number space I created. If you find this useful, or use it in some way, please email firstname.lastname@example.org. I would very much like to know some of the things I work on are being of use and are being appreciated. I could always use a pick me up of encouragement.
What I would like to do is create a video using the Mandelbrot Set using a new number set I defined. This new number set doesn’t break any of the rules, it also has a defined exponential function and I have code for an approximation of the natural logarithm. It is essentially an extension of the complex number space.
This is some audio, with some guitar over automatically generated melodies/electronic drums (The testing of work from decades of playing guitar)
These images are 2d slices of the Mandelbrot Set using the 4D number space I created. The area inside the slices are all the same. So some large numbers in this number set may be inside the set.