you have a lot of nice renders going on there
I suggest you to try tan(z)*z+c - that one turned out to be incredibly detailed.
The diamond one, is that based on split complex numbers?
(a+b*j where j²=1 but j!=1)
Because it looks a lot like that...
If so, you might as well want to try dual numbers:
<Quoted Image Removed> where <Quoted Image Removed> but <Quoted Image Removed>
that's <Quoted Image Removed> - seems incredibly simple as the real part is not at all dependend on the previous imaginary part but it certainly looks nice
- I actually prefer it over the split complex one.
That one turns out to have a beautiful fan-like structure
Also very interesting is the set of polynomials of degree 5 (aribitary choice) where you could try either random parameters between -1 and 1 (bigger will basically shrink the features) or maybe some user input boxes with sliders so you can have nice comparisons
Just some ideas I tried myself already
for the z*tan(z) one, you'll need very deep iterations. It will heavily oscillate between 0 and infinity but it does produce very nice images
- seriously, that's the Beauty and the Beast in a single function.
Thanks again for your reply. I'm very
interested in trying out your suggestions. One thing I should mention straight up: I'm primarily an artist and only secondly a programmer so it takes quite a bit of extra effort for me to understand some of these equations. (I flunked algebra and geometry). I tend to learn best though example and some of the cryptic algorithms tend to lose me.
My main algorithm for my program is the following:
xb=zx*zx-zy*zy+xa; // real
yb=a*zx*zy+ya; // imaginary
It would help if you could show me how your equation relates to my code so that I can understand it better.
The diamond equation is a simple variation on the above Mandelbrot but with negatives:
xb=-zx*zx-zy*zy+xa; // real
yb=-a*zx*zy+ya; // imaginary
I'm really curious to try your examples out (and especially the Tan function) so if you have some spare time (and patience) to show me how your equations relate that would be great.
P.S. I had implemented proper powers in my Fractus 2D plugin but I found the computations far too slow to add to my Buddhabrot program. Perhaps one of these days if I find an optimized cheat...