Twisted Mandelbrot

[doncasteel8587]

I'm still working on this one, but thought it was interesting enough to share.

Made with my own formulas in Fractorama

Sometimes Java.net doesn't like to link correctly, here it is on Deviant Art: http://www.deviantart.com/deviation/57785099/

[cKleinhuis]

nice one, i am interested in the formulas, is it just a certain filling method?

[Nahee_Enterprises]

I'm still working on this one, but thought it was interesting enough to share.
Made with my own formulas in Fractorama

Yes, this is quite interesting!!  I am glad you shared this image with us here.     

And like Christian Kleinhuis (Trifox), I too would like to know something about the formula used.

[doncasteel8587]

I'm not sure how to answer Christian's question, it's more than just a coloring algorithm, but it's not truly a fractal either.
The function is iterated, but is not infinitely zoom-able. The number of iterations controls how many subdivisions it makes, and more iterations produces more detail, but it's more of a structure change.

In this case, I applied the z=z*z+c function to the pixel 4 times then passed the result through the spiral function twice, then applied the coloring algorithm.

Here's the code (the extra parentheses are required due to a precedence bug in fractorama):


formula
   {
   $maxcount = 2;
   $remapScale = 1;
   c= [-0.1,0.2];
   d= [real(sqrt(c)),imag(sqrt(c))];

   z=rotate(current,[0,0],90);
   w= z;//[0.529412,-0.529412];
   z=z^2+w;
   z=z^2+w;
   z=z^2+w;
   z=z^2+w;
   $zPow=3;
   z=rotate(z,[0,0],30);

   y=z;
   u=z;
   v=z;
   $yPow=$zPow;

   while ($count < $maxcount)
      {
      z=(z*y)-(y*z);
         z=((pow(z,$zPow)*c)+(c))/((pow(z,$zPow)*c)-(c));
         y=((pow(y,$yPow)*d)+(d))/((pow(y,$yPow)*d)-(d));
      $zPow=   $zPow^2;
      $yPow=$zPow;
      }
   set_color
      (
      1.585*((1+cos(rad(z^(5*c))*2))/2)*255-((1-sin(rad(y^(5*c))*2))/2)*255+255
      );
   }

[doncasteel8587]

Here's a similar function applied to a Julia set, then animated..... sorry these gif's are so large, but I haven't figured out how to embed an mpeg here.

[Nahee_Enterprises]

....it's more than just a coloring algorithm, but it's not truly a fractal either.  .........
Here's the code.....

Great!!  Thank you!!   

And the animated .GIF is really interesting as well.  I like what is taking place at the center of each spiral, kind of a flashing, extremely fast, sub-animation taking place.

[doncasteel8587]

I like what is taking place at the center of each spiral, kind of a flashing, extremely fast, sub-animation taking place.

Honestly I hadn't noticed that happening until you mentoned it 
Turns out it's just aliasing, but it is interesting!