Deep Cubic with 5 x 5 anti-aliasing

I am adding arbitrary precision arithmetic for formula types in Fracton. While debugging the new code, I did some exploring in the cubic mandelbrot set: z = z ^ 3 + c. I was curious to see if I could make long features using a similar approach to the line method I posted for the mandelbrot set. I was pleased to see it is possible even though the places you zoom into are a little different. As you might have guessed, the cubic mandelbrot makes 3 armed features. Instead of period doubling you get period tripling and to find minibrots you zoom into a 3 way symmetry instead of the 2 way symmetry of the Mandelbrot set. One interesting thing is that you can make curved or straight arms unlike the Mandelbrot set where I was only able to make straight arms. The higher order seems to bring things closer together so you don't have to zoom as deep to get to the next feature. The deepest image is at a magnification of about 2e62. This fractal is too deep to work using double precision arithmetic so a FractInt parameter file would not be useable. If you have Fracton version 1.2 or later, you can use this zipped Fracton file Deep Cubic to recreate the fractal. The following images show the progression of zooming from the initial cubic minibrot. |