$ultra fractal 6 tutorial$

Iterations of w -> w 2 + s should now be equivalent to iterations of z -> (rz) 2 - z - r, where w = A z + B z = (w - B)/A. We can solve for the parameters by conjugating:(Az+B) 2 + s = A((rz) 2 - z - r) + B gives A = r 2, B = -1/2, s = -3/4 - r 3 Not quite an answer you might hope for, but I think it's possible by affine conjugacy (equivalence of quadratic polynomials) with a change of coordinates z -> Az + B: So what can be done with perturbation is probably not much more than what stardust4ever already exploited and I implemented in KF. Replace z with z+d and r with r+c, then minus the original formula. I received a formula, (z*r)^2-(z+r) which I didn't succeed render with perturbation. Since r is an high precision variable, which very probably is out of bounds for hardware datatypes, it is as important to be removed as the high power of z! Perturbation of the standard mandelbrot is (z+d)^2+(c+r) - (z^2+r) => 2*z*d + d^2 + cĪs you can see, both z^2 and the start of the reference r are eliminated.

$ultra fractal 6 tutorial$

Set d as delta and c is the start point of delta, z is the reference and r is the start point of the reference: Take the standard mandelbrot formula as example.

$ultra fractal 6 tutorial$ $ultra fractal 6 tutorial$

I have reasons to doubt that UF6 would be able to take any formula and make perturbation of it.

$ultra fractal 6 tutorial$

Ultra fractal 6 tutorial