![]() Practically speaking, you would convert from the unusual polynomial to the standard polynomial, then iterate that, converting back to the unusual polynomial for escape tests to get the right iteration count. 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. ![]() 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. This is a paid program, so I do not expect to be having this problem.I have reasons to doubt that UF6 would be able to take any formula and make perturbation of it. In the "Fractal Mode" pane, lower right part of screen, I click the third item down, "Switch Mode", and it displays "Contains errors." This is the only helpful feedback I've been able to find. And I keep changing only the minus sign or the subtraction to make it stop working, so I suspect that there is a bug (or an arbitrary limitation of not being able to use this particular formula? - doesn't make sense.) The only difference in the above two is the minus sign.īut if I add a line negating cc, it doesn't work again: init:Īs I think I've proven, negation and subtraction seem to be working. So I tried to enter the formula into UltraFractal, but no matter what I try, I can't get it to work. Here is the XaoS source code (*.xpf file contents): Position file automatically generated by XaoS 4.2.1 I found the following fractal, which I really like:Īs you, perhaps, can see, I have run up against the resolution wall (floor?), which means that the deeper I zoom at that point, the more pixelated and boxy the image gets: While using the real-time Fractal zoomer XaoS to explore the infinite universe having user formula "sin(z^2)-cos(z^2)+c", we start out here (important for universe identification and formula matching with other zoomer software applications, libraries or frameworks.):
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