I have been working for some time on ways to generate new fractal shapes, and also to be able to switch easily from Mandelbrot type (M-type) to Julia type (J-type). Here is what I’ve come up with. UltraFractal formulas usually depend on two complex values, z and c. Usually z starts with the pixel value and changes throughout the iterations. Usually c does not change with the iterations; for M-type, c is usually the pixel value; for J-type, c is usually the same value for all pixels, the “seed.” In order to mix M-type formulas and J-type formulas, and for other technical reasons, I’ve come up with a new class of formulas, SFormulas (S for State). The details are not of interest to most users. Start a new fractal and for the top formula choose Switch Combo Formula in jlb.ufm, which loads SwitchCombo from jlb.ulb. (You’ll want to download the latest versions of jlb.ufm and jlb.ulb.) SwitchCombo allows an Initial Formula that is repeated for a number of times, or until bailout is attained, or the Maximum Iteration limit is reached. Then a Main Formula is repeated until bailout is attained or the Maximum Iteration limit is reached. The Initial Formula can have a different bailout criterion from the Main Formula. There are several SFormulas in jlb.ulb (and none anywhere else, so far). There are some formulas that do iterations, like Mandelbrot, Lambda, and Phoenix; each of these can be changed between M-type and J-type by checking a box. The Two Formulas formula (surprise!) does n1 repeats of Formula #1 followed by n2 repeats of Formula #2. The Combo formula combines two or three formulas in various ways. For added complication, both Two Formulas and Combo can use one of them in place of any of the formulas. Check out the examples that follow and experiment. Tweak parameters, try different bailout criteria, try different plug-ins. All three examples are single layer fractals with simple coloring.
Example 1 uses Power as the Initial Formula and Poly Newton as the Main Formula. Both are M-type, and the bailout criterion is Convergence. I like having the outer part be symmetric and the inner part only partially symmetric.