new feature release of kalle's fraktaler 2.14 (development) branch

mathr.co.uk/kf/kf.html#kf-2.14

- new feature: nanomb2 algorithm for power 2 Mandelbrot (experimental) (originally by knighty)
- new feature: display Newton period (and set limit for nanomb2 algorithm) in Location dialog
- new feature: Ctrl-Shift-W shortcut to set image size (suggested by gerrit)
- bugfix: distinguish dialog titles for set window size and set image size
- bugfix: fix corrupt images when zooming out from the default view
- new feature: dialogs to en/disable derivatives when opening file with/out
analytic DE; automatically enabling derivatives if needed in CLI mode (reported by gerrit)
- default zoom size changed from 4 to 2 (press Ctrl-4 to reset to 4, or load a settings file with your preference) (suggested by gerrit, to avoid the dreaded "zoom size is not 2" warning when saving zoom out sequence).
- merged changes from 2.13.11

(experimental means sometimes images are bad, like the attached)

of course, the nanomb2 algorithm (aka "super series approximation") does work sometimes, and when it does it is often much faster than the older series approximation algorithm, which in turn is much faster than perturbation iterations alone, which in turn is much faster than using plain iteration with high precision numbers for each pixel

the algorithm works by approximating the orbit near a periodic cycle (usually a minibrot island) by a polynomial in *two* variables representing small changes in C and Z. you end up with a polynomial that does P iterations at once (a "super iteration"), where P is the period of the cycle.

this polynomial is only valid while dC and dZ are small, but when they get big you can switch to a different polynomial corresponding to a nearby less zoomed in minibrot of lower period. one "super-iteration" takes longer than one perturbation iteration or one plain iteration, but you need far fewer, so it works out faster.

combined with interior checking, you can set the iteration count exceedingly high (100100100 is routine for me now) with little-to-no slowdown, and get super-crisp minibrot boundaries

Follow

fractalforums.org/fractal-math is the thread where knighty introduced the idea, first implementation source code starts to be posted around page 8 or so

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