• May 22, 2022, 10:31:48 AM

### Author Topic:  Fractional Iteration Mandelbrot  (Read 89 times)

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#### v

• Posts: 66
##### Fractional Iteration Mandelbrot
« on: May 02, 2022, 11:10:27 PM »

This is a domain colouring animated plot of the M-set function $$f(z) = z^2 + C$$, ie f(f(f(f...f(z)))) using domain colouring for complex functions rather than the conventional escape time algorithm.

But on the very last iteration, the exponent is fractionally increased, as in:
$f(z) = z^{1 + t} + Ct$
for $$t \in [0, 1]$$

and t for time.

There are various ways to smooth or interpolate the M-set evolution and this is one.  Notice the branch cuts that show up with non-integer exponents

« Last Edit: May 03, 2022, 07:19:55 AM by v »

• Fractal Frankfurter
• Posts: 641
##### Re: Fractional Iteration Mandelbrot
« Reply #1 on: May 03, 2022, 07:07:40 AM »

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