• May 22, 2022, 10:31:48 AM

Author Topic:  Fractional Iteration Mandelbrot  (Read 89 times)

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Offline v

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Fractional Iteration Mandelbrot
« on: May 02, 2022, 11:10:27 PM »
https://www.shadertoy.com/view/flsBzS

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


Linkback: https://fractalforums.org/index.php?topic=4741.0
« Last Edit: May 03, 2022, 07:19:55 AM by v »



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