3D Complex Logistics Map Set - Zo initial condition mapping

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Offline RobinB

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« on: December 17, 2018, 09:27:16 PM »
Inspired by the well noted correlations between the Mandelbrot set and the Logistics Map:

https://upload.wikimedia.org/wikipedia/commons/b/b4/Verhulst-Mandelbrot-Bifurcation.jpg
https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcQmjpt8W-yDEiMCIQOzCkYUS8RyymbWTxkGDyNXl6XEdKIvZ7bL

I sought out any other publication on this topic, finding:
http://www.cit.iit.bas.bg/CIT_2014/v14-3/2N-2-4-Prasad_Katiyar-3-2014-m-Gotovo.pdf

So decided to construct a 3D set with X and Y the real and complex parts of the driving factor 'r' (in Zn+1 = r*Zn*(1-Zn)) and Z spanning the real part of Zo, the initial value of Z. Bailout was Z>4.

First time post attempting to upload the resulting animations (YouTube) so apologies if it doesn't work out...

First up the Z axis (real component of Zo) sweep:

Then the 3D set itself:

Then a zoom into one part of the above:

Matlab's Iosurface rendering does leave something to be desired but working with complex matrices directly is quite sweet.

After a few years of searching I've not come across such 3D sets, not to say someone hasn't before, but it was nice to see some 3D nature of the higher periodic set 'bulbs'.
« Last Edit: December 18, 2018, 10:11:25 AM by RobinB »