Logistic Map Part 2: Complex Numbers and 3D Bifurcation

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We continue our exploration with of the logistic map by looking at its behavior with complex coefficients. In particular we focus on attractors, period double, and chaos as the emerge on the complex plane. If you have not already seen Part 1 of this series, we recommend checking that out first.

Chapters:
00:23 Recap
01:33 Programming the logistic map for complex numbers
02:55 Exploring the complex attractor plot of the logistic map
06:54 Setting up a 3D bifurcation plot
07:25. Exploring the 3D bifurcation plot

Background music by Amanda Chaudhary:
Fibonacci rhythmic patterns using Kiltratrick Audio Carbon Sequencer and Yamaha RX5 drum machine; processed using Qu-Bit Prism and Strymon StarLab reverb. Additional music via original patch made in Arturia Pigments.

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Комментарии
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This is absolutely INCREDIBLE! Thank you so much for putting this together. It is wonderful.

TheParadoxOfParadox
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Thank you for the fascinating video! Can I ask what you use to visualize the diagram? It's really cool that you can zoom in to that deep while keeping the resolution.

xinzhewu
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great video! i have a question: the output of the complex logistics map is a complex number, but in the 3d bifurcation model you used only one dimension to represent a complex number, from what i understood of it. (you got 2 dimensions for the possible choices of complex parameters, and one dimension for the logistics map output, right?) did you project it into one of the coordinates?

violacosmo
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so I’m imagining a scenario where you have a cobweb diagram with multiple curves. They all represent different r values maybe even different k values.

some number is entered into the first plot, and the number is returned, then it is submitted to the next curve, and then the next. Are there any good tools for understanding a sequence of operations like this?

Sagitarria