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https://github.com/jeremy-rifkin/mandelbrot-trajectory-infima

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Host: GitHub
URL: https://github.com/jeremy-rifkin/mandelbrot-trajectory-infima
Owner: jeremy-rifkin
Created: 2021-12-26T07:41:50.000Z (about 3 years ago)
Default Branch: master
Last Pushed: 2024-05-05T16:35:30.000Z (9 months ago)
Last Synced: 2024-10-28T21:23:01.454Z (3 months ago)
Language: C++
Size: 8.35 MB
Stars: 2
Watchers: 1
Forks: 0
Open Issues: 0
Metadata Files:
- Readme: README.md

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README

        ## Mandelbrot Trajectory Infima

These renders below are the result of considering the "trajectories" of points inside the mandelbrot

set when iterating $z \mapsto z^2 + c$. Specifically, looking at the closest point on such a

trajectory to the origin $a(c) = \inf \{\left|z_n\right|\} = \inf \{\left|P_c^n(0)\right|\}$. As far

as I can tell, this was first described / explored in a 1986 book "The Beauty of Fractals".

![](photos/png/1440.png)

![](photos/png/smooth_inside_1.png)

![](photos/png/smooth_inside_4.png)

### References

* [Displaying the Internal Structure of the Mandelbrot Set](https://www.acsu.buffalo.edu/~adamcunn/downloads/MandelbrotSet.pdf)

* The Beauty of Fractals, 1986, by Prof. Dr. Heinz-Otto Peitgen and Prof. Dr. Peter H. Richter.