Great explanation of how fractals work and the chaotic behaviour you can get. If you are interested in generating your own fractal Jean Francois Puget [0] has a great article on how to do it using Python and matplotlib. It is very easy to experiment with different values of the initial costant when you refactor the code to generate a Julia set.
Re: the Mandelbrot set as a map of the connected Julia sets.
This means the Mandelbrot and Julia sets can be seen as different slices of a higher dimensional structure. Recently I found a video[1] with very high quality render of both sets that explores this relationship, with a focus on what happens at the boundary of the Mandelbrot set (where the Julia set becomes (dis)connected. The video also makes several good attempts at rendering 3D projections of the complete Mandelbrot+Julia "object".
(or, if you just want to look at the beautiful complexity of the Mandelbrot's border for a while, this[2] 2^1116 zoom is amazing. The rapidly increasing complexity[3] in the last 1/3 is maddening)
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[ 4.3 ms ] story [ 19.9 ms ] thread[0] https://www.ibm.com/developerworks/community/blogs/jfp/entry...
This means the Mandelbrot and Julia sets can be seen as different slices of a higher dimensional structure. Recently I found a video[1] with very high quality render of both sets that explores this relationship, with a focus on what happens at the boundary of the Mandelbrot set (where the Julia set becomes (dis)connected. The video also makes several good attempts at rendering 3D projections of the complete Mandelbrot+Julia "object".
(or, if you just want to look at the beautiful complexity of the Mandelbrot's border for a while, this[2] 2^1116 zoom is amazing. The rapidly increasing complexity[3] in the last 1/3 is maddening)
[1] https://www.youtube.com/watch?v=vfteiiTfE0c
[2] https://www.youtube.com/watch?v=PbwaFQ2r2c4
[3] https://imgur.com/a/qtlQc