The Mandelbrot Fractal Table of Contents  

10. Conclusion
 
One more point. In paragraph 5 we discussed strange attractors and their connection to chaos.
Where can this chaos be found in the Julia and Mandelbrot Fractals?
In the Feigenbaum bifurcation tree there was chaos for c between -2 and -1.40155.... except in small pieces.
Below that part of the antenna is enlarged again. Chaos (that is to say that there are strange attractors) occurs in the thin line to which the mini Mandelbrots are strung, as it were.
As explained earlier, that line is visible here because of the symmetry, but all Mandelbrots are connected to each other via these kinds of lines. Only they are too "thin" in the complex plane to be observed. That is why the chaotic behavior is not visible in the Mandelbrot Fractal.

There is of course much more to tell about Fractals in general and the Mandelbrot Fractal in particular.
But for a first introduction this is enough.

There is a lot of information to be found on the Internet. Google for "feigenbaum interactive", "Julia interactive" , " Mandelbrot interactive", to find links to webpages where you can experiment yourself. I have selected those that fit best with my tutorial.

Comments, (critical) remarks etc. are welcome at Jan Stuivenberg.

The Mandelbrot Fractal Table of Contents