Studying Mathematics Thread

[polymath257]

Is there any mathematician who chose Fractals as his specialy? Hard to imagine anyone who wants to dive into that madness

Other than Mandelbrot himself? Oh yes. At least one difficulty is that there is no agreed upon definition of what it means to be a fractal. yes, self-similarity is one key, but the notion of Hausdorff (fractal) dimension is also widely recognized. The two lead to different notions, however.

Here's an actual mathematics book:


https://www.amazon.com/Geometry-Fractal-...s+falconer

There are many unanswered mathematical questions even concerning the Mandlebrot set: for example, is it locally connected?

Here are some recent papers:
https://scholar.google.com/scholar?hl=en...nsion&btnG=

In any case, fractals seem to be less 'in vogue' than they were 20 years ago, but still being actively studied in various ways.