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>How would you describe Mandelbrot sets without pictures? It's literally easier to describe Mandelbrot set without the picture than with it. The set of complex
by Grue3 9y ago
>How would you describe Mandelbrot sets without pictures?
It's literally easier to describe Mandelbrot set without the picture than with it. The set of complex numbers c where recursive equation "z_n = z_(n-1)^2 + c, z_0 = 0" does not diverge.
In fact, the picture of a Mandelbrot set is actively misleading! You think you can see the set, but it's a fractal! It's infinitely complex in a way that cannot be shown in a picture.
>Eversion of a sphere?
Pretty sure that one was figured out way before anyone was able to visualize it. Same with Banach-Tarski paradox. These things resist visual intuition in the first place, so it's much safer to rely on equations when dealing with problems like these.
- wglb 9y agoIf you read of the early work that Mandelbrot did on this equation, you will recall that despite having those symbols in front of him, he had to plot it out, crudely at first on a line printer, before he fully understood the implications. Thus pictures are not only tutorial but a fundamental necessity for understanding mathematics.
- Simon_says 9y agoYou picked possibly the worst example for what you're trying to say. Nobody knew it was a fractal until it was plotted. Proving it's a fractal was done with a written, rigorous proof, but the intuition for where to look came from the pictures.