3Blue1Brown
7 HN recommenders · recommended in 10 months, 2017–2024
21:36 · 4.6M views · Jan 27, 2017
3Blue1Brown explains fractal dimension and shows why many fractals are not strictly self-similar. Self-similarity turns out to be a special case of the broader idea of fractional dimension.
It is the standard pointer for a clear, visual explanation of what fractals are, and for correcting the idea that fractal means self-similar.
11 comments from Hacker News
Here is are two very clear explanations of fractal dimension by the man himself, Grant from 3b1b. [1] Fractals are typically not self-symmetric: this video [2] Fractal charm: Space filling curves: [LINK]
Actually, you make a good point. The social dynamics are themselves a dimension. Social network graphs can behave as fractals. In a gymnasium filled with people, there is a significant 'fractallyness' to the social network. In traffic, the fractallyness is very limited to just about all the people in the road near you. The social graph, though more fluid in a traffic jam than a pep-rally, is still fairly small. 3Blue1Brown has a great video on the dimensionality of fractals [0] that is useful here. I'm just going to spitball, but I'd bet that the dimensionality of the social graph of a traffic jam is really close to 1. So in the end, the DoFs of a traffic jam are probably very close to 3, but just a bit over. Say, 3.14-ish. ;) [0] this video
When something is referred to as fractal, does it always imply a degree of self-similarity? As I understand it, Mandelbrot developed fractal geometry as a tool to examine the "roughness" of reality as opposed to the smoothness of calculus and fractal dimension is a measure of complexity at every scale, with a self-similar pattern being an easy example to follow. If that is so, that the universe has a high degree of complexity at every scale, is that really controversial? Here is an excellent 20 min introduction to fractals: this video
This is a more detailed explanation of what fractals actually are, and what mathematics actually mean by 'fractals are everywhere in nature': this video It might help connect some dots. Short version: simple rules -> can create self-similar shapes -> which can have fractal dimension -> cellular automata can create fractals but nature -> creates shapes which have fractal dimensions does not mean that the processes that create fractal shapes in nature are based on simple rules or cellular automata (but that's not to say they aren't!)
Trying to explain fractional dimensions is probably not conducive to an HN post. but fortunately, 3blue1brown converted this: this video Which also nicely and conclusively shows why self-similarity is just a special case of things that have fractional dimension.