Fractals are typically not self-similar

Here is are two very clear explanations of fractal dimension by the man himself, Grant from 3b1b. [1] Fractals are typically not self-symmetric: [VIDEO] [2] Fractal charm: Space filling curves: [LINK]

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: [VIDEO]

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] [VIDEO]

Trying to explain fractional dimensions is probably not conducive to an HN post. but fortunately, 3blue1brown converted this: [VIDEO] Which also nicely and conclusively shows why self-similarity is just a special case of things that have fractional dimension.

This is a more detailed explanation of what fractals actually are, and what mathematics actually mean by 'fractals are everywhere in nature': [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!)

3blue1brown has some good fractal videos; one in particular being relevant to this discussion: "Fractals are typically not self-similar" - [VIDEO]

"Fractals are not self-similar" [VIDEO] If you want to learn more about the fascinating world of fractals.

I am unable to answer your questions for you, but I wanted to talk on the topic because it is something I've been thinking a lot about lately There recently was a lot of talk and reporting surrounding YouTube 'changing their algorithm' and hurting a lot of YouTubers I watch frequently One of my thoughts was that unfortunately the best solution would probably mean content creators would need to seek their own advertising'sponsorships I can tell you the only ads I have clicked on in any recent memory are all, every single ad, of the ones that 3blue1brown places at the end of thaer videos(o) Considerate effort like this really made me think how inconsiderate and detrimental the current hands off one size fits all ad networks are Some content creators will surely protest 'im a creator stead a salesman' which is a fair complaint but I'd argue 3blue1brown really brings an artistry to the personal ad network the channel is creating.. self curated ads has the potential to be another medium of self expression (o) [LINK] .. an aside: the ad that YouTube ran in front of the video I linked when I first clicked on it was offensive and jarring, it depicted an animated Albert Einstein literally scribbling on a black board while a student looked on in dread and three words came in the screen, two of which I can remember 'math ___ sucks' the middle was either: teachers, lessons, or tutors; this ad actually upset me.. contrast that with this great 3blue1brown ad(i) and I am more confident in m