Fractals are typically not self-similar

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Strong rec SavantIdiot · 2021-07 · on “A Closer Look at Fractals”

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]

Recommends FullMtlAlcoholc · 2017-08 · on “The Hindu Temple as a Model of Fractal Cosmology (2015)”

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]

Recommends Balgair · 2019-04 · on “Ford CEO says the company 'overestimated' self-driving cars”

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, bu

Recommends jerf · 2019-12 · on “Recursion and Fractals”

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.

Recommends jameshart · 2020-02 · on “Cellular Automata in the Browser”

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!)

Recommends coremoff · 2023-05 · on “Fern leaves and cauliflower curds are not fractals”

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

Recommends jrvieira · 2024-11 · on “The Matrix: Infinite-Horizon World Generation with Real-Time Interaction”

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

Cites justifier · 2017-05 · on “Ask HN: Anyone monetizing their sideproject with direct ads / sponsorships?”

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 of