🧵 Untitled Thread
Anonymous at Sat, 15 Mar 2025 20:12:14 UTC No. 16620024
Explain how understanding the concept of "fractals" has any application to real-life advancements.
Anonymous at Sat, 15 Mar 2025 20:47:59 UTC No. 16620059
>>16620024
https://en.wikipedia.org/wiki/Multi
Anonymous at Sat, 15 Mar 2025 21:13:55 UTC No. 16620080
>>16620024
fractal antennas, also procedural generation and cryptography
Anonymous at Sun, 16 Mar 2025 00:17:32 UTC No. 16620190
>>16620024
Surface roughness and friction between surfaces is likely best understood in terms of the fractal dimension of the surface, rather than the average difference in height between peaks and valleys that is currently used in manufacturing.
Anonymous at Sun, 16 Mar 2025 02:04:31 UTC No. 16620256
>>16620024
The Multiverse is a fractal
Anonymous at Sun, 16 Mar 2025 10:20:09 UTC No. 16620590
>>16620190
Wrong.
Anonymous at Sun, 16 Mar 2025 10:32:19 UTC No. 16620600
Have you ever looked really hard at a tree dipshit.
Go wipe your ass.
Anonymous at Mon, 17 Mar 2025 02:40:23 UTC No. 16621328
>>16620024
Non-linear dynamic systems are ubiquitous.
Anonymous at Mon, 17 Mar 2025 07:14:19 UTC No. 16621427
>>16620024
holograms are fractals and holograms can store information so fractals are actually relevant to high density information storage
Anonymous at Mon, 17 Mar 2025 09:40:22 UTC No. 16621496
life is a pepe looking at himself in a fractal mirror
Anonymous at Mon, 17 Mar 2025 10:40:24 UTC No. 16621525
>>16621427
>fractals are actually relevant to high density information storage
But in real life, the fractal pattern doesn't last forever. It lasts for about five iterations. Or less.
Just like bull markets never last.
Anonymous at Mon, 17 Mar 2025 11:02:32 UTC No. 16621535
>>16620024
It could explain how consciousness works
https://www.youtube.com/watch?v=KYC
Anonymous at Mon, 17 Mar 2025 12:33:42 UTC No. 16621577
>>16620024
Scaling dimension in condensed matter and solid state physics is related to fractals.
Anonymous at Mon, 17 Mar 2025 13:44:22 UTC No. 16621596
>>16620590
Nah this is true. I have studied fractals and it turns out that fractals with Hausdorff dimension between 1 and 2 look like rough 1 dimensional objects (zigzaggy lines), with higher dimensions being rougher. As you approach a Hausdorff dimension of 2, the fractal gets so rough that it starts to fill in a 2 dimensional area.
Same kinda goes for fractals with hausdorff dimension between 2 and 3. You start with a surface that gets rougher and rougher as dimension increases, eventually ending up at hausdorff dimension 3 where the surface is so rough it fills in a 3 dimensional area.
Anonymous at Mon, 17 Mar 2025 13:53:13 UTC No. 16621601
>>16621596
I found the same wikipedia and intro articles you have. They're edited by the people whose pet theory is to use fractals to derive coefficient of friction. It's a weak model and receives more attention than it deserves, like MOND. For fucks sake dude, it doesn't even make physical sense as an origin for friction.
Anonymous at Mon, 17 Mar 2025 14:07:23 UTC No. 16621611
>>16620024
Hey dude. So like, the notion of a "fractal" is often erroneously taken to mean "infinitely self-similar shapes" like the Sierpinski triangle or the Koch snowflake. Those just tend to be the easiest fractals to study because they're easy to construct, but in reality a fractal is just any shape which has in some sense a non-integer (fraction dimensional) shape.
To be a little more specific, the notion of "dimension" we're talking about here is roughly "How does the amount of mass of this shape has change as we scale it?" Some typical examples are:
1. Line segments are 1-d because because if we make a thin rod twice as long, it has twice the mass. in other words [math] m = k * l^1 [/math], where m is mass, k is some constant scalar, and l is length.
2. Squares, circles, and triangles are 2-d because if we keep them as the same basic shape but scale them by a factor of 2 in every direction, their mass goes up by a factor of [math] 4 = 2^2 [/math]. In other words [math] m = k * l^2 [/math]
3. Cubes, spheres, and pyramids are 3-d because if we keep them as the same basic shape but scale them by a factor of 2, their mass goes up by a factor of [math] 8 = 2^3 [/math]. In other words [math] m = k* l^3 [/math]
But something weird happens with "rough" shapes. If you take a Sierpinski triangle (which you get when you follow the process in the image infinitely many times), and scale it by a factor of 2, its mass triples, since you end up with one of the 3 smaller triangles growing to be the size of the the original triangle, with two identical copies sitting next to it. Doing a little algebra yields that the Sierpinski triangle therefore has a dimension of [math] \log_2(3) \approx 1.585 [/math].
Anonymous at Mon, 17 Mar 2025 14:18:58 UTC No. 16621615
>>16621611
Turns out though you can compute this dimension for all sorts of stuff which is not self-similar, and almost all "rough stuff" will have noninteger dimension. In the real world, obviously stuff eventually smooths out once we start getting down to an atomic or subatomic level, and fractals are typically things that look rough no matter how far you zoom in, but even finitely rough approximations of fractals in the real world can have interesting properties. We live in a world of very rough stuff so looking at how rough stuff behaves in physical systems is very useful. Take for example insulating foam, which tends to look quite fractally under a microscope. You can get the thermal properties you want out of it by tailoring the distribution of bubble sizes in the foam. Studying fractal dimension can give you a way of thinking about what different bubble size distributions in the foam would do for its thermal properties. This sort of insight has lead to the development of a lot of "metamaterials".
Another practical use is for detecting irregularities in systems that have a well-known fractal dimension (level of roughness). Some cancers have been known to change the measured fractal dimension of tissues and cells since cancer tends to make cell growth less restrained and more chaotic. So you could use the concept of fractals to detect cancer from a biopsy, or even to measure how progressed the cancer is.
Anonymous at Tue, 18 Mar 2025 13:04:05 UTC No. 16622372
>>16621615
>why is the average brain so smooth
Anonymous at Tue, 18 Mar 2025 13:59:42 UTC No. 16622401
>>16621535
this guy is great, fantastic series of videos
Anonymous at Tue, 18 Mar 2025 14:30:59 UTC No. 16622415
>>16621601
Are they claiming it's the origin of friction, or is the self-affine surface just a model for trying to explain how dynamic friction varies with pressure, roughness and lubrication like Persson 2001 https://pubs.aip.org/aip/jcp/articl
Anonymous at Tue, 18 Mar 2025 15:06:28 UTC No. 16622422
>>16620024
Fractal vise. Very useful tool, I want one.
Anonymous at Tue, 18 Mar 2025 21:18:51 UTC No. 16622711
>>16620024
you can make cool computer images
it's a computer but computers are real