I think my favorite is the Fern Fractal. That’s the one that broke my brain. It has the same property as Cantor Dust in that you’re making something less than 1 dimensional by breaking it up into itself, but because it’s describing an identifiable shape, it’s waay more trippy. The idea that the shape you’re seeing is essentially made up of nothing kinda hurts to think about

I prefer my fractals simply steamed, with a bit or olive oil and black pepper. My favourite ones are cauliflower (D≈2,8) and broccoli (D≈2,7) (S.H. Kim 2008). But of all cabbage there is, Romanesco of course steals all the looks, and has a distinction of having been taken a 3.2 Gpixel image of as an alignment test target of the Vera Rubin telescope. But it tastes somewhat bittery to me. :(

Fractals are awesome! My YT avatar background was generated by a Basic program I wrote on a Commodore 64 computer when it was new. I was inspired by an article in Scientific American, a paper magazine at that time.

Absolutely mesmerizing! The intricate patterns and infinite beauty of fractals never fail to captivate me. It's like getting a glimpse into the mathematical fabric of the universe!

This reminds me of a joke abstract published in transactions of the American Geophysical Union by Marc Spiegelman and Chris Scholz in 1991: "Recent high resolution mapping of deep-sea topography shows clearly that there’s a hole in the bottom of the sea. To repeat, there’s a hole in the bottom of the sea. There’s a hole - there’s a hole - there’s a hole in the bottom of the sea. Moreover, most careful analysis indicates that there is a multitude of scale lengths in the bathymetric data. For instance, there’s a log in the hole in the bottom of the sea. There’s a bump on the log in the hole in the bottom of the sea. There’s a frog on the bump on the log in the hole in the bottom of the sea. And there’s a flea on a frog on a bump on a log in a hole in the bottom of the sea. There’s a flea - there’s a frog - there’s a hole in the bottom of the sea. Figure 1 shows the 5 orders of magnitude inherent in the data plotted in log-log space and indicates a fractal dimension d = 2.76. Plotting in log-frog space gives d = 2.5. No attempt has been made to understand this result. "

My favourite fractal is the Daubechies 2 wavelet function. It's a fractal used in signal processing to analyse patterns at different scales. There are infinitely many fractal (self similar) wavelets too!

The next time you visit the library, look for The Beauty of Fractals by Heinz-Otto Peitgen and Peter Richter. It's a coffee table book full of interesting renderings, but the discussion of the background of the presented images addresses some sophisticated mathematics. I picked up my copy after seeing a presentation by Peitgen and Richter when I was in college way back when. My favorite fractal is generated by inverted video feedback loop. Point a video camera mounted on a tripod at a television set that has been rotated 180 degrees and port the camera output to the television input to create a feedback loop. I don't know if it will work the same with digital equipment, but it looks awesome on a CRT!

I do want to point out that having a fractal dimension of 2 does not mean it will necessarily fill the plane. For example, the boundary of the Mandelbrot set has a fractal dimension of 2.

There is an organism from the Ediacaran Biota called Charnia, that grew in a fractal pattern. Since this was a very early organism, it's possible that fractals are a clue to the very nature of life itself. That sounds like a bit of a reach, but if youve read Thompson, you'll know what I mean.

i feel like we're living in a tibees renaissance rn and im loving it

Favourite: Koch snowflake - in one project we worked on it appears as the perimeter of the difference-vectors from points in a hexagonal-cantor-dust.

Well, that put all of it together. Your video has helped a lot of loose ideas coalesce. Think I have finally worked out my goals for higher education. Thank you!

What a great video! I watched it yesterday and today I found the Mandelbrot book by chance while looking for a book about relativity in the library of my college. Thank you for the recommendation!

I find it quite ironic how the commonly known fractals, the Mandelbrot set, though named after their discoverer, have a name that could be translated from German to 'like bread' - which is funny when you see their structures, and compare it to the white loafy part of bread!

The Cantor Curtains are pretty cool.

The (here not shown) circular fractal you get from zeros in polynomials is interesting as it has an unusual generation method and as it is it rarely seen.

Your second channel is also very good! Keep up the good work!👍

It's funny. I had forgotten the Peano curve and now it makes Peano arithmetic and primitive recursion more interesting.

Interesting & mind blowing 😊 My favourite is the classic Mandlebrot set

Really cool! Thanks for the video!

I love you and your work. Thank you so much!

This! Also, your random spitball is something i think a lot about.

fractals are the most interesting area of math ive been introduced to so far, though as i’m only just getting into multivariable calculus, there’s still so much to learn :D

Why am I absolutely fascinated by areas of study that I'll never have the time to be proficient in, nor has any practical application to my life or occupation 😂?

Wonderfull ! What was the app used to make those fractals animations ?

I'm not sure if this counts, but my favourite fractral is a wave graph where you can zoom in and the waves look the same. y = x*sin(pi * log2(|x|))

Your voice is so soothing.

Wonderful video! I'm making generative art and I'm just discovering fractals :) I find very interesting how fractals occur in nature

Next time ur at the library, check out Patterns in Nature by Peter S. Stevens. 😊

I recently made a Hilbert Curve Level 3 by Pixels, which out of a Hilbert Curve Level 3 wirh a Laser Cutter (40m Cut line 😅).

great video thx

I've always considered fractals interesting and wanted to get into them. Is there some kind of fractal sandbox or 2D/3D engine that can be used just to "play around"?

you are so brilliant

very good!

Infinite tetration (x^x^x^x...) convergence in the complex plane looks pretty neat.

Hello Tibees:) Does there exist a fractal with fractal dimension=pi or fractal dimension= e?:):):)

Wow. Your video precipitated a bazillion internet dives every few sentenses. It took me about 2 hours to get through ten minutes of video 😊 Thanks for the inspirational content!

nice!

cool

Nice

Interesting. It's hard to imagine a fourth dimension but I guess there are fractals of dimension slightly higher than 3. Maybe those are easier to "picture" in the head than a pure fourth dimension....

6:17 that one looks a bit like Austria-Hungary to me

Braided rivers can create a nice semi-random seeming fractal structure, but I never seen math generating it and making it completely scale invariant. I managed to get image AI creating a nice black & white version after lots of trying.

6:10 looks like Texas. name fits well.

by connecting our nerves system which can cure many diseases caused by unconnected/broken nerves, super computers should use in the most important issues like cure diseases by amend our DNA to generate our nerve system to be actively connected again to get people recover from many diseases.

God bless you

fractals iceberg chart when?

The monkey tree fractal is reminiscient of the wave woodblock print created by the Japanese artist, Hokusai in 1831.

As a generative artist, I found this video very inspiring and instructive

Yes very basic in understand ing the interior landscape

Just one question. What's a fractal lol?

For every real number we take does there exist at least one fractal who's fractal dimension is equal to that real number?:) are two fractals with the same fractal dimensions the same in some sense?:) A lot of questions comes to the mind when we start thinking:):):)

Sweeet 🔥

Space is the distance between objects, not a thing.

💮🌸🌺

7:32 That's Netflix

1:22

Oh so basically everything is equations like computer code..

3:19 totally unsuspicious symbol

8:12 - ApollONian

3:44 what?

👽

Can I please come over to your house and read books..... And play games?!

0:59 0:12

hi

🤍

is this the same lady that stole from that 2d person😑

A straight line is technically a fractal.

why don't you ever pause between sentences?

This is awesome! Thought i hope that i can find one of those in peru