Fractal charm: Space filling curves

A montage of space-filling curves meant as a supplement to the Hilbert curve video.

These animations are largely made using a custom python library, manim. See the FAQ comments here:

You can find code for specific videos and projects here:

Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld

[yungmonkk]

Is it just me or is everyone here smart as hell and I just like the video because it’s satisfying

[NoriMori]

0:54 "This one has the most delightful name"
Me: "Snowflake curve?"
1:01: "FLOW SNAKE"
Me: 😮

[bengski]

Flow snake = snow flake! Just got that.

[Kabitu]

So the last one has an area of 0 when the seed angle is infitessimally close to 0, but when the angle is exactly 0 it turns to have a non-0 area? I need to lie down..

[caleblimb]

The title's great and all, until someone decides to read your internet history.

[wtdt]

At theta=180‎° the final iteration is 1 dimentional, at thera=0‎° the final iteration is 2 dimensional. But for every angle in between the final iteration is neither 1D or 2D, but in between.

[Pooopers]

Flow Snake seems like a spoonerism for Snow Flake, and it looks much like the Koch Snowflake, but with a seemingly angular tilt.

[theindiangeek]

For the first time in my life, I felt that mathematics is so beautiful. <3

[Hwd]

Any mathematical "porn" gets me interested tbh

[shreyasbhatt]

Sometimes I feel that the math we have is little dubious, but can't find anything wrong in it. Everything is so nicely connected and still the some of the end results are so weird.

[ABDULAZIZ-vs]

The bacteria when I drop my food for a millisecond:

[kummer]

I haven't seen a video without explanations from Brown. I guess that such video is considered art. It comes from 3Blue1Brown, his educational work is a work of art.

[peterhale]

This is what im thinking to fall a sleep i would think about a box and fill it with lines and curves until theres no more space left. Damn yt recommendation know me

[NotBigSurprise]

I thought of a way to make a single 1D line that goes through all of 3D space. First you make a Hilbert curve for a slice of space, then you extend it to all of space, and then you unfold it. With this, now you have the entirety of 3D space on a 2D plane, in which you can draw a Hilbert curve, turning the entirety of 3D space into a single 1D line.

[ammarraz.]

Nobody:
Youtube: Hey kid.. wanna see some sick shapes?
1.2 million people: Sure why not

[blasumlily]

would you do a video on 3 dimensional fractals, ones that blurr the line between 2 and 3 dimensions instead of 1 and 2?

[ktovv]

I love fractals and space filling curves because they are so beautiful; looks like a whole new universe, and I absolutely love to look and play with settings to create new ones. Is funny how simple math generates the most beautiful and amazing visions one could have, many times even by accident.

[theepicshifter]

And then he turned into more of himself. Funniest shit I've ever seen

[raighteous]

The new Mother 4 PSI effects are looking great!

[nija]

He: Says something about science.
My brain at 3a.m.: Huh? It's lookin' cool