How to make fractals by counting
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- Опубліковано 19 чер 2020
- Algorithm Archive: www.algorithm-archive.org
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3:03
"We then did the same for the square and called it quits"
*_Video ends_*
I thought about that! The joke was that base-4 trits are sometimes called quits. Well, that's what we called them anyway
This video took a really long time to make, but I think it turned out pretty well! It was a follow-up to 4 other videos, so it's a bit more complicated than my normal content, but I hope it was still clear! I was blown away when I realized we could do a Breadth-First Search of a full n-ary tree by counting in (a particular version of) trit space.
Anyway, let me know what you think. I will be experimenting with methods in the near future to minimize the amount of time I spend editing and therefore get content out to everyone faster, so keep an eye out for future videos.
Also: if anything I said here sounds cool, please consider stopping by twitch (www.twitch.tv/simuleios) or supporting the project on github sponsors (github.com/sponsors/leios). I am working on the project every day, but the videos are the very last part of that process, so even if it takes a while for content to find it's way on youtube, there is a lot more going on on different platforms!
The digit for binary is called bits,
so let’s call ternary digits trits.
quarternary? I’m just going to call it quits.
yup!
Love the continued work and streams LeiosOS! Keep it up!
Glad you like them!
Thanks for the insightful content as always!
Thanks for watching!
The video turned out great
Thanks! I'm glad you liked it!
Very nice, I like
Thanks!
Nice!
now you really over-engineered it :)
That was the plan!
most robust approach is to use space subdivision with functional approach. I did in this way dragon curve in very high resolution several years ago.
This works well for Sierpinski drawing, but here I was mostly interested in optimizing a BFS. Drawing Sierpinski was just the product.
That said, I want to cover subdivision methods now...
Great video! What software are you using for the simulation?
We are using out own library: github.com/algorithm-archivists/GathVL
Still a work in-progress, but it's slowly getting there!
What an awesome video! GG! but I don't get why you need to define tryts (on the small program you shown), why don't you just store them as integers and convert them into base 3 when needed?
Ah, we could definitely do that. The tryte definition was a bit of a hyperoptimization. I was actually going to just use integers and not worry about it, but twitch chat helped out and I think it was nice to use some bitlogic as well!
Wouldn't reorganizing the set-up to work with a depth-first search have a best-of-both-worlds result regarding computation and memory? Then you could represent the tree as a stack and re-use the computation of the higher levels. Maximum "nodes" would be depth of the tree, and each node needs to be computed only once.
There are 2 ways to use DFS for this:
1. Redo the animation so you follow one child down 10 generations, then the next child, and so on... This would provide a fundamentally different animation. We definitely needed a BFS.
2. Reframe the DFS so that we do all DFSs up to a certain level. This has the same amount of computation as our solution.
Honestly, we could have made these solutions work, but we decided against it for 2 reasons:
1. We are over-engineering the problem, so we might as well fully over-engineer it. I was interested in doing a BFS, not a DFS.
2. I am used to the world of GPUs with limited recursion depth (recursion was not supported at all until recently). This means that the DFS solution would be bound to CPU architecture, which kinda left a bad taste in my mouth.
I had this discussion in the video, but ended up removing it because I couldn't think of a good way to animate it.
Very cool and feeling some 3blue1brown vibes in the video.
Haha, that's a huge complement in my book. Thanks!
wow
+1 for D Knuth name-drop
Knuth is super cool!
thanks
No problem
Oh. Hai serpinski
Yeah, I don't have plans to revisit it after this video. No plans I can think of, at least
@@LeiosLabs I enjoyed it. Used to do those on my graphing calculator.
Any problem worth solving is worth overengineering
That's a new motto to go by!
for myself 1:13