Levy Curve from the Chaos Game

In this video, we show how to use a random process of iteratively applying two linear transformations in the real plane to generate fractal curve known as the Lévy Dragon. What happens if you do something similar with different affine linear transformations?
If you like this video, consider subscribing to the channel or consider buying me a coffee: www.buymeacoff.... Thanks!
Check out these videos for related constructions:
• Mandelbrot Quintet Fra...
• Chaos Game in a Hexagon
This animation was inspired by an article written by Larry Riddle that appeared in the the November 2016 issue of Math Horizons:
doi.org/10.416...
See more here (larryriddle.ag...) and on his website: larryriddle.ag...
#chaos #chaosgame #levy #levydragon #mathvideo​ #math​ #mtbos​ #manim​ #animation​ #theorem​​​ #iteachmath #mathematics #dynamicalsystems #iteratedfunctionsystem #dynamics #fractals
To learn more about animating with manim, check out:
manim.community

[@NickH-o5l]

I'm a huge fan of chaos theory. My grandfather did some stuff with the 3 body problem when he was younger and told me about this stuff. Absolutely beautiful.

[@rutabega306]

Ok but this is not chaos theory

[@NickH-o5l]

@@rutabega306 yea it is It’s based of a set of simple rules and gives something that has no general solution, like strange attractors or the Mandelbrot set

[@daseapickleofjustice7231]

Reminds me of that Chinese series, not the Netflix one that adaptation is like a whole other series.

[@starboi141]

​@rutabega306 but it's just a theory

[@PoopyMcStinkertons]

My grandfather had dementia and I was born after him developing it and died when I was a toddler.

[@Fitsz]

i have no idea what anything means but it looks cool

[@СоняБарахнина]

same lol

[@walterclarkiv5526]

It means that geometric patterns occur out of pure randomness. That is the law of the universe that right there is what makes all plants all subatomic structures everything from the microscopic to the cosmic scale​@@СоняБарахнина

[@blue-uv4mh]

Me neither, but it looks like even though it is random, it still always makes this shape. Maybe it says that randomness is finite, or just "random" within a confined space making randomness not truely random? Does the randomness follow the pattern of the first two dots? Idk. That was just my conclusion from this one video without background info. It looks cool too. And the matrixes end up mirroring each other? I don‘t even know where to even start with the real world implications of how randomness truely works (or maybe I‘m dumb, idk)

[@Fitsz]

@@blue-uv4mh random or not, wowie cool dots cool looking idk

[@delsinhays6421]

​@@blue-uv4mh there is no chaos, only a beginning. Look at it, when you are at the beginning then you'll know the ending since you were at the start of the equation. When you're in the middle of the equation with seemingly infinite past options, it seems chaotic. And it is. Chaos is perspective based on ones reality, in my opinion.

[@20icosahedron20]

If mathematicians show their power 💪🏻💪🏻💪🏻

[@RadenWA]

Looks more like tentacles 🦑

[@kirb4089]

That's a octopus tentacle right there

[@narrativeless404]

Buff Squidward

[@hmkim8097]

looks like two fetuses for me

[@jamesittraining3206]

Ahaego

[@Flesh_Wizard]

Fractal says "C"

[@shadow19734]

😏

[@AChangedMansDream]

Me: tries to follow along "Let's do this 25,000 times" Me: Oh... Ok

[@Quietkid69420]

Minecraft tutorial builders:

[@missmarymack06]

I’ve taken finite mathematic class and we finished the course with matrices. We didn’t talk about this! Heckin cool!

[@Sahlokniir325]

Just don't take an infinite mathematics class, it'll never end

[@GabeTheSilly]

@@Sahlokniir325 oh nooo

[@gugoluna]

I have no idea what you're talking about, but it looks hella pretty

[@jbear3478]

Who even discovered this crap

[@AndroidIndustry]

😢

[@somedude4087]

mathmatical croissant

[@MajorHellstrom_1]

Bodybuilding motivation by maths 🗿🍷

[@VashVicious2]

Dragon? Dude that's chtulhu, yall summoning a creature between worlds, true chaos indeed.

[@sk_lxr2920]

stuff as whimsical as this (like the one Disney documentary about math and how it's displayed in nature) makes me love math. I'm still studying trigonometry but I can't wait to get to the weirder stuff like this, it's fascinating.

[@mateocastro6005]

hey, what's the name of that documentary u talking bout?

[@sk_lxr2920]

@@mateocastro6005 maybe documentary is not the right word for it. either way, it's called "Donald in Mathmagic Land", from 1959.

[@WobblesandBean]

​@@mateocastro6005 There's another one specifically about fractals narrated by Arthur C Clarke with music from Pink Floyd. It's awesome. That one's called "the shape of infinity", or something like that?

[@Frostgiantbutsmall]

​@@sk_lxr2920 Yes, love that one! I've never enjoyed doing math but Donald at least made me grow to appreciate it for what it is.

[@RandyKing314]

ahhhhhhh yes that will do nicely. helps bring my brain back online after spring break

[@TheStrings-83639]

It looks like some kind of a lovecraftian entity to me.

[@vincentcrow6075]

Agree

[@МаксимГорюнов-м7и]

This might be a mistake, but I have this to say: it is called a Levy Dragon because, in a sense, this curve is a brother to another, possibly even more famous, Dragon Curve. I found this out when I tried to create a program in C which draws the Dragon curve. Basically, you start with two points and then create a third point between them so that they form two sides of the square. Then you repeat this process recursively for each part, but for one part you draw a new point, let's say, to the left of the direction from point 1 to point 2, and for the second half you draw it to the right of the direction from point 2 to point 3. I had a variable which changed from -1 to 1 and back to -1 to indicate the direction, but the first time I coded it I forgot to change the direction and the point were always to the left. I got this Levy Dragon curve.

[@lgooch]

Dragon curve can also refer to the self isogonal cubic on a quadrangle

[@anujagrawal4404]

MATHEMATICS IS BEAUTIFUL

[@Nate_Allen]

Okay so I watch a lot of chess content and was so confused when I saw this video suggested, makes a lot more sense now

[@barnabasrsnags4828]

Who watches chess content? Thats so lame/s

[@nishyanthkumar]

gothamchess curve

[@LemonadetvYT]

Le croissant

[@catmacopter8545]

Is it possible to create the levy c-like curves with different angles (in this case it is 45 degrees) with different matrices?

[@graphicmaths7677]

This is an example of Micheal Barnsley's collage theorem. The entire curve maps onto itself twice if you shrink it and rotate it, The blue area and red area are each an exact copy of the original curve. The two matrices perform the mapping.

[@tommytress77]

Cartoon character muscles be like:

[@Cookie82772]

Make a visualization that shows how the final shape varies as you tune the affine transform params

[@MathVisualProofs]

Yes, this is on my list to do. I haven't been able to make it look right yet.

[@KaliFissure]

L system drawing tools are my fidget toy

[@MathVisualProofs]

And mine!

[@darkfent]

Or tentacles...so it is a hen...shin

[@quagsiremcgee1647]

The mathematicians they broke my random coin. Now it just forms Levy curves

[@TristanTheChessPlayer]

Didnt know Gothamchess was a math man

[@karen_jaeger]

Lol

[@pablovelasco4270]

Ah, yes, the Pythagorean Croissant.

[@therealmagmalord3479]

That looks like a good profile picture

[@DionysiosVasilopoulos007]

That's not a dragon. That's the motherf*cking Cthulhu!

[@vlinnstone6919]

what

[@VibeDPyro]

My question is why it’s called a dragon when it resembles a kracken

[@omega7057]

Should be called the kraken curve

[@peridotgaming5894]

That is a buff man flexing his biceps.

[@GilCosta1965]

le croissant

[@iamseamonkey6688]

Levy sideways strongboy curve

[@ilyasworld2035]

It looks like a dude flexing his muscles

[@Eta_Carinae__]

If you just selected both points, would it not also make the same shape, since also selecting the other point is also as random, which should make the same fractal, at which point you just have two of the same fractal just layered onto eachother.

[@WittyBit13]

It looks like an octopus flexing

[@S.G.W.Verbeek]

Red andblue croissant 🥐🥐

[@Rakshasa1986]

I like this screen saver.

[@MrAdamo]

Is this because you’ve outlined some kind of function or space, and we’re just “probably” choosing some point along that space?

[@ВалентинГражданкин]

Это же почка!😮 вот формула кровяного фильтра позвоночных!

[@derekhasabrain]

I knew about the Levy C Curve cause it’s like generating the dragon curve with opposite rules. I have no idea how matrices work though so I don’t understand what this means lol

[@ipnade]

I know very little about matrices but if you tried with a 4x4 would you end up with a complete square?

[@blackholesun4942]

You can make this shape very easily in ms paint! From one small line, you can copy+rotate+paste untill a fractal appears ! 😁

[@yurei8525]

mathematically accurate cthulhu

[@The_Totes_Adorbs]

ASCII text has just learned about r34 and is now becoming a tentacle monster

[@Algebralien_fan_number_1]

Me watching this at 2 AM: "I like you're words magic man"

[@veggiet2009]

Looks like a croissant

[@MegamanZero410]

Looks more like the mathematical model of Cthulhu with the tentacles reaching from the void.

[@paul_warner]

Levy never fails to draw a dragon with an iterated function system

[@Tasorius]

No idea what any of those words meant, but the result is clearly an eldritch abomination...

[@draketungsten74]

I love dragon curves and Julia sets and stuff.

[@wildfire3986]

Mathematical Cthulhu

[@52392daner]

RELEASE THE KRAKEN!

[@georgesmith4225]

I love fractals but you can’t tell me they’re not the work of some eldritch power I mean look at it

[@lightningwingdragon973]

I'm here for the pretty pictures... Now where are the dinosaurs?

[@infinityzer054]

Fractal boomerang

[@AnnaArmellino]

Oh, hello Cthulhu!

[@0therun1t21]

I thought I'd seen all the fractal variants, but no and this one is really cool! Thank you! I bet there's a lot I haven't seen yet.

[@ayaan_maan]

Very nice game. Ill play it with the cousins next time.

[@Sumpydumpert]

Wow great video I like the name too Levi’s dragon bc it looks like wings

[@michaelh5314]

Cool! I was able to recreate these results in LabVIEW, neat stuff

[@psykol-1]

cool math dragon

[@Hexagy]

Bro i just felt like a kid in a candystore after seeing my favorite fractal appear from thin fucking air

[@toxicv972]

I like this cuz it cool but hate it cuz i have a personal vendetta against math.

[@Peter-Slash]

Why would I do this Why would I then do it 25,000 times

[@S1ushyHead]

Can’t wait for the English version of this comes out

[@Indira-minuaga]

It looks like a kidney, mitochondria,and a foetus at the same time

[@tumage8592]

Should be called the levy kraken but im no mathguy

[@davidmartin5483]

Dragon? Idk. Looks more like a pair of tentacles to me

[@theobamaprism]

golden ratio haunts me everywhere its even HERE

[@DRENS2131]

Aang and Zuko finding out the Levy Curve.

[@Jesusesbiggestfan]

Brain hurt make stop bad flash back ☹️

[@kaifikri9265]

Looks like a kidney 🤔

[@CKREnKA]

у моей бабушки на ковре, который на стене - такой же узор

[@errolluck8347]

I didn't understand a thing but damn it is surely beautiful

[@TheRuancarlo]

Nice to see Cthulhu making his appearance

[@thepacifistgirl7071]

i did like an ms paint of this curve i forgot how to to it but it was cool

[@JohnsonJohnsonJohnson-j6r]

I just woke up and yt is shoving math in my face, on the other hand I got to see a cool dragon thing.

[@necro-claud6370]

Not just chaos theory but also large numbers

[@wildfire3986]

Cthulhu

[@Blackchain119]

It's really cool but...that's an octopus.

[@kawakebcookie5826]

It’s looks like a man flexing his muscles

[@Humberto_Fernando]

Compreensível, tenha um bom dia

[@janethmcraya5639]

That's definitely a croissant

[@mathijsjacke1915]

In the beginning, why does transformation f2 shift the origin to the left. Then it wouldn't be a linear traansformation right? Is this just a mistake in the animation or what's up?

[@MathVisualProofs]

The term "affine linear transformation" includes shifts along with a linear transformation. So you do need one of them to have the shift.

[@Wheatley_Crab]

How to attract any chess player Type levy

[@benheideveld4617]

Nothing about Levi, it is the Julia set of the Pythagoras tree. Hausdorff dimension 2.

[@communistpropagandist4608]

Uh huh, yeah, I know some of these words.

[@jessicacrider813]

I have no clue what you just said, but I like it

[@seta6185]

it looks like advanced migraine aura

[@yungpm]

Even in chaos there is order.

[@barnabasrsnags4828]

Your mom

[@fluffypig8206]

It looks like a buff man flexing

[@eliasvonbrille]

Wooow there is so much stuff in math that is absolutely mind blowing!

[@jogiff]

Boy, I sure wish KZbin didn’t cover up the screen with so much junk for shorts.

[@MathVisualProofs]

I agree. I don’t have any idea how to remove some of it. Like can I remove the “shop” icon?

[@charlescase1232]

"Nice, a fractle reality." *arc5*

[@leucminh440]

i remember you can also do it in paint

[@adrianmacias9144]

Levy C? As in the same Levi as the Levi Cevita symbol??

[@TwoJaysMoon]

🐙 🦑