Chaos Game - Numberphile
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- เผยแพร่เมื่อ 26 เม.ย. 2017
- Catch a more in-depth interview with Ben Sparks on our Numberphile Podcast: • The Happy Twin (with B...
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based
Are all the dice rolls done by hand or is it simulated random?
"I'm not going to go into the details. It's worth looking up".
Dammit, you are the "looking up" process.
This is suspiciously interesting.
One might even say Auspiciously interesting...
Anything mathematical is eventually auspicious. Just a matter of when.
It makes me fascinated to how mathematical reality is. Many assume biology and math are far apart, but then there's the affiliations like that in the video
That idea can be taken too far, Tate H, and often has in the past. It is possible today to extend the ancient fascination with numerology far beyond the positive integers.
Spaciously interesting!
This is the shape of procrastination, always changing your mind halfway through different task.
So prpcrastination is a fractal
As someone who is watching this while procrastinating from homework this hit closer to home than I'd like.
So that's how you end up Jack of all trades and master of none, because of all the holes in your skills..🤔
so the shape of procrastination is the triforce...makes sense
See the big triangle that gets left out? Your 1st class honours degree is hiding in there!
Ben: "this is a familiar shape"
Me: Yes of course it is, after many years of gaming I know it's a trif-
Ben: "it's the Sierpinski gasket"
Me: -erpinski gasket, yes... Worked with it a lot, sure.
It's a triforce fractal
What is a Sirepinski triangle? I only know about the triforce.
SPSheep
It’s what you get when you replace each filled triangle in the Triforce with a smaller Triforce, and repeat infinitely many times.
@@ragnkja It's triforces all the way down...
(1) those three points... move them a bit, so that it's not an equilateral triangle. Make it a long, skinny triangle if you want. Then the resulting Sierpinski gasket will be long and skinny. (2) OK, you want a SQUARE?? Easy: have four points, not three. Go halfway towards a (randomly-chosen) corner point, and plot your position as a point. Repeat it all day. (3) How about a distorted square, one that's seriously knocked out of shape. The same rules will result in a bent/twisted quadrilateral version of the Sierpinski gasket.
THIS IS THE WEIRDEST MATHS THING IVE EVER SEEN
I read a book a long time ago that had a quote in it that sums this up perfectly. "You look around and see the whole world falling apart. But you are wrong. The world is NOT falling apart. It is falling into place."
look for = hanoi binairy :D
You will be amazed again
lifeinsepia just look up iterated function systems, it's almost the same thing but better
DeutschMaga Was isn dat? XD
towers of hanoi
and the link to binary counting
very amazing :D
This man can't roll dice to save his life.
It's because of the paper. It cushions the dice faling and makes it slide instead.
I don't know, if his survival depended on rolling a 1 or 2, I think he'd be pretty safe!
Is this a Kaiji reference?
I guess that means he's going to... die.
That is not a dice it is a camouflaged Parker cube.
“Slightly disturbed about reality” prefectly describes how I felt when that shape appeared. I am a changed man
Chaos theory is literally my favorite area of mathematics, I would honestly love an entire channel dedicated simply to that one field.
Same
This is probably my favourite numberphile video ever made
After the "Amazing Circles" one, its my favorite!
Lila_Kuh98 that one was great too
The Feigenbaum Constant video is as mindblowing as this one.
SAME!
Interested
Please more vids with this guy about chaos theory!
When that simulation ran, my jaw genuinly dropped. That is so amazing I have no words.
same I thought how? just how?
@@jamiedonaldson794 Yes Bro.....This Is Crazy
Watching this video is like peeling back the curtain on reality. I need to go sit down for a bit.
what did you ever think math was in the first place?
im a clock I couldn’t have put it better. People who don’t like math confuse me.
I'm a clock and unique user name, so this is just obvious and not profound in any way? So what has this video got to say about mathematics, if you are fantastic at maths be humble about it
?
Actually, I take that back, it doesn't mean anything profound about reality, it's just a shape that has to happen given the rules etc
Disappointed there wasn't a giant eye in the middle.
Or a ganja leaf lol
@@theliamofella honestly though imagine something like that emerging from iterated randomness. Probably is some way to do it...
Thank you, numberphile, for another great video. Every video my fascination for fractals grows stronger
+
Moustache
If you play the same game in 3D with the vertices of a cube and the midpoints of the edges and instead of dividing the distances by 2 dividing them by 3, after enough iterations you will get a Menger sponge.
Would that be going one third the distance, two thirds the distance, or either/or?
@@Benny_Blue one third the distance. I'm actually not entirely sure what would happen if you took 2/3 the distance instead.
_"You unlock this door with the key of imagination. Beyond it is another dimension - a dimension of sound, a dimension of sight, a dimension of mind. You're moving into a land of both shadow and substance, of things and ideas. You've just crossed over into the Twilight Zone."_
Wayne S t
Sounds like something the pot gods would say.
That gave my goose bumps' goose bumps goose bumps
Justin Booby your goose bumps became fractals.
Buffalo buffalo buffalo buffalo buffalo buffalo buffalo.
@@stone7327 Here's a fractal: bufbufbufbufbufbufbufbufbufbufbufbufbufbufbufbuffalofalofalofalofalofalofalofalofalofalofalofalofalofalofalofalo
I'm genuinely baffled by this result :O I would have never guessed that rolling a dice could be linked to fractal theory!
it has to do more with he fact hat he always moves half the distance and he only has specific point where to aim
the rules are the fractal, not the randomness, the rules chosen in these scenarios are more like stencils, with the dice being more of a spray paint.
cool analogy! :)
There is no information that can create structure in the random set of numbers generated by the dice. The structure comes from the number of dots and the rules.
The die just takes you on a random walk through the possibilities. The rule (i.e. move half-way to one of the three fixed points) defines the shape. The die just causes you to sample all possible combinations of moves. You could EQUALLY WELL systematically try moves 1,2,3 then 11 12 13 21 22 23 31 32 33 then 111 112 113 121 122 123 131 132 etc. then all combinations of 4 points then all combinations of 5 points, etc.
That would be a SYSTEMATIC sample, but you'd visit every possible combination eventually. The die makes you visit every possible combination/point but in RANDOM order.
One way makes you visit every point systematically; the other way makes you visit every point in random order.
This is one of the few math things that made me go "holy sh*t"
3:49 "This is a familiar shape" , of course it is! That's the Triforce from The Legend of Zelda
*Vi Hart screaming in the distance*
yes!
SbAsAlSe HONRe yey
Yes!
I WAS LOOKING FOR THIS COMMENT
*whispering in the distance*
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hmm
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..▲
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The bit starting at 3:15 is almost magical, and the music really makes it even more so!
I love the whole concept of emergent behaviour, it's the computer science equivalent of the importance of hearing someone in the laboritory repeating an experiement and saying the equivalent of "That' odd/strange/cool/unbelievable!"
Thanks as always folks 🙂
"The rules of the universe can be written down on a single piece of paper"
Math is the language of god it seems.
It's the language of structure/patterns, and without those (think pure chaos) life can't form or exist long enough to become intelligent. no intelligent life => noone to discover math
Look up nikola Tesla and his 369 theory
Makes you think. The universe could have been invented one evening in a bar, as a brief and sketchy calculation on a napkin.
S
can you share that drawing dots program with us? it looks fun to play with
edit: it's in the description now =D
It's called geogebra, I have no idea how he did it though
then he should share the .ggb (or whatever) file. the fern doesn't look like it was in geogebra though.
whoeveriam0iam14222 I could code this quickly and i probably will. If enough people are interessted then I will share it and make it open source on github.
we are very interested
I am very interested.
This is absolutely mind-blowing
I couldn't resist but stay late and create this on Excel after work... on a Friday....
I was just thinking that this could be created in excel
Me: *furiously opens matlab to create this so I can play with it*
Triforce confirmed
GermanLoLCaster my first thought was "oh it looks like a triforce"
Seems like the Triforce is indeed the Power of the Gods.
It specially reminds me of Deus Ex. Like, this is the most Deus Ex thing I've seen in a while.
%triforce
you mean infiniforce
Wow wow.
Predictable in the relative macro-scale, chaos system is insane, and beautiful.
This is soooo cool!!! I wrote and tried out the program at home and it came beautifully! It never ceases to fascinate me!
Loved the mystical sitar chord during the computer fractal render.
how dislike the video, this is the most interesting video ever...
because it's kinda misleading...
4:56 the fact that also the starting point is replicated in the smaller triangle at the bottom right just blow my mind that's Crazy
I just managed to program the thing in Octave(GUI). It's simply amazing, and the code is so simple. Breathtaking.
3:14
I immediately recognized that as serpinsky’s triangle.
I drew it in my grade 7 science binder!
Cool things happen if you go twice the distance instead of half. Doesn't diverge and looks different every time, kind of like DNA in its densely packed state in the nucleus.
Could you link to an example of that? And maybe comment after you do? TH-cam likes to tell you that it's posted comments with links when it really didn't.
@@fakename3344 You can easily do it in the link I posted as another comment and on my Twitter (@Nonaz_jr). You can DM me if you need help.
Please do more on this, it's so fascinating!
This was incredible!!!! Thank you for taking the time to make this video!
First time seeing the fern before, blew my mind.
Years ago I was playing around on my calculator in maths class and I noticed something strange:
tan 89= 57.28996163
tan 89.9= 572.9572134
tan 89.99= 5729.577893
tan 89.999= 57295.77951
tan 89.9999= 572957.7951
tan 89.99999= 5729577.951
If you compare this to how many degrees in a radian (57.29577951) you notice two things:
(i) the order of the digits get closer and closer to the order of 1 radian (in degrees),
(ii) each time the numbers increase by approximately a factor of ten.
I'm not a professional mathematician. I wonder if anyone can give me an answer after all these years. Then I can die peacefully lol.
As you keep going to 1/10th the remaining distance from your angle to 90 degrees you keep multiplying the tangent by 10/1... 10/1 and 1/10 are reciprocals, as you might expect for a line approaching infinite steepness.
I hope you still get this notification after 2 years. As x (in degrees) approaches 0, tan(90-x)/tan(90-(x/n)) approaches n, n=10 in this case. This is because tanx=sinx/cosx. As x approaches 0 and 90-x approaches 90, sinx is basically 1, while cos x becomes nearly proportional to x (zoom in real close on cosx at x = 90 degrees and you'll see it's basically a line going straight through the origin, that is to say, y is x times a constant.) So, when you divide the difference from 90 by 10, sin stays pretty much the same, while cos goes down by a factor of pretty much 10, and so tanx=sinx/cosx gets multiplies by 1/(1/10)=10. If my statements about the behaviour of sin and cos don't make sense to you, you should know that their values correspond to the y and x axes respectively for sin and cos, which should serve as an intuitive/visual basis for understanding all this. I didn't look this up, I figured it out from intuition of the trig functions, it's a valuable skill.
It's just an exercise of limits. If you want to see the proof to your question just tell me, I'll post it on imgur
@@dieselguitar1440 hey, you never know when someone stumbles upon this two years later and wants to know the answer too. 😋
Someone posted this to reddit without linking this. Took me a little digging but I finally found YOUR video. Had to make sure you got the view and a like here. Have to give credit and respect where it's due. Love the video
6:21 that is incredible! I shouted out loud Wow!
This is the best video of numberphile
Together with the pizza one and minus one by 12 one.
At first I thought - oh, this seems a lot like my life (changing goals all the time and not reaching anything, no matter how close I get). But seeing the result got me thinking..
I learned this in an extra curricular maths course and about the applications of serpkinski triangles! It's honestly fascinating
Its a strange pattern that makes me think deeply...thanks Numberphile for such an amazing video...as a math geek I will be waiting for more videos like this
I am pretty sure that if you do it too much you end up summoning some kind of demon.
I've seen this shape before when working with Cellular Automatons
Can we have that argument about "automatons" v. "automata" ? Please? Please please PLEEEEEEEEEEEEASE?
This is beyond interesting! More videos with Ben please.
This is one of the most intense surprises I have ever experienced
But what if Wil Wheaton rolled the dice?
This comment
A straight line that infinitely points towards one.
Excellent question.
I can think of no other man who fails so hard he breaks chaos...
Brilliant!
Is that a pit of acid?
I genuinely went "what the...."
What a delightful moment, that revelation! I love it.
Thank you Ben Sparks, your subjects are amazingly beautiful 🙏
Astounding! But what shape would appear if we tried that with 3D object?????
the sierpinski tetrahedron
Or a circle with infinitely many points
Very interesting but I wouldn't say it's baffling. Just reverse engineer the point in the middle of the Serpinski Triangle. How do you get there? No point in that triangle is halfway between anything and one of the vertices.
***** not halfway between two vertices. Halfway between a vertex and SOMETHING. Consider the middle empty triangle. What would that something have to be in order to land inside it? It would have to be outside the triangle.
Andrew Pearce exactly what I was thinking. Those areas are empty because they are impossible to reach with the given restraints.
@@CorrectHorseBatteryStaple472 Maybe it would have to be outside the triangle, but that is allowed and possible according to what he said.
This is my second favorite video after the sum of all natural numbers video series. So interesting!
your videos always leave me stunned!!
Interesting
this is crazy
MINDBLOWING. Great video! really gives some perspective on how evolution (a random event) was able to generate complex things.
This blew my mind. Thanks for this.
So close to the triforce, but yet so far
Sierpinski's triangle is actually made up of an *infinite* number of Triforces.
*Infinite triforce = pretty cool.*
(Also probably a nintendo-core band name.)
Cool!
We live in a simulation.
A simulation where we live in.
Incredible ! You make my day !! Thanks !!!
In the Sierpinski gasket, there is a very simple way of proving that the central large triangle is always empty. You imagine that a point lies in that central triangle, i.e. it has started somewhere and it has gone half-way towards one of the points. Pick point A as an example. If we go half-way towards point A, and land in the central triangle, all you do is ask the question: WHERE DID WE START FROM? You will find that, if you land in the central triangle, you must have been outside the overall shape, in order to land inside that central triangle. Since the rules are that you always start inside the triangle, you can never get out of the triangle, therefore you will never land in that central triangle. Ergo, the central triangle is always empty.
Is this the sort of thing that's known as procedural generation?
Yep.
the only thing in common between all the things known as procedural generation is they go
random numbers -> things
Nope, you don't even need random numbers for procedural generation. Just - as the name suggest - a procedure. Does not have to be random at all (can be deterministicly based on previous events for example) , but randomness can be quite useful.
illuminati confirmed
I was looking for this comment.
Varun Patil Only fools can deny us now! Illuminati! ∆∆∆
George Abreu r
Nimit Dave 😂😂
Nimit Dave 😂😂😂😂😂😂😂😂😂😂
I can’t describe how incredible this video is
This is my favourite kind of Numberphile video
Illuminati confirmed *queue X-Files theme*
What was the website used here?
Stormageddon +
if you mean the software for that simulation, they're not using a website but the geometry program GeoGebra
Great Work! Application which makes sense in many fields!
The best video from Numberphile for a while
For the first time....
I'm seeing that a video has not got any dislikes till now.
(Right now, it has got 181 likes)
now it has 3 dislikes ;-;
Well....even the best videos have thousands of dislikes. I don't know why !!!!
Correct !!!! The ratio is 400:1 right now.
WHAT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
This video is arousing, literally arousing. Kudos Ben Sparks
This is really interesting. Would love to see more on this subject!
wow.....
Chaos in "orderly" math?!
I guess *the Earth really is flat* after all.
die dice
I came to conclusion a few years back that chaos is a system and order is just quantifiable part of it.
To reject chaos is to reject the opportunity to learn something new about things we already know.
Yo, PlayTheMind! I love your channel, your videos are always so interesting!
constanza86 neat.
New Yorker : Thx! Very much appreciated
This is actually mind-blowing for me.
Probably the coolest Numberphile video
this just makes me think we really are in a 3d simulation made by 4d creatures. hold me. im scared.
Nico Griffin Don't worry. Just because something natural is creepily mathematical doesn't mean we are in a computer program. It just means we don't understand. Our universe is amazing. Simple.
There is no correlation between the two ideas.
Repeat after me: die is singular; dice is plural! die is singular; dice is plural!
Keep doing that until you get it right.
Slarti Bartfast except for engineers, where a die is a tool to cut a thread on a rod and the plural is dies :)
You still say it the same, so the mantra still works.
dice can actually refer to single
dice can actually refer to multiple as well, and what's with the weird punctuation?
wasn't sure I would enjoy this video at the start but it turned out to be extremely interesting!
Wow, I hadn’t expected the pattern of fern at all. Amazing.
Great marijuana fractal
ähhhhh nope.... its a fern.
Math is the language in which God spoke to create the universe.
Atheists literally cannot help but spill their spaghetti all over the place. Calm down, fellas. Just scroll past it.
Spill their spaghetti? That is the best thing I've ever heard.
"He made a universe with very specific and structured rules, of course there's going to be an underlying pattern, even if the events within that universe appear random."
6:00
Unverifiable hypothesis much?
Come on, Autodidactus Communitati ; Don't spill your spaghetti.
More chaos theory stuff please, the previous video with this guy was also awesome!
I was expecting some ready links to Barnsley fern and related topics. Of course I will look it up now :) Amazing.
Am the only one who feels creepy ?
Yes.
notification squaaaaad
scrambo here
One the best videos on this great channel
This is fascinating and mind blowing.
That is not just amazing, it is absolutely crazy! To me there is no logical reason WHY this should happen.
No? Image where the point would have to be the step before it would reach one of the blank areas. ;)
Uh, this sounds interesting...
Treufuss: Oh I see it now! That's much simpler
The framing of this is totally misleading. Yes, the results are randomized, but the randomness is forced through constraints. Of course there is going to be a pattern.
It definitely is interesting how nature forms patterns based on randomness but it isn't disturbing or spooky, that's just how it is.
sadly nobody on the internet seems to know what logic is anymore :/ I dont resent you for your lack of understanding, but I really wish people would stop misusing the word "logic"
The framing of this is totally misleading. Yes, the results are randomized, but the randomness is forced through constraints. Of course there is going to be a pattern.
It definitely is interesting how nature forms patterns based on randomness but it isn't disturbing or spooky, that's just how it is.
I think the fact that's how it is is what makes it disturbing or spooky to people.
Immediately liked at 3:16 - awesome stuff
The last bit about ferns is certainly fantastic and inspiring for the computer folks out there, myself included. A million upvotes I would like to give to this one, if possible.