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.
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.
(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.
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."
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.
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
_"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."_
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.
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.
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.
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 🙂
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
Two questions about the “attractors” you mentioned: 1) When you put the point in the middle to start, it’s obviously NOT on the Sierpinski Triangle in that case. But very quickly, it appears to reach it, and stay there. Does it really reach it that soon, and then always hit points on it? Is it constantly getting closer and closer to the triangle, but never reaching it? Or is it constantly very close to it, but never touching it until the point “almost certainly” gets lucky and lands on a genuine point on the triangle, at which point it stays on it forever? 2) The case you show of a point in the middle has the point move towards the same corner several times in a row. If you started with an arbitrarily long string of luck, and never moved towards the same point twice in a row, would it still approach the triangle? Or is that streak necessary for the attractor to work?
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? UA-cam likes to tell you that it's posted comments with links when it really didn't.
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.
The origin of the pattern gets easier to intuitively grasp if you think about the problem backwards, e.g. note that if a midpoint is in the central void, all the points twice that distance from each of the three corners are outside triangle ABC, so no point inside the triangle will result in a midpoint inside the central void*. Once you have that you can see that the next order of voids can only be reached when stepping from points inside the central void and so on down from there.... *there's an extra zeroth step if you want to consider the "outside start" version, which is to convince yourself that an outside start will result in points moving steadily towards the triangle and once they are inside the triangle will stay there forever
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..
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.
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
Now(I'm watching this 2nd or 3rd time) I understand this and see the beauty. Beauty in randomness. π, triangles, everything is hidden in randomness. Math is the one and only true art.
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.
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.
Sierpinski's triangle is actually made up of an *infinite* number of Triforces. *Infinite triforce = pretty cool.* (Also probably a nintendo-core band name.)
Before I watched the video entirely, I created a Processing program to see what you were up to, and when I saw that the Sierpinskí triangle appeared out of nowhere, according to the rules, it completely blew my mind. This is some crazy stuff going on.
I'm very familiar with the chaos game generating the gasket, and that changing the vertices and distances generates other similar geometries. But the two triangles ruleset is new to me and my mouth genuinely dropped open as soon as I saw what it generated.
"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
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've been thinking about this. I would say the dice is not really an essential part of this emergent property. But the rule of the movements are. By randomly drawing from the possible actions from every spot we then converge to the true mean which ends up to be this form. So we have in a way encoded this form/attractor by choosing that set of rules.I wonder if we can do it the other way around. Define the set of rules that leads to a specifc form
Really cool! I didn't expect the outcome. It would be fun to talk/watch a video about why the structure emerges. One observation is, say I land in the dark spot in the middle. Then I must have started at a point twice as far away WRT one vertex, which would be outside the triangle, which shouldn't have happened. So I won't land in the dark spot in the middle. And then...fractal...
That Sierpinski gasket program was one of the first programs I ever wrote years ago! I had no idea how it worked at the time and this video finally explained it! :D
You can get this by generating a Linear Recursive Sequence and graphically raster the binary sequence of 0's and 1's at specific widths. The function f(x) = X^15 + X^1 + 1 rastered on widths of 239 or 9538 or 32528 or 23229 will produce Sierpinski triangles.
Catch a more in-depth interview with Ben on our Numberphile Podcast: ua-cam.com/video/-tGni9ObJWk/v-deo.html
based
Are all the dice rolls done by hand or is it simulated random?
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!
"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!
Chaos theory is literally my favorite area of mathematics, I would honestly love an entire channel dedicated simply to that one field.
Same
Please more vids with this guy about chaos theory!
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 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
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
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
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.
Thank you, numberphile, for another great video. Every video my fascination for fractals grows stronger
+
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
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.
_"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.
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...
The bit starting at 3:15 is almost magical, and the music really makes it even more so!
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
“Slightly disturbed about reality” prefectly describes how I felt when that shape appeared. I am a changed man
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.
5:20 if you are wondering why it doesn't work, the rule is move 2/3 of the way
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.
That gave my goose bumps' goose bumps goose bumps
Justin Booby your goose bumps became fractals.
@Stone H Here's a fractal: bufbufbufbufbufbufbufbufbufbufbufbufbufbufbufbuffalofalofalofalofalofalofalofalofalofalofalofalofalofalofalofalo
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.
3:49 "This is a familiar shape" , of course it is! That's the Triforce from The Legend of Zelda
This is one of the few math things that made me go "holy sh*t"
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hmm
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This is absolutely mind-blowing
Wow wow.
Predictable in the relative macro-scale, chaos system is insane, and beautiful.
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 🙂
*Vi Hart screaming in the distance*
yes!
SbAsAlSe HONRe yey
Yes!
I WAS LOOKING FOR THIS COMMENT
*whispering in the distance*
6:21 that is incredible! I shouted out loud Wow!
how dislike the video, this is the most interesting video ever...
because it's kinda misleading...
This is soooo cool!!! I wrote and tried out the program at home and it came beautifully! It never ceases to fascinate me!
"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
Two questions about the “attractors” you mentioned:
1) When you put the point in the middle to start, it’s obviously NOT on the Sierpinski Triangle in that case. But very quickly, it appears to reach it, and stay there. Does it really reach it that soon, and then always hit points on it? Is it constantly getting closer and closer to the triangle, but never reaching it? Or is it constantly very close to it, but never touching it until the point “almost certainly” gets lucky and lands on a genuine point on the triangle, at which point it stays on it forever?
2) The case you show of a point in the middle has the point move towards the same corner several times in a row. If you started with an arbitrarily long string of luck, and never moved towards the same point twice in a row, would it still approach the triangle? Or is that streak necessary for the attractor to work?
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? UA-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.
Loved the mystical sitar chord during the computer fractal render.
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*
This video is arousing, literally arousing. Kudos Ben Sparks
3:14
I immediately recognized that as serpinsky’s triangle.
I drew it in my grade 7 science binder!
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.
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
I just managed to program the thing in Octave(GUI). It's simply amazing, and the code is so simple. Breathtaking.
This is the best video of numberphile
Together with the pizza one and minus one by 12 one.
The origin of the pattern gets easier to intuitively grasp if you think about the problem backwards, e.g. note that if a midpoint is in the central void, all the points twice that distance from each of the three corners are outside triangle ABC, so no point inside the triangle will result in a midpoint inside the central void*. Once you have that you can see that the next order of voids can only be reached when stepping from points inside the central void and so on down from there....
*there's an extra zeroth step if you want to consider the "outside start" version, which is to convince yourself that an outside start will result in points moving steadily towards the triangle and once they are inside the triangle will stay there forever
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..
This is one of the most intense surprises I have ever experienced
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. 😋
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.
Now(I'm watching this 2nd or 3rd time) I understand this and see the beauty. Beauty in randomness. π, triangles, everything is hidden in randomness. Math is the one and only true art.
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?
This is my second favorite video after the sum of all natural numbers video series. So interesting!
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.
The best video from Numberphile for a while
2:35 Parker randomness?
Probably the coolest Numberphile video
I've seen this shape before when working with Cellular Automatons
Can we have that argument about "automatons" v. "automata" ? Please? Please please PLEEEEEEEEEEEEASE?
I learned this in an extra curricular maths course and about the applications of serpkinski triangles! It's honestly fascinating
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.
This was incredible!!!! Thank you for taking the time to make this video!
Astounding! But what shape would appear if we tried that with 3D object?????
the sierpinski tetrahedron
Or a circle with infinitely many points
wasn't sure I would enjoy this video at the start but it turned out to be extremely interesting!
I genuinely went "what the...."
This is my favourite kind of Numberphile video
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!
I'm majoring in Electrical Engineering but I love Mathematics. It's logical, precise, absurdly useful, and highly mysterious at the same time.
this is crazy
Math is a discovery, invention and art.
We live in a simulation.
A simulation where we live in.
Before I watched the video entirely, I created a Processing program to see what you were up to, and when I saw that the Sierpinskí triangle appeared out of nowhere, according to the rules, it completely blew my mind. This is some crazy stuff going on.
Interesting
I can’t describe how incredible this video is
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
Before you even mentioned the part about the computer, I wrote a script to do it and I was extremely amazed at what was showing up on my screen.
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.
Incredibly complex patterns arising from simple rules. Amazing
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'm very familiar with the chaos game generating the gasket, and that changing the vertices and distances generates other similar geometries.
But the two triangles ruleset is new to me and my mouth genuinely dropped open as soon as I saw what it generated.
WHAT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
He is one of my favorites because the things he chooses to talk about are like the secret low key super interesting ones.
wow.....
When I saw the Sepinski triangle emerge I gasped, my mind was so utterly blown by this
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.
This is actually mind-blowing for me.
Am the only one who feels creepy ?
Yes.
PLEASE I NEED MORE BLOWING MIND THINGS LIKE THIS!!
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.
I've been thinking about this. I would say the dice is not really an essential part of this emergent property. But the rule of the movements are. By randomly drawing from the possible actions from every spot we then converge to the true mean which ends up to be this form. So we have in a way encoded this form/attractor by choosing that set of rules.I wonder if we can do it the other way around. Define the set of rules that leads to a specifc form
Really cool! I didn't expect the outcome. It would be fun to talk/watch a video about why the structure emerges. One observation is, say I land in the dark spot in the middle. Then I must have started at a point twice as far away WRT one vertex, which would be outside the triangle, which shouldn't have happened. So I won't land in the dark spot in the middle. And then...fractal...
I sprinted to my math professor with this video. He audibly gasped when the shape began to be revealed.
Thank you Ben Sparks, your subjects are amazingly beautiful 🙏
A lot more interesting that I was expecting!!
That Sierpinski gasket program was one of the first programs I ever wrote years ago! I had no idea how it worked at the time and this video finally explained it! :D
Almost fell out of my chair when those triangles appeared! Amazing!
Ikr
One of the much better videos you have posted! Not that there are any bad videos...
You can get this by generating a Linear Recursive Sequence and graphically raster the binary sequence of 0's and 1's at specific widths. The function f(x) = X^15 + X^1 + 1 rastered on widths of 239 or 9538 or 32528 or 23229 will produce Sierpinski triangles.
I was expecting some ready links to Barnsley fern and related topics. Of course I will look it up now :) Amazing.
Once I heard "triangle" and "half way", "Sierpinski" rang in my ears. I guess I'm officially numberphiled 4 life!