Sequences 10: Fractals and Chaos

[msjessypp]

some really good stuff here

[jessyjessy4]

This is a great video

[grisgrisy]

i enjoyed this vid

[prchecker]

love the video man

[Iamyoubestfreind]

... WHAAAAAAAAAT????????????

> . <

[8644371]

Mind blown.

[G0ttaBeFresh]

Thanks for making these vids!

[alihandro9]

the cool thing is that music brought me here.... the Fibonacci sequence in the song lateralus by tool blew my mind. i never knew math could be so interesting. so i did a little more research on the fibonacci sequence and found these videos and got hooked. i see math in a whole different perspective than i used to before.

[Avatar230594]

After this guy made these vids I started liking math

[SparklesMr]

Thank you, you are an inspiration and a motivator. After watching this video I'm encouraged to continue to study mathematics and pursue my degree.

[magicman0617]

Thank you so much for your videos! Every one of your presentations is extremely fascinating. I'm looking forward to viewing many more!

[Bebander144]

This is why I love math so much!

[xXSparky117Xx]

If you like chaos theory and fractals I recommend reading Jurassic Park.

[easethebeat]

Is it a good sign when a video starts by advocating why you should watch it all the way through?

[ThatGuyCalledPhillip]

Can you teach us how to create that chaos program in our graphing calculators? Thanks!

[raoulhery]

there is no such a thing as chaos, only thing the human mind doesnt understand

[99XiNUZ]

mind = blown :O

[hatsoff456]

that was amazing!! thank u so much!

[asphyxiateDrake00]

4:40 My mind was blown seeing the fibonacci numbers in the fractions.

[furyberserk]

Chaos = irrational

Golden triangle = growth

love = 1 or 2, but less than 3 so love is <3, which is also irrational and can grow.

... so that is what god is!!!

[wirechair]

i love maths!

thanks for the video!

i like your simple explanations and that u explain everything that u do. u dont just assume we would realize certain things. keep it up!

[keishafabio]

12:18 :O

oh my goodness!!! the best surprise I had this year!!! :D I really enjoy 'Chaos' and how it reflects life and everything! Thank you for your videos... *subscribes*

[TheToid]

I wrote a little proggy in C# to perform the chaos game, i wanted to see what happened with geometric shapes with more than 3 sides, had it and running, triangle worked as expected. However I found that with a pentagon it works, creating a tesselating pattern of pentagons (of course even numbers of sides dont work). However, with any number of odd sides above 5 it didnt seem to work, you just end up with a single shape in the center the same as the main geometric shape, no extra tesselations?

[yutzwagon2]

Even oldfags can't triforce like this guy.

[joanhwilson]

I never passed a math class in my life.... but does this mean there's no such thing as chaos?

[jmaioran]

@joanhwilson That's a really profound question, and not sure that i'm answering it properly. I would just say that all things are interrelated, Einstein called the universe deterministic. Nature is so complex, yet also so simple (check out videos on fractals, the mathematics of nature)

[enkhuizenddg]

can someone tell me how to get that random program. i have a Casio CFX-9850 PLUS.

[nothingstopskings]

Sir,

I really like Math, but it seems a lot of folks (both tutors and "teachers") try to use it as a tool to make themselves appear smarter than they actually are by intentionally confusing others. Which is an attitude I find to be a huge turn off. Well, your videos are great, and you do not do what the above type of people do.

Thank you for sharing,

-Nothing Stops Kings

[eaglefer]

Haha!! I didn't expect the fractal would emerge from a rule which involves perfect randomness. Do any other fractals have this property, so they can be constructed using a random algorithm?

[infantileretard]

@eaglefer There is order in the "chaos"; the rules that determine where the next point should go geometrically determines all possible points in that equilateral triangle. When you run the iterations on the calculator, it just shows you all the possible points that the rules allow. It is not chaotic at all except the order in which the points appear.

[whisperr33]

THIS IS SO CRAZY AND AWESOME

[GeneralOJB]

So on and so forth....

Let's go to the next board...

lol

You rock. :D

[matematicario]

This is AMAZING!!! You have an incredible way to teach some though subjects. Thank you for this MathTV. :)

[ramaynard77]

so cool..........

[thecaster]

That was amazing.

[jmartm050179]

Sir, do you think it would be possible that the DNA has 3helixes instead of two not counting the central one. Since life is unpredictable and we evolve within it, would DNA evolve chaotically. In which case we would actually be evolving without knowing by changing our own DNA with random info coming from the outside world, our environment? What do you think?

if you think that's stupid be cool about it.

Would there be then a relationship between this "chaotic" triangle and our "chaotic" DNA?

[cesfigas]

Great method of teaching, it dust gets in a guys head.

[kimkhmer]

Thanks

[ODBastardW]

what about the point in the middle where it should be a blank space?

[sheean42]

that is a part of the line across the middle that forms the top of the large blank triangle. :)

[Paulancar]

The power of the simple.

[GR1o6180339887498948]

Holy crap, how did that happen, I'm speechless.

@.@

[Arycke]

I love your videos, sir, and I was curious as to what the basic code was for that program, I assume it is just a simple program using a rng, but I'm having some trouble making it and I was wondering if you could post the code please :) Thank you for your time.

[jacobbis4lovers]

Are the topics in this video covered in calculus?

[Arycke]

No, not really. Chaos theory and fractals aren't really the focal point of high school calculus or even undergraduate calculus courses, more along the lines of derivatives (differentials), integrals, sequences, series, vector calculus etc. I studying Pascal's triangle in 7th grade, and that was my first exposure to a fractal (Serpinski Triangle), and the only other time I saw a fractal in was in Pre-Cal, we were studying Fibonacci's numbers, which relates to Binomial expansion.

[Supuhstar]

Can I get the code for that program? That's awesone!

[Supuhstar]

O.O It's the Sierpinski Triangle! I noticed at 12:16

[Supuhstar]

That graph looks like a perspective drawing of a construction site...

[mechwarreir2]

12:46 its the triforce! jk...

[TheAdisonic]

ooohh that ending was freakish n good

[0PsycoDad0]

Now I´ve learend how to fry my brain with the Syrpinski-Trialngle but I understood nothing about the chaotic structure of the logarithmic scaling process; plz help me out...

plz (again!) remember I´m in no way talented in math!

[09205479428]

Wow. We are getting near. Math picking up with the grand unified field theory... singularity !

[doesthismakesense123]

I'm a stats major, math minor. I was never taught this, and I really enjoyed this video. Thank you so much!

[LordGodofIsrael]

why didn't I have you as my teacher in high school? i would have definetly done better than I did

[Elliot137]

I should imagine the way that teachers would like to teach if they didn't have to constantly tell the class to be quiet and go around helping everyone would be better than the way that they are forced into teaching.

[Yurmamaismybitch]

damn math is intresting i mean i hate it to the bottom of my heart but i need to pass my math so i'm trying to search some vids about math and damn it's more intresting than you could imagine thanks ;)

[ruufeeooh]

@Yurmamaismybitch wise words from Yourmamaismybitch.

[eyeojo]

Love your videos, even as someone double the age of a high school senior!

[SaintJimmy0017]

.. wow.. now why is that??????

[DeeDoubleYou81]

That's awesome! What happens if you started right in the middle of the sierpinski triangle on the calculator?

[jens009]

That's what he did. But you can see that the overall end result still produces that triangle. The initial input doesn't really matter. =D

[DeeDoubleYou81]

Hmmm... I see what you are saying, but I guess I'm still confused. The triangle has a void in the center, what happens if the very first "dot" is in there? Or do we not count the first "dot"?

[greywolf424]

Very cool

[lmcdowall]

yeah that was cool

[JasoniumGH]

how do i do that on my calculator?

[tomthecool]

I didn't really like the first part of this video - you over simplified things a LOT.

But the ending was very cool.

[IckleMcMan452]

I wish you had been my math teacher in high school.

[HubertCumberdale22]

hm... where is the first point?

If the first point is in the middle of the triangle you won't get the sierpinsky triangle...

(0/0)?

[ProKatted]

LOVE THIS! EXCELLENT! GOOD JOB!

[rozeboosje]

Nice! Loved it.

[wtblessing]

very well done. fantastic ending!

[Waranle]

Thank you alot Sir :) always enjoy your videos

[Galahad14of13]

Outstanding!

[friendlyfire53]

Great ending.

[sonofagunM357]

is the key to immortality

[l2m3c7778]

Math is POWER!!!!

[RouletteRog]

YES!!!! Chaos is one of my favorite areas of mathematics, and one of the reasons why I became a math major. I read about this game in Fractals For The Classroom, by Peitgen et al. A lot of the work done in chaos theory relies on differential equations, but as FFTC shows, it's easily grasped by students with a reasonably strong background in algebra.

Thanks for this awesome video. I regret that I have only five stars to give.

[FezTube11]

Nice! I don't think I ever learned about this in math class, but that was definitely the type of concept that we should always be taught: everything is related, and even if we don't learn how, that fact should at least be mentioned. It certainly makes me a lot more enthusiastic about math class, but I already like math, so I'm sure this would help someone else a lot more.

Great video. Long, but it went by fast. :)

[DavidAKZ]

Very informative, thanks. Do you think there are some physical examples based on this sort of determinism ?

[BrianTheMusicMan]

Chaos game = God's game

[sdfdsv]

omg :o

[ScientiaPerceptum]

This is great and I will work with my math teacher (I'm the science teacher) to work it into our already established interdisciplinary unit for next year.

Thanx

[mathgeek37]

Very interesting...

[marjan15]

This is amazing, thank you for nice presentation.

I wonder how intelligent you have to be to know the result "from the guts". It looks so unintuitive...

[Koujinkamu]

Who knew it from the guts?

[marjan15]

Maybe all people with IQ over 160 ?

[Koujinkamu]

I asked for a name - specifically the name of the guy who found out about this. Do you think all people with IQ over 160 can figure this out?

[marjan15]

Well, that would be cool! :)

Anyone with IQ > 160 reading this? Please respond.

[kurtu5]

IQ is bullshit. It really doesn't exist. And this is comig form one who tested higher than 180.

[marjan15]

Where did you scored so high? Official test? Are you Mensa member?

Are you saying that IQ tests are not really testing your certain mental skills? Please explain.

[kurtu5]

I was a problem child. So they sent me to psychologists and I took a test a few times.

I got a 160 the first time around, and the second time I got 180+. As far as mensa? Never. Too smug.

I realized then, and have the supporting peer reviewed evidence now, that the measure of man is utterly flawed. IQ tests are shitty tool sold to parents. They sell a lot of them.

[kurtu5]

Steven Gould does a decent introduction to the problem of IQ in, "The Mismeasure of Man".

The reason I scored so highly, was that I was already familiar with the abstractions the test "tested". I was familiar with the tricks used to make you pick the wrong answer.

I am just good at taking tests. It doesn't mean I am smart. I have meet so called dumb "girls" who are ignorant on a large variety of subjects, who are actually quite smart, yet ignorant in the domain of questions an IQ test.

[ariesvids]

One can believe an anonymous commenter on YouTube -- or the leading researchers on intelligence. Google "Mainstream Science on intelligence."

Claims that "IQ is bullshit" are politically correct bullshit. IQ tests are highly g-loaded (see "g factor".) What they measure is ability to deal with complexity. The greater the ability to deal with complexity, the higher the intelligence.

[Giggungungap]

Very well said.

[0PsycoDad0]

really?

[MathMikie]

great video there are great relationships btween things that seem really complicated

[CousinoMacul]

So we can get the Sierpinski Triangle from not only Pascal's Triangle, but from a random iterated function. Wow!

*****

Favorited!

[websnarf]

Ok, exercise #1) Prove it. :)

Actually, the point is that if the starting point is ON Serpinski's Gasket, each random step will continue to stay on it, and if the point is in one of of the empty gaps it will stay in one of the empty gaps at each random step.

[CousinoMacul]

Funny you should say that because that's exactly what I was thinking. When you draw Sierpinski's Gasket, the outer triangle is the set of all points midway between a corner and another points on the adjacent side. The first inner triangle you draw marks all the midway points between each corner and the points on the opposite side. The next set of triangles are the set of midway points between each corner and the points on the first inner triangle. Etc. :-)

[netinfoseek]

When I programmed my computer to graph Sierpinski's triangle using the iterated function and placed the first point on an empty gap all the following points were on the gasket. Try it for yourself.

[VeritasEtLibertas82]

This is fantastic!~

Can you show me how you programed your TI?

[kid29a]

I made this in Java. PM your email I can send you if you're interested :)

fantastic lecture!

[recon455]

The TI manuals actually have this an example program for TI-BASIC. Check out your manual or look for it online on the TI website.