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Speaker 1: Brought to you by the reinvented two thousand twelve Camray.

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Speaker 1: It's ready. Are you welcome to Stuff you Should Know

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Speaker 1: from House Stuff Works dot Com. Hey, and welcome to

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Speaker 1: the podcast. I'm Josh Clark, hanging on by my fingernails

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Speaker 1: with me as always as Charles W. Chuck Bryant, doing

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Speaker 1: much the same as we were about to start speaking

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Speaker 1: on stuff you should know about fractals, more math, theoretical

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Speaker 1: man even, Yeah, a new branch of geometry. It's non

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Speaker 1: Euclidean since you brought it up, okay, very new Euclidean

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Speaker 1: geometry was like, and fractals are. So there's a little

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Speaker 1: bit of a gap there. There is a little bit

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Speaker 1: of a gap. And uh, there's a lot of animosity

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Speaker 1: among the Euclideans towards Fractillians. They need to loosen up

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Speaker 1: and look at some of those far out pictures. I know,

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Speaker 1: you know it's funny. Did you watch um, did you

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Speaker 1: watch that one doc on? Yeah? Okay, did you see

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Speaker 1: the other the Arthur C. Clark one. It was made

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Speaker 1: in like maybe eighties, six eighty seven, and it had

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Speaker 1: nothing but like um delicate sound of thunder rip off

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Speaker 1: music going on the whole time. It was really really trippy. Well,

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Speaker 1: I posted a picture I don't know if you saw

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Speaker 1: today on the stuff, you should know all of the

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Speaker 1: of the Mandel brought set. It's beautiful, it is and

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Speaker 1: it's very cool. And I didn't even say what it was.

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Speaker 1: I just posted it, and like I'd say, about half

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Speaker 1: the people were like, very cool, man, this is rattle

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Speaker 1: of the Mantal brought set, like fractals, talk about fractals.

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Speaker 1: And then the other half were like, well, you guys

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Speaker 1: tripping out like what you did, grateful dead day. That

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Speaker 1: is actually math, believe or not. But it does look

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Speaker 1: very it's very tie dye in nature, and that's why

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Speaker 1: the hippies like it. Plus also, I mean, if you've

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Speaker 1: ever seen a fractal play out on the computer screen,

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Speaker 1: like yeah, um, so we are talking about fractals. I

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Speaker 1: don't necessarily want to give a disclaimer. Chuck and I

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Speaker 1: are not theoretical mathematicians. We're not even like normal mathematicians.

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Speaker 1: I balanced my checkbook my hand just to keep that

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Speaker 1: little part of my brain going. So I don't like

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Speaker 1: forget how to add and subtract later on in life.

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Speaker 1: I make myself to that, and I don't let myself

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Speaker 1: jump ahead. I show my work. Yeah. Um, and that's

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Speaker 1: about the extent of math and my life normally. See,

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Speaker 1: I was the kid in math that when they said

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Speaker 1: you're not allowed to use calculators, I would go like,

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Speaker 1: there are calculators in life, so why can't we use them. Yeah,

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Speaker 1: Like they made calculators so we didn't have to do maths, right,

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Speaker 1: But at the same time, I find that shoddy because

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Speaker 1: it's like you're not you're not You're just circumventing learning something,

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Speaker 1: and it's like the calculators there to support you after

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Speaker 1: you know what you're doing. I disagree. Well, I think

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Speaker 1: this is a pretty prime example of like going around

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Speaker 1: to get to the end. So when when I was

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Speaker 1: researching this, I was like, Okay, well, they don't really

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Speaker 1: know what they're doing with this stuff yet, so we

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Speaker 1: can just totally be like, well it's it's there anything

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Speaker 1: you wanted to be and nothing at all. And then

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Speaker 1: like I started looking a little more deeply into I'm like, oh, no,

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Speaker 1: they do kind of know what they're doing. We really

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Speaker 1: do know what we're talking about. So I feel like

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Speaker 1: I have, just from researching this a little bit um,

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Speaker 1: something of a grasp of what fractals are at. For

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Speaker 1: those of you who who don't know what we're talking about, like,

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Speaker 1: take a second to um, look up just typing fractal

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Speaker 1: and search images on your favorite search engine and you'll

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Speaker 1: be like, oh, yes, of course it's a fractal, um

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Speaker 1: And that's what we're going to talk about, because fractal

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Speaker 1: fractals are a new field, like we said, in geometry,

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Speaker 1: and they do have use and they have usefulness that

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Speaker 1: I think people haven't even considered yet. But the the

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Speaker 1: stuff that they have figured out how to use it

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Speaker 1: for is pretty amazing stuff. Can what if fractal is

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Speaker 1: at least so people know this should clear it all up.

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Speaker 1: It is a geometric shape that is self similar through

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Speaker 1: infinite iterations in a recursive pattern and through infinite detail exactly.

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Speaker 1: So there you have it. Boom. Do we need to

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Speaker 1: even continue? No? But um, And that sounds like really

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Speaker 1: that put me off, Like this article was pretty well

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Speaker 1: done by a guy named Craig Haggett. I don't know

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Speaker 1: who that is, freelancer, I guess, um, And it's a

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Speaker 1: pretty well done article. But that a sentence like that

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Speaker 1: can put a person off pretty easy, and he even

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Speaker 1: put it, you know, he made a joke about it like,

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Speaker 1: oh you know that, you get it, you know whatever.

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Speaker 1: But um, when you think about it, if you take

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Speaker 1: that apart, one of the hallmarks of fractal fractals um

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Speaker 1: is that they are a very complex result from a

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Speaker 1: very simple system. And there's like basically three hallmarks two

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Speaker 1: fractals that you just pointed out right. There is um

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Speaker 1: self similarity, which is if you if you cut a

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Speaker 1: chunk like a microscopic piece of a fractal off and

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Speaker 1: compare it to the whole fractal, it's going to be

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Speaker 1: virtually the same, yeah, like or a fern. And the

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Speaker 1: cool thing about practicals is is, to me, the coolest

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Speaker 1: thing is that practicals. The point they made in the

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Speaker 1: Nova documentary is that all of our math up until

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Speaker 1: they discovered fractals and described practicals, was based on things

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Speaker 1: that we've basically created and built. Like all geometry, right

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Speaker 1: Euclidean geometry. You have length, width, and height, which which

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Speaker 1: should be the three dimensions, right, yes, for like pyramids

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Speaker 1: and buildings, cones and all those things. And you it's

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Speaker 1: extremely useful and we've done quite a bit with this.

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Speaker 1: But what Euclidean geometry, as far as the fractal geometrists

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Speaker 1: or geometers um insist fail That is when they said, okay,

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Speaker 1: look at that mountain, that's a cone. It's an imperfect cone,

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Speaker 1: it's a rough cone, but it's a cone shape, right,

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Speaker 1: So yeah, Clidean geometry holds sway. What the fractal geometers

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Speaker 1: say is, yeah, you could say that it's a cone,

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Speaker 1: but if you tried to measure and describe it as such,

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Speaker 1: you're not going to come up with a very descriptive,

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Speaker 1: a very um detailed description of that mountain. So what's

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Speaker 1: the point. What fractal geometry does is it says we're

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Speaker 1: going to describe that mountain in every little craig and

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Speaker 1: peak possible. And so what you have is the fractal dimension,

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Speaker 1: which exists in conjunction with length, widthin height. And what

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Speaker 1: the fractal dimension describes is the complexity of the object

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Speaker 1: that exists within those three dimensions as well. So, finishing

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Speaker 1: my point, the cool thing about practicals is that everything

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Speaker 1: that we had done previously in geometry were because of

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Speaker 1: things we built. Practicals help describe things that were have

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Speaker 1: been here since the beginning of time in nature, and

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Speaker 1: one of the truest examples of that is the fern.

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Speaker 1: Right with self similarity, you take a little snippet off

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Speaker 1: of a fern, all that you shouldn't do that, let's

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Speaker 1: just look at it. Uh, it's gonna look the same

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Speaker 1: as the larger part of the fern, and then the

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Speaker 1: whole fern itself very self similar but not necessarily exact. No,

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Speaker 1: it can be. There is a form of self similarity

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Speaker 1: that is exact and precise, but in nature that's rare,

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Speaker 1: if not just completely not found. Right, that's right. So

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Speaker 1: you've got self similarity, which is the smaller part is

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Speaker 1: virtually the same or looks the same or structured the

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Speaker 1: same as the whole um. And this process of self

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Speaker 1: similarity um going larger smaller in scale, it's called recursiveness, right, yeah,

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Speaker 1: And recursiveness is um like you know those paintings where

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Speaker 1: it's like a guy I think Stephen Colbert, the one

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Speaker 1: that he gave to the Smithsonian has recursiveness in it,

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Speaker 1: where it's a man in a painting standing in front

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Speaker 1: of like mantle, and above the mantle is the painting

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Speaker 1: that you're looking at, and then it goes on and

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Speaker 1: on and on and on and on anything that's infinitely repeating, right,

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Speaker 1: same with if you're in a dressing room and there's

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Speaker 1: a mirror on either side of the wall, you just

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Speaker 1: keep going on infinitely. It's recursiveness, and with fractals the

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Speaker 1: recursiveness of self similarity. Right, So there's two two traits.

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Speaker 1: Um is produced through this thing called iteration, that's right.

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Speaker 1: And that's where you say, here's the whole I'm gonna

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Speaker 1: put it into this formula, and the formula has has

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Speaker 1: the formula. The output of the formula produces the input

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Speaker 1: for the next round of that same formula. It's a

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Speaker 1: loop exactly, so it's self sustaining and it can go

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Speaker 1: on infinitely recursion. Right. That's right. So what we've just

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Speaker 1: come up with is the fractal is anything that has

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Speaker 1: a self similar structure and it recursive through iteration. That's okay.

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Speaker 1: So um A, really I came upon this kind of

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Speaker 1: easy one easier explanation of a fractal from Ben wal

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Speaker 1: Mandel brought site. He died, by the way in two

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Speaker 1: he seemed like a pretty good guy. He was definitely

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Speaker 1: thinking different um. And the way that Mandel brought described

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Speaker 1: A really easy way to think of a fractal is um.

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Speaker 1: There's this thing called the Serpentsky gasket. And you take

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Speaker 1: a triangle and you can combine them into a bunch

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Speaker 1: of little triangles and spaces, triangular spaces that form a

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Speaker 1: larger triangle. Right, So that that one initial solid triangle

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Speaker 1: is called the initiator, that's the original shape. And then

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Speaker 1: all those other triangles combine that form that larger triangle

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Speaker 1: or a self similar version of that larger triangle, the

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Speaker 1: original triangle. That's called a generator. Right. So the formula

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Speaker 1: for creating a fractal would be to go into that generator,

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Speaker 1: the version that has all the little smaller triangles and

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Speaker 1: make up a larger whole triangle. And say, all the

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Speaker 1: ones that look like the initiator, the original just solid

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Speaker 1: black triangle, take that out and swap it with the

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Speaker 1: generator version, and all of a sudden you have one

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Speaker 1: that's exponentially more detailed. There's more to it, And that's

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Speaker 1: a fractal. That's all there is to it. You know

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Speaker 1: what else is a fractal? What the coastline? Yeah, that

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Speaker 1: was a big one. Lewis fried Richardson was an English

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Speaker 1: mathematician early twenty century, and he very brilliantly said, you

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Speaker 1: know what, if you take a yardstick and you measured

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Speaker 1: the coastline of England, you're gonna get a number. If

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Speaker 1: you take a one ft ruler and measure the coastline,

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Speaker 1: you're gonna get a different number. If you take a

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Speaker 1: one inch ruler and measure the coastline, you're gonna get

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Speaker 1: a different number. And it's basically infinite in that the

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Speaker 1: smaller you go with your your unit of measure or

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Speaker 1: your tool is the larger number you're gonna get, because

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Speaker 1: the coastline is so infinitely varied in its little nooks

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Speaker 1: and crannies, right exactly. It's a very cool way of

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Speaker 1: thinking about it. There's a second part of that too, Chuck.

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Speaker 1: Is that so depending on the you, what you're using,

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Speaker 1: the measure, the tool you're using the measure, the number

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Speaker 1: the perimeter of that coastline could go on infinitely, but

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Speaker 1: it still contains the same finite amount of space within paradox.

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Speaker 1: That is a big time paradox because things aren't supposed

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Speaker 1: to be infinite and finite at the same time, right

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Speaker 1: Um and uh Lewis Fry Richardson. He basically established in

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Speaker 1: that coming up with that paradox, the this kind of

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Speaker 1: revolution and thought that fractal geometry is based on that

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Speaker 1: you can have the infinite mixed with the finite, and

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Speaker 1: you can get it from pretty simple formulas that create

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Speaker 1: very increasingly complex systems, right, Um, And Fry wasn't the

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Speaker 1: He wasn't He was the first guy to really kind

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Speaker 1: of put forth this idea of thought, but he wasn't

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Speaker 1: the first one to notice this paradox. Yeah, and before

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Speaker 1: people even knew there were fractals, there were there were

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Speaker 1: artists like Da Vinci that saw this pattern and tree branches.

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Speaker 1: That was um. I know. In the Nova documentary and

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Speaker 1: the article they point out the uh Catsu Chica Hokusai

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Speaker 1: Japanese artists created the Great Wave off Kanagawa and uh

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Speaker 1: those are fractals. It's a it's ocean waves breaking and

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Speaker 1: at the top of the crest of the waves are

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Speaker 1: little self similar waves breaking off into smaller and smaller

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Speaker 1: self similar versions. And that's a natural fractal, or in

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Speaker 1: this case, it's a depiction of one. So they were

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Speaker 1: you know, early African and Navajo artists were doing this

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Speaker 1: and they didn't realize that they were fractals and there

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Speaker 1: were fractals all around us. No, they just saw crystals

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Speaker 1: in a snowflake or another good one, Yeah, exactly. Um.

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Speaker 1: They were just they saw that there was what they

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Speaker 1: were looking at was a repeating pattern that was self

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Speaker 1: similar and recursive. Right, yeah, that's it. That's a fractal.

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Speaker 1: Right yeah. And and Ben Wha mandel Brought was the

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Speaker 1: first one to say, you know what, we can we

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Speaker 1: can use math equations to actually apply to this. And

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Speaker 1: he was a big star for a while. And then

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Speaker 1: they sort of turned on him and said, you know what,

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Speaker 1: this is all cool and trippy looking, but it's useless,

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Speaker 1: right And he said, oh yeah, screw you guys. Watch

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Speaker 1: this And he wrote another book which started to uh

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Speaker 1: give some practical applications which are pretty exciting. UM. So

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Speaker 1: the whole thing, the whole principle that this is based

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Speaker 1: on UM is that you can take a formula and

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Speaker 1: plug in a very simple UM, well, a relatively simple

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Speaker 1: formula like mantel Brought's formula. Will take that one. For example,

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Speaker 1: his is um Z goes to zed squared plus c. Right,

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Speaker 1: that's what it's called. If you're in England, z we

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Speaker 1: say z z Well, anyway zed goes to which is

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Speaker 1: and the goes to is the key right here, this

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Speaker 1: is what makes it fractal. Goes to means that um,

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Speaker 1: it's an error. It's an equal sign. It looks like

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Speaker 1: an equal sign with an part of an arrow pointing

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Speaker 1: towards ZED, the other point pointing toward the rest of

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Speaker 1: the formula, which means that the the there's that feedback

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Speaker 1: loop where it's like, okay, once you have the number

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Speaker 1: that this punches out, you have you feed it back

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Speaker 1: in and you'll get another number and just keep going

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Speaker 1: and going and going. And every time, remember you're swapping

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Speaker 1: out the original the initiator for the the detailed version

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Speaker 1: the generator, and it's just getting exponentially more complex with

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Speaker 1: just the one iteration of that's very simple formula UM

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Speaker 1: and Mandel brought set uh. This is the one that's

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Speaker 1: like it's probably the most famous one. That's the one

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Speaker 1: that the Deadheads like because it's like this crazy juxtaposition

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Speaker 1: between like black and like different colors and everything. And

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Speaker 1: with his formula, two things happen with the number that

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Speaker 1: you put in. It either goes towards zero, or it

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Speaker 1: shoots off to the infinite. And what they did for this,

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Speaker 1: for the the Mandel brought set fractals was they assigned

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Speaker 1: a color to a number based on how quickly it

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Speaker 1: goes off to towards infinity. Right, So let's say that

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Speaker 1: you have like four, If you plug four into this

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Speaker 1: and in ten generations, it'll it'll become an infinite number. Um.

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Speaker 1: Then say that that would be grouped into a blue

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Speaker 1: color like ten generations blue, eight generations is red, ninety

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Speaker 1: generations is orange. See what I'm saying, um. And then

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Speaker 1: the other direction, like say if you put in four

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Speaker 1: point two or something like that, it'll go towards zero.

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Speaker 1: And any number that eventually will go towards zero is

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Speaker 1: represented as black. So what you have then is this

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Speaker 1: really intricate depending on where you're zooming in or out

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Speaker 1: on the fractal, this intricate change of colors, and what

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Speaker 1: you're really just seeing our numbers that are plots on

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Speaker 1: a plane, and that's your fractal, and then the black

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Speaker 1: parts are numbers that will eventually be be zero. Right,

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Speaker 1: And most of the mental mental brought set is black. Yeah,

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Speaker 1: but if you zoom in like that's the whole point

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Speaker 1: you zoom in on one of those little uh what

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Speaker 1: do we even call those little spikes? Uh? I guess

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Speaker 1: you could call it a plot. A plot, and it's

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Speaker 1: gonna look like what you just saw. And that The

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Speaker 1: Nova documentary is very cool when they zoom in on

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Speaker 1: these and it's sort of mind blowing. Yeah, it is

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Speaker 1: very I strongly recommend watching that because they explain it

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Speaker 1: way better than us. Well it helps to see it

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Speaker 1: for sure. So um, it's a pretty nice little friend,

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Speaker 1: um chuck. So we've talked about fractals, we talked about

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Speaker 1: the Mandel brought set, we talked about where they started

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Speaker 1: to come from, UM, and the the idea. Remember Lewis

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Speaker 1: fried Richardson, he was talking about measuring the coastline and

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Speaker 1: going off into the infinite but still containing a finite

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Speaker 1: amount UM. A guy came after him named Helga von Coke.

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Speaker 1: He came up with a Coke snowflake, which is pretty cool.

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Speaker 1: If you take a straight line, or you take a triangle,

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Speaker 1: and then on each side of the triangle in the

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Speaker 1: middle you bust out the middle into another triangular hump.

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Speaker 1: You do that over and over and over again. It

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Speaker 1: goes off into infinity. Although it contains a finite amount

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Speaker 1: of space, the perimeter goes off to the infinite. A

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Speaker 1: guy named Georg Cantor came up with the Cancer set,

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Speaker 1: which is just take a straight line and you take

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Speaker 1: the middle out of it, and then for each of

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Speaker 1: those two lines that produces, you do the same thing

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Speaker 1: and it just keeps going on and on and rather

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Speaker 1: than going to nothingness like you're like, well, if you

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Speaker 1: take a six inch line, eventually you're gonna bust it

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Speaker 1: down and nothingness again, that doesn't happen. They found that

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Speaker 1: it goes off to the infinite. So they realized ben

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Speaker 1: Wa Mantel brought was plugging all these into computers. Because

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Speaker 1: that's what it took. People realize it's like George Cantor

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Speaker 1: um Man, I hope that's how you say his first name.

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Speaker 1: He was he was working in the eighteen eighties. Um

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Speaker 1: Gaston Julio came up with the Julius sets for producing

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Speaker 1: a repeating pattern using feedback loop. All these guys were

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Speaker 1: like nineteenth century early twentieth century mathematicians, and it was

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Speaker 1: strictly theoretical until the late seventies, when guys like Mantel

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Speaker 1: brought who worked at IBM started feeding these things into

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Speaker 1: these new fangled computers and seeing the results like this,

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Speaker 1: fractals like the mantel brought set that he saw right,

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Speaker 1: so um, almost immediately there was a practical use for

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Speaker 1: fractals that came in the form of c g I. Yeah,

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Speaker 1: they interviewed that one guy and the documentary um who

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Speaker 1: worked on the first c g I shot in motion

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Speaker 1: picture history, which was Star Trek to the Wrath of

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Speaker 1: con and uh. He was tasked with making a c

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Speaker 1: g I uh land surface like mountain range and pretty

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Speaker 1: mind blowing with it. Yeah, and he did. I mean,

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Speaker 1: now you look back and it kind of looks silly,

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Speaker 1: but at the time it was completely revolutionary. And once

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Speaker 1: he learned about fractals in the geometry and the math

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Speaker 1: of practicals, it was pretty easy for him. And he

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Speaker 1: made it seem like he's like, oh, well, this is

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Speaker 1: the key, this is how you do it right. So well,

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Speaker 1: and it is kind of easy, especially if you know

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Speaker 1: what you're doing with computer programming and math, because what

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Speaker 1: you're basically doing to create a fractal generator is teaching

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Speaker 1: your computer to to do something within a certain formula

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Speaker 1: that's a fractal formula, right, and so what Lauren Carpenter,

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Speaker 1: the guy who created them the star Trek to landscape

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Speaker 1: for the first c G all c g I shot. Ever,

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Speaker 1: what he basically did was created a computer program that said, hey, computer,

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Speaker 1: I'm gonna give you a bunch of triangles. Because I

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Speaker 1: think that was the earliest stuff he was working with. Um,

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Speaker 1: I'm gonna give you a bunch of triangles, and I

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Speaker 1: want you to take those triangles and generate a new

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Speaker 1: fractal set from it, right, And then I want you

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Speaker 1: to do it again and again and again, and then

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Speaker 1: every third time I want you to start turning them

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Speaker 1: forty degrees. So that's going to change the pattern slightly,

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Speaker 1: and then all of a sudden you have these infinite variations.

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Speaker 1: The reason why when you go back and look at

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Speaker 1: that shot that it still looks kind of you know today,

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Speaker 1: is because the computer he was working at didn't have

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Speaker 1: the computing power to do that many times. Now we

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Speaker 1: have higher computer computing power, and so what we're doing

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Speaker 1: is telling our computers to keep going and going and going,

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Speaker 1: swapping out the initiator that one single black triangle everywhere

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Speaker 1: it can find it in this pattern. This pattern of

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Speaker 1: triangles in the fractal with a brand new fractal. So

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Speaker 1: it's just creating more and more and more and more fractals,

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Speaker 1: which creates a finer and finer and finer resolution, which

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Speaker 1: makes something look all the more realistic. Yeah, like the

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Speaker 1: part in the doc about the Star Wars's making the

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Speaker 1: lava splashing, it's amazing. Yes, it was because they showed

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Speaker 1: the first one that he did. It looks kind of plain,

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Speaker 1: and then once you fed it through this infinite feedback loop,

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Speaker 1: it just like shattered and and and uh, fractured, not fractal,

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Speaker 1: although I want to say fractal off and just look

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Speaker 1: more detailed, more detailed, more detailed, until it looked like

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Speaker 1: lava splashing, right, it's pretty amazing. Well, that's where the

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Speaker 1: word fractal comes from. Is um Mandel brought coined in

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Speaker 1: to say, to indicate how the things fracture off and

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Speaker 1: they form irregular patterns. Um, you can create to fractal

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Speaker 1: that that is regularly repeating, but it doesn't look as natural.

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Speaker 1: And with like say, if you're creating lava, right, you've

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Speaker 1: got to have that one rule that like every third

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Speaker 1: generation kicks forty degrees or whatever. The rule is that

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Speaker 1: just kind of throws a little bit of dissimilarity into it,

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Speaker 1: because if something's too self similar, it's not going to

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Speaker 1: look right. It's not gonna look natural, it's not gonna

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Speaker 1: look real, which kind of leads you to think, chuck,

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Speaker 1: then that there is a an application for studying natural

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Speaker 1: phenomenon using fractals, right, while there are I guess all

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Speaker 1: kinds um, well, this isn't so much natural. But the

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Speaker 1: documentary interviewed Nathan Cohen who was a ham radio operator,

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Speaker 1: and his landlord said, dude, you can't have that huge

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Speaker 1: antenna hanging out of your apartment. So he started bending

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Speaker 1: wires a straight wire into essentially a fractal and found

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Speaker 1: that on the very first go it got better reception

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Speaker 1: um merely by the fact that it was bent in

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Speaker 1: that way and it was self similar. So he eventually

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Speaker 1: used that two I hope make a lot of money.

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Speaker 1: I got the imperson that he did, okay, um by

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Speaker 1: applying that technology to cell phones um, and the way

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Speaker 1: that they describe it as all the different things a

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Speaker 1: cell phone can do, if you were to have a

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Speaker 1: different antenna for each one of those functions, it would

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Speaker 1: be like carrying around a little porcupine. So what cell

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Speaker 1: phones now are based on is a fractal design called

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Speaker 1: Manger sponge Minger sponge and uh, it's basically a box fractal.

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Speaker 1: And if you crack up in your little cell phone,

401
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Speaker 1: you're gonna see it wired that way. Yeah, You're going

402
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Speaker 1: to be looking at a fractal it's a square, right,

403
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Speaker 1: and then within it or a bunch of little squares

404
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Speaker 1: in a recursive, self similar pattern. And you friend, are

405
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Speaker 1: looking at a fractal. It's all around us. Yeah, Um,

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Speaker 1: it's also all around us in nature. There's uh in

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Speaker 1: that same UH documentary, that Nova program, there was a

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Speaker 1: team from i think University of Arizona. There's a team

409
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Speaker 1: of academics. That was pretty cool. Who Um, we're trying

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Speaker 1: to figure out if you predict the amount of carbon

411
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Speaker 1: capturing capacity an entire rainforest has just by measuring UM

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Speaker 1: and figuring out this self similar system that a single

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Speaker 1: tree in that rainforest UM has. That makes sense, Well,

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Speaker 1: it does, but it's kind of a leap. It's like, okay,

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Speaker 1: so it's one tree, does it follow the same system

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Speaker 1: that the whole rainforest does? And they apparently found that yes,

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Speaker 1: in fact it does right. The same branching uh system

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Speaker 1: found in that tree is similar to the the growth

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Speaker 1: of the trees in the rainforest as a whole. Pretty cool, yes,

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Speaker 1: um in the human body, uh, one of the keys

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Speaker 1: to getting rid of cancer is or any kind of

422
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Speaker 1: tumors spotting these tumors early on. But with our ultrasound

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Speaker 1: technology you can only get so small and so detailed

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Speaker 1: that you can't see some of these natural fractals that

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Speaker 1: you know, your blood vessels are fractals essentially, just like

426
00:25:15,520 --> 00:25:18,600
Speaker 1: the branches of a tree are um So they are

427
00:25:18,640 --> 00:25:24,040
Speaker 1: now using geometry two. Now if I'm not sure if

428
00:25:24,080 --> 00:25:25,960
Speaker 1: I got this right, but I think it shows up.

429
00:25:26,440 --> 00:25:29,959
Speaker 1: It shows the flow of the blood because ultrasound can

430
00:25:30,000 --> 00:25:31,880
Speaker 1: pick that up through these fractals when they can't even

431
00:25:31,920 --> 00:25:36,960
Speaker 1: pick up the vessels themselves. Is that right? Early earlier

432
00:25:37,080 --> 00:25:40,040
Speaker 1: tumor spotting right. Well, for all intents of purposes, they're

433
00:25:40,040 --> 00:25:42,479
Speaker 1: looking at the vessels by finding the blood because they

434
00:25:42,520 --> 00:25:45,720
Speaker 1: see where it's flowing. But yeah, depending on the pattern

435
00:25:45,760 --> 00:25:48,840
Speaker 1: that it follows. If it follows like a like a

436
00:25:48,840 --> 00:25:52,240
Speaker 1: tree branching shape, it's healthy, right, Yeah, And then the

437
00:25:52,280 --> 00:25:55,160
Speaker 1: tumors all the veins are all bent and crooking, going

438
00:25:55,160 --> 00:25:58,560
Speaker 1: in all crazy directions. The readoubt of a heartbeat, it's

439
00:25:58,600 --> 00:26:01,360
Speaker 1: not consistent. It's a fractal Yeah, So the use fractal

440
00:26:01,400 --> 00:26:05,600
Speaker 1: analysis now to study your heart rate and use that

441
00:26:05,680 --> 00:26:11,760
Speaker 1: to better understand how arrhythmia happens through math. So there's

442
00:26:12,520 --> 00:26:16,119
Speaker 1: the especially with natural systems. That's kind of like the

443
00:26:16,119 --> 00:26:20,720
Speaker 1: biggest contribution that um fractal geometry is produced so far,

444
00:26:20,920 --> 00:26:24,359
Speaker 1: I think, aside from c g I is what medical

445
00:26:24,560 --> 00:26:28,920
Speaker 1: uh well, just that that whole understanding that was first

446
00:26:28,960 --> 00:26:32,159
Speaker 1: really kind of um voiced by Lewis Fry Richardson with

447
00:26:32,200 --> 00:26:37,360
Speaker 1: the coastline that there's, um, there are natural systems out

448
00:26:37,359 --> 00:26:40,200
Speaker 1: there that we can't really that we're not quite paying

449
00:26:40,200 --> 00:26:43,480
Speaker 1: attention to, we don't really know how to deal with that.

450
00:26:43,520 --> 00:26:46,960
Speaker 1: We're trying to apply something like Euclidean geometry to something

451
00:26:47,000 --> 00:26:51,040
Speaker 1: that you can't really use that for um. That that's

452
00:26:51,080 --> 00:26:53,520
Speaker 1: what fractal geometry is really contributed so far, is to

453
00:26:53,600 --> 00:26:56,560
Speaker 1: basically say, hey, there's a lot of natural systems out

454
00:26:56,560 --> 00:27:00,719
Speaker 1: here that are self similar and recursive and now that

455
00:27:00,760 --> 00:27:03,840
Speaker 1: we kind of see in the fractal world, we see

456
00:27:03,880 --> 00:27:06,480
Speaker 1: them everywhere, and we have a better understanding of them.

457
00:27:06,800 --> 00:27:09,280
Speaker 1: And one of the best examples of that, I thought

458
00:27:09,359 --> 00:27:14,639
Speaker 1: was figuring out how larger animals use less energy and

459
00:27:14,800 --> 00:27:18,560
Speaker 1: smaller animals they use energy more efficiently. And um, this

460
00:27:18,640 --> 00:27:21,400
Speaker 1: is a kind of a biological paradox for a really

461
00:27:21,400 --> 00:27:24,480
Speaker 1: long time, and these guys figured it out using I guess,

462
00:27:24,560 --> 00:27:28,080
Speaker 1: kind of the um same kind of insight that fractal

463
00:27:28,080 --> 00:27:32,960
Speaker 1: geometry has. That if you take genes and genes are

464
00:27:33,000 --> 00:27:37,960
Speaker 1: the mathematical formula or the equivalent of a mathematical formula,

465
00:27:38,720 --> 00:27:43,720
Speaker 1: and you UH feed in uh these genetic processes, what

466
00:27:43,800 --> 00:27:49,000
Speaker 1: it's going to put out is this self similar recursive

467
00:27:49,080 --> 00:27:53,840
Speaker 1: pattern to where the bigger the organism is, the more

468
00:27:53,960 --> 00:27:56,440
Speaker 1: this thing goes and goes and goes, the less energy

469
00:27:56,480 --> 00:27:59,040
Speaker 1: it's going to use because there's more of it and

470
00:27:59,080 --> 00:28:01,679
Speaker 1: it doesn't require very much energy to produce past a

471
00:28:01,720 --> 00:28:04,320
Speaker 1: certain point. So if you have a very small animal,

472
00:28:04,480 --> 00:28:06,480
Speaker 1: it's using a lot of energy to do these things

473
00:28:06,480 --> 00:28:09,280
Speaker 1: to carry this out. But there's that economy of scale

474
00:28:09,280 --> 00:28:14,320
Speaker 1: because you're still using a relatively simple formula, your genetic code,

475
00:28:14,560 --> 00:28:18,880
Speaker 1: right UM, to carry out a very complex, seemingly complex

476
00:28:19,440 --> 00:28:24,240
Speaker 1: um system, which is your organs or you as an organism.

477
00:28:24,359 --> 00:28:26,399
Speaker 1: So in the end, an elephant uses less energy than

478
00:28:26,400 --> 00:28:30,280
Speaker 1: a mouse, Yes, because they're both using the same formula,

479
00:28:30,520 --> 00:28:33,440
Speaker 1: the same input. And then eventually you reach a point

480
00:28:33,520 --> 00:28:37,560
Speaker 1: where it just gets easier and easier and easier to

481
00:28:37,560 --> 00:28:40,160
Speaker 1: to use something simple to create a complex system. I

482
00:28:40,240 --> 00:28:43,680
Speaker 1: love it too. Uh. I got one more thing. You

483
00:28:43,720 --> 00:28:47,440
Speaker 1: heard this guy Jason Paget, Huh, this is pretty crazy. UM.

484
00:28:47,480 --> 00:28:52,120
Speaker 1: This guy, like nine years ago, I think UM, was

485
00:28:52,200 --> 00:28:55,680
Speaker 1: mugged in Tacoma, Washington, got hit in the back of

486
00:28:55,680 --> 00:29:01,040
Speaker 1: the head really hard, knocked him out, and he acquired UM,

487
00:29:01,080 --> 00:29:05,280
Speaker 1: a form of synesthesia in which he sees fractals from

488
00:29:05,320 --> 00:29:08,600
Speaker 1: being hit in the head and UM basically it's an

489
00:29:08,640 --> 00:29:13,160
Speaker 1: acquired savant savantasm, which is pretty rare to acquire this.

490
00:29:13,280 --> 00:29:18,480
Speaker 1: Later on, UM, and this guy hated math, and his

491
00:29:18,520 --> 00:29:20,560
Speaker 1: family used to make fun of him, he said, because

492
00:29:20,920 --> 00:29:23,880
Speaker 1: he was the worst at pictionary. Uh. I couldn't draw

493
00:29:23,880 --> 00:29:26,760
Speaker 1: a thing, couldn't draw a lick. Now this guy can

494
00:29:26,880 --> 00:29:33,680
Speaker 1: draw reportedly mathematically correct fractals by hand, and he's the

495
00:29:33,680 --> 00:29:36,320
Speaker 1: only person on earth that can do this. And you

496
00:29:36,320 --> 00:29:39,680
Speaker 1: should see these things. They're like, you know, a huge

497
00:29:40,160 --> 00:29:43,719
Speaker 1: you know, two by two fractal that looks like it

498
00:29:43,800 --> 00:29:46,600
Speaker 1: was plotted by like a supercomputer. And this guy does

499
00:29:46,640 --> 00:29:49,200
Speaker 1: these by hand now out of nowhere because he got

500
00:29:49,280 --> 00:29:51,560
Speaker 1: hit on the head. That's pretty amazing. Yeah, it's crazy.

501
00:29:51,680 --> 00:29:54,680
Speaker 1: He got him in the fractal center. Huh. Did that's

502
00:29:54,840 --> 00:29:58,400
Speaker 1: strange that we would have like that ability latent in

503
00:29:58,520 --> 00:30:01,680
Speaker 1: us you know. Yeah, Well they studied his brain of course, um,

504
00:30:01,760 --> 00:30:04,160
Speaker 1: and they found that the two areas that lit up

505
00:30:04,520 --> 00:30:07,800
Speaker 1: in the left hemisphere were the areas that control exact

506
00:30:07,840 --> 00:30:12,680
Speaker 1: math and mental imagery. So they dont have it. And he's,

507
00:30:12,680 --> 00:30:14,480
Speaker 1: you know, he's fine with it, although he says that

508
00:30:14,960 --> 00:30:17,400
Speaker 1: he's a bit obsessive about it because he's it's one

509
00:30:17,400 --> 00:30:20,720
Speaker 1: of those deals where everywhere he looks now he sees fractals.

510
00:30:20,720 --> 00:30:23,480
Speaker 1: Oh yeah, well I got the impression that people who

511
00:30:23,520 --> 00:30:27,240
Speaker 1: are who are fractal geometers have the same thing. Yeah,

512
00:30:27,480 --> 00:30:29,320
Speaker 1: you know, they're like, look at that cloud. I I

513
00:30:29,400 --> 00:30:33,320
Speaker 1: can figure out how to describe it completely. Yeah with math, Yeah,

514
00:30:33,440 --> 00:30:36,400
Speaker 1: it's crazy. Um. And then it's everywhere canopies of the trees. Like.

515
00:30:36,480 --> 00:30:38,480
Speaker 1: I got that impression as well that once you start

516
00:30:38,560 --> 00:30:42,800
Speaker 1: seeing fractals in natural systems, like then everything becomes um,

517
00:30:43,040 --> 00:30:46,720
Speaker 1: fractals and a lot simpler to understand. I realized today

518
00:30:46,720 --> 00:30:50,040
Speaker 1: that I have always doodled in fractals. Yeah yeah, because

519
00:30:50,040 --> 00:30:52,440
Speaker 1: I can't really draw, so whenever I doodle, it's like

520
00:30:52,960 --> 00:30:57,160
Speaker 1: it's always been um little fractal shapes, Like I would

521
00:30:57,200 --> 00:30:59,959
Speaker 1: draw some kind of geometric shape, then split off from

522
00:31:00,080 --> 00:31:03,040
Speaker 1: that and make it smaller, and in the end they're

523
00:31:03,120 --> 00:31:05,440
Speaker 1: sort of like fractals. Oh, your fractal tree that you

524
00:31:05,440 --> 00:31:09,360
Speaker 1: showed me, it's pretty awesome. So you got anything else?

525
00:31:10,000 --> 00:31:13,440
Speaker 1: Uh No, I would strongly urge you to read this

526
00:31:13,560 --> 00:31:16,320
Speaker 1: article a few more times and then maybe go off

527
00:31:16,360 --> 00:31:18,680
Speaker 1: and read some more about fractals, because we definitely have

528
00:31:18,680 --> 00:31:21,760
Speaker 1: not covered all of it. I'll watch that Nova documentary. Yeah,

529
00:31:22,000 --> 00:31:24,440
Speaker 1: good stuff. What is it chasing the hidden? To mention?

530
00:31:25,280 --> 00:31:28,520
Speaker 1: Is that what it's called? Diould call it chasing the dragon? Well,

531
00:31:28,520 --> 00:31:31,200
Speaker 1: there's the dragon curve fractal. It's pretty boss, that's right,

532
00:31:31,240 --> 00:31:35,120
Speaker 1: it is. UM. So you want to type fractals in

533
00:31:35,200 --> 00:31:38,480
Speaker 1: the search bar how stuff works dot com to start,

534
00:31:38,520 --> 00:31:40,960
Speaker 1: and that will bring up this very very good article.

535
00:31:41,640 --> 00:31:43,280
Speaker 1: And I said search bar, which means it's time for

536
00:31:43,320 --> 00:31:48,600
Speaker 1: listening to ma'am Josh. I'm gonna call this, uh, don't

537
00:31:48,640 --> 00:31:51,720
Speaker 1: eat your peanuts around me, jerk. Yeah. Remember when the

538
00:31:51,760 --> 00:31:56,120
Speaker 1: Air Traffic Control remarked that I never heard the announcement that, uh,

539
00:31:56,360 --> 00:31:58,520
Speaker 1: no one can eat peanuts on the plane. Yeah. I've

540
00:31:58,520 --> 00:32:00,880
Speaker 1: flown a lot in my life and I've never heard

541
00:32:00,880 --> 00:32:04,440
Speaker 1: that before. So Ian Hammer writes in on the Air

542
00:32:04,520 --> 00:32:07,520
Speaker 1: Traffic Control episode, you were talking about peanuts being completely

543
00:32:07,560 --> 00:32:10,960
Speaker 1: absent on some flights, And as a person that is

544
00:32:11,040 --> 00:32:13,960
Speaker 1: really allergic to peanuts, I can shed some light. My

545
00:32:14,040 --> 00:32:16,680
Speaker 1: allergy is bad enough to wear. The smell of peanuts,

546
00:32:17,000 --> 00:32:19,320
Speaker 1: which is really just the presence of peanut molecules in

547
00:32:19,360 --> 00:32:22,520
Speaker 1: the air, will cause me to get itchy and swollen. Uh.

548
00:32:22,560 --> 00:32:24,760
Speaker 1: In the case that I am in contact with a peanut,

549
00:32:25,120 --> 00:32:28,120
Speaker 1: have the superpower of becoming a balloon, and I'll swell

550
00:32:28,200 --> 00:32:29,760
Speaker 1: up to the point where I will be dead in

551
00:32:29,760 --> 00:32:33,080
Speaker 1: a matter of minutes. I can delay the anaphylactic shock

552
00:32:33,160 --> 00:32:36,240
Speaker 1: for ten minutes, give or take with an injection of epinephrin,

553
00:32:36,640 --> 00:32:42,160
Speaker 1: and this will only work twice, I think. So um,

554
00:32:42,200 --> 00:32:44,400
Speaker 1: if I do have reaction, I have twenty minutes plus

555
00:32:44,400 --> 00:32:48,160
Speaker 1: the fifteen minutes I have before normal anaphylactic shock would

556
00:32:48,240 --> 00:32:50,240
Speaker 1: kill me. There really is in a way to save

557
00:32:50,280 --> 00:32:53,360
Speaker 1: me in that instance, unless I can be administered the

558
00:32:53,360 --> 00:32:56,120
Speaker 1: proper treatment that you can get only at a hospital,

559
00:32:56,200 --> 00:32:57,880
Speaker 1: because you can imagine when a plane is at thirty

560
00:32:58,240 --> 00:33:00,960
Speaker 1: feet there's not much can be done and to get

561
00:33:01,040 --> 00:33:03,440
Speaker 1: me to a hospital within that thirty five minute time frame.

562
00:33:04,280 --> 00:33:06,120
Speaker 1: So flying can be a pretty scary thing when someone

563
00:33:06,200 --> 00:33:08,880
Speaker 1: near you. Besides that they really want a peanut buttercup.

564
00:33:09,440 --> 00:33:11,320
Speaker 1: People do this sometimes and it's a real pain to

565
00:33:11,360 --> 00:33:13,320
Speaker 1: have to deal with. I just wanted to give you

566
00:33:13,320 --> 00:33:16,240
Speaker 1: guys an overview of peanut allergy sufferers when it comes

567
00:33:16,280 --> 00:33:19,480
Speaker 1: to flying. Keep up the incredible work. Look forward to

568
00:33:19,480 --> 00:33:23,320
Speaker 1: seeing a TV pilot Ian Hammer. So incredible, is right.

569
00:33:23,480 --> 00:33:28,160
Speaker 1: If we were insensitive to that, then all apologies. He

570
00:33:28,160 --> 00:33:30,440
Speaker 1: didn't indicate that, but I think we weren't. I just

571
00:33:30,480 --> 00:33:33,080
Speaker 1: remember being surprised. Yeah, I was surprised, but and I

572
00:33:33,160 --> 00:33:36,720
Speaker 1: knew allergies could get bad, but man, that I think

573
00:33:36,760 --> 00:33:38,920
Speaker 1: on the plane, I was like, what I've known about

574
00:33:38,960 --> 00:33:40,920
Speaker 1: this since I saw an episode of Freaks and Geeks

575
00:33:40,960 --> 00:33:43,680
Speaker 1: wherein one of the characters almost died because like some

576
00:33:43,920 --> 00:33:47,600
Speaker 1: bully at school, like you gave him some peanuts. Oh yeah,

577
00:33:47,960 --> 00:33:51,800
Speaker 1: was that it was the Martin Star character, the analog

578
00:33:51,920 --> 00:33:58,840
Speaker 1: to Paul from Wonder Years, Okay, which was I can't

579
00:33:58,840 --> 00:34:03,120
Speaker 1: remember something, illok freaks some Yeah, it's good good. Um,

580
00:34:03,160 --> 00:34:07,200
Speaker 1: well let's see allergen. How about a practice story if

581
00:34:07,200 --> 00:34:09,600
Speaker 1: you know something about fractals that we don't, or can

582
00:34:09,640 --> 00:34:12,440
Speaker 1: correct us or explain it better than we did, which

583
00:34:12,560 --> 00:34:16,000
Speaker 1: I'm not sure that that's much of a long shot. Um,

584
00:34:16,040 --> 00:34:17,799
Speaker 1: we want to hear about it. You can tweet to

585
00:34:17,880 --> 00:34:20,680
Speaker 1: us at s Y s K podcast. You can visit

586
00:34:20,719 --> 00:34:23,800
Speaker 1: us on Facebook at Facebook dot com slash stuff you

587
00:34:23,800 --> 00:34:27,279
Speaker 1: Should Know, or send us an email at Stuff Podcast

588
00:34:27,400 --> 00:34:35,640
Speaker 1: at Discovery dot com. For more on this and thousands

589
00:34:35,680 --> 00:34:45,799
Speaker 1: of other topics, visit how Stuff works dot com. Brought

590
00:34:45,840 --> 00:34:49,040
Speaker 1: to you by the reinvented two thousand twelve camera. It's ready,

591
00:34:49,239 --> 00:34:49,640
Speaker 1: are you