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Fractals: Whoa · Stuff You Should Know

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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
2:04
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
7:50
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
13:19
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,
14:05
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
16:39
Speaker 1: you zoom in on one of those little uh what
16:42
Speaker 1: do we even call those little spikes? Uh? I guess
16:46
Speaker 1: you could call it a plot. A plot, and it's
16:48
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
16:53
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
16:59
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
17:13
Speaker 1: the Mandel brought set, we talked about where they started
17:16
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.
17:34
Speaker 1: He came up with a Coke snowflake, which is pretty cool.
17:36
Speaker 1: If you take a straight line, or you take a triangle,
17:40
Speaker 1: and then on each side of the triangle in the
17:42
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
17:49
Speaker 1: goes off into infinity. Although it contains a finite amount
17:52
Speaker 1: of space, the perimeter goes off to the infinite. A
17:55
Speaker 1: guy named Georg Cantor came up with the Cancer set,
17:59
Speaker 1: which is just take a straight line and you take
18:01
Speaker 1: the middle out of it, and then for each of
18:03
Speaker 1: those two lines that produces, you do the same thing
18:05
Speaker 1: and it just keeps going on and on and rather
18:07
Speaker 1: than going to nothingness like you're like, well, if you
18:10
Speaker 1: take a six inch line, eventually you're gonna bust it
18:12
Speaker 1: down and nothingness again, that doesn't happen. They found that
18:15
Speaker 1: it goes off to the infinite. So they realized ben
18:18
Speaker 1: Wa Mantel brought was plugging all these into computers. Because
18:22
Speaker 1: that's what it took. People realize it's like George Cantor
18:26
Speaker 1: um Man, I hope that's how you say his first name.
18:28
Speaker 1: He was he was working in the eighteen eighties. Um
18:32
Speaker 1: Gaston Julio came up with the Julius sets for producing
18:35
Speaker 1: a repeating pattern using feedback loop. All these guys were
18:38
Speaker 1: like nineteenth century early twentieth century mathematicians, and it was
18:42
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
18:51
Speaker 1: these new fangled computers and seeing the results like this,
18:54
Speaker 1: fractals like the mantel brought set that he saw right,
18:58
Speaker 1: so um, almost immediately there was a practical use for
19:04
Speaker 1: fractals that came in the form of c g I. Yeah,
19:10
Speaker 1: they interviewed that one guy and the documentary um who
19:13
Speaker 1: worked on the first c g I shot in motion
19:17
Speaker 1: picture history, which was Star Trek to the Wrath of
19:20
Speaker 1: con and uh. He was tasked with making a c
19:24
Speaker 1: g I uh land surface like mountain range and pretty
19:29
Speaker 1: mind blowing with it. Yeah, and he did. I mean,
19:31
Speaker 1: now you look back and it kind of looks silly,
19:33
Speaker 1: but at the time it was completely revolutionary. And once
19:37
Speaker 1: he learned about fractals in the geometry and the math
19:40
Speaker 1: of practicals, it was pretty easy for him. And he
19:42
Speaker 1: made it seem like he's like, oh, well, this is
19:44
Speaker 1: the key, this is how you do it right. So well,
19:47
Speaker 1: and it is kind of easy, especially if you know
19:49
Speaker 1: what you're doing with computer programming and math, because what
19:52
Speaker 1: you're basically doing to create a fractal generator is teaching
19:56
Speaker 1: your computer to to do something within a certain formula
20:00
Speaker 1: that's a fractal formula, right, and so what Lauren Carpenter,
20:04
Speaker 1: the guy who created them the star Trek to landscape
20:07
Speaker 1: for the first c G all c g I shot. Ever,
20:11
Speaker 1: what he basically did was created a computer program that said, hey, computer,
20:14
Speaker 1: I'm gonna give you a bunch of triangles. Because I
20:16
Speaker 1: think that was the earliest stuff he was working with. Um,
20:20
Speaker 1: I'm gonna give you a bunch of triangles, and I
20:22
Speaker 1: want you to take those triangles and generate a new
20:26
Speaker 1: fractal set from it, right, And then I want you
20:29
Speaker 1: to do it again and again and again, and then
20:31
Speaker 1: every third time I want you to start turning them
20:35
Speaker 1: forty degrees. So that's going to change the pattern slightly,
20:39
Speaker 1: and then all of a sudden you have these infinite variations.
20:42
Speaker 1: The reason why when you go back and look at
20:44
Speaker 1: that shot that it still looks kind of you know today,
20:48
Speaker 1: is because the computer he was working at didn't have
20:51
Speaker 1: the computing power to do that many times. Now we
20:54
Speaker 1: have higher computer computing power, and so what we're doing
20:58
Speaker 1: is telling our computers to keep going and going and going,
21:01
Speaker 1: swapping out the initiator that one single black triangle everywhere
21:05
Speaker 1: it can find it in this pattern. This pattern of
21:08
Speaker 1: triangles in the fractal with a brand new fractal. So
21:11
Speaker 1: it's just creating more and more and more and more fractals,
21:14
Speaker 1: which creates a finer and finer and finer resolution, which
21:17
Speaker 1: makes something look all the more realistic. Yeah, like the
21:20
Speaker 1: part in the doc about the Star Wars's making the
21:23
Speaker 1: lava splashing, it's amazing. Yes, it was because they showed
21:27
Speaker 1: the first one that he did. It looks kind of plain,
21:29
Speaker 1: and then once you fed it through this infinite feedback loop,
21:32
Speaker 1: it just like shattered and and and uh, fractured, not fractal,
21:39
Speaker 1: although I want to say fractal off and just look
21:42
Speaker 1: more detailed, more detailed, more detailed, until it looked like
21:45
Speaker 1: lava splashing, right, it's pretty amazing. Well, that's where the
21:47
Speaker 1: word fractal comes from. Is um Mandel brought coined in
21:51
Speaker 1: to say, to indicate how the things fracture off and
21:56
Speaker 1: they form irregular patterns. Um, you can create to fractal
22:00
Speaker 1: that that is regularly repeating, but it doesn't look as natural.
22:07
Speaker 1: And with like say, if you're creating lava, right, you've
22:11
Speaker 1: got to have that one rule that like every third
22:13
Speaker 1: generation kicks forty degrees or whatever. The rule is that
22:17
Speaker 1: just kind of throws a little bit of dissimilarity into it,
22:20
Speaker 1: because if something's too self similar, it's not going to
22:23
Speaker 1: look right. It's not gonna look natural, it's not gonna
22:25
Speaker 1: look real, which kind of leads you to think, chuck,
22:28
Speaker 1: then that there is a an application for studying natural
22:32
Speaker 1: phenomenon using fractals, right, while there are I guess all
22:37
Speaker 1: kinds um, well, this isn't so much natural. But the
22:42
Speaker 1: documentary interviewed Nathan Cohen who was a ham radio operator,
22:46
Speaker 1: and his landlord said, dude, you can't have that huge
22:49
Speaker 1: antenna hanging out of your apartment. So he started bending
22:53
Speaker 1: wires a straight wire into essentially a fractal and found
22:58
Speaker 1: that on the very first go it got better reception
23:01
Speaker 1: um merely by the fact that it was bent in
23:04
Speaker 1: that way and it was self similar. So he eventually
23:09
Speaker 1: used that two I hope make a lot of money.
23:13
Speaker 1: I got the imperson that he did, okay, um by
23:15
Speaker 1: applying that technology to cell phones um, and the way
23:18
Speaker 1: that they describe it as all the different things a
23:20
Speaker 1: cell phone can do, if you were to have a
23:22
Speaker 1: different antenna for each one of those functions, it would
23:25
Speaker 1: be like carrying around a little porcupine. So what cell
23:28
Speaker 1: phones now are based on is a fractal design called
23:33
Speaker 1: Manger sponge Minger sponge and uh, it's basically a box fractal.
23:39
Speaker 1: And if you crack up in your little cell phone,
23:42
Speaker 1: you're gonna see it wired that way. Yeah, You're going
23:44
Speaker 1: to be looking at a fractal it's a square, right,
23:46
Speaker 1: and then within it or a bunch of little squares
23:50
Speaker 1: in a recursive, self similar pattern. And you friend, are
23:54
Speaker 1: looking at a fractal. It's all around us. Yeah, Um,
23:58
Speaker 1: it's also all around us in nature. There's uh in
24:01
Speaker 1: that same UH documentary, that Nova program, there was a
24:06
Speaker 1: team from i think University of Arizona. There's a team
24:09
Speaker 1: of academics. That was pretty cool. Who Um, we're trying
24:12
Speaker 1: to figure out if you predict the amount of carbon
24:15
Speaker 1: capturing capacity an entire rainforest has just by measuring UM
24:21
Speaker 1: and figuring out this self similar system that a single
24:24
Speaker 1: tree in that rainforest UM has. That makes sense, Well,
24:30
Speaker 1: it does, but it's kind of a leap. It's like, okay,
24:32
Speaker 1: so it's one tree, does it follow the same system
24:36
Speaker 1: that the whole rainforest does? And they apparently found that yes,
24:40
Speaker 1: in fact it does right. The same branching uh system
24:44
Speaker 1: found in that tree is similar to the the growth
24:49
Speaker 1: of the trees in the rainforest as a whole. Pretty cool, yes,
24:54
Speaker 1: um in the human body, uh, one of the keys
24:58
Speaker 1: to getting rid of cancer is or any kind of
25:02
Speaker 1: tumors spotting these tumors early on. But with our ultrasound
25:05
Speaker 1: technology you can only get so small and so detailed
25:08
Speaker 1: that you can't see some of these natural fractals that
25:12
Speaker 1: you know, your blood vessels are fractals essentially, just like
25:15
Speaker 1: the branches of a tree are um So they are
25:18
Speaker 1: now using geometry two. Now if I'm not sure if
25:24
Speaker 1: I got this right, but I think it shows up.
25:26
Speaker 1: It shows the flow of the blood because ultrasound can
25:30
Speaker 1: pick that up through these fractals when they can't even
25:31
Speaker 1: pick up the vessels themselves. Is that right? Early earlier
25:37
Speaker 1: tumor spotting right. Well, for all intents of purposes, they're
25:40
Speaker 1: looking at the vessels by finding the blood because they
25:42
Speaker 1: see where it's flowing. But yeah, depending on the pattern
25:45
Speaker 1: that it follows. If it follows like a like a
25:48
Speaker 1: tree branching shape, it's healthy, right, Yeah, And then the
25:52
Speaker 1: tumors all the veins are all bent and crooking, going
25:55
Speaker 1: in all crazy directions. The readoubt of a heartbeat, it's
25:58
Speaker 1: not consistent. It's a fractal Yeah, So the use fractal
26:01
Speaker 1: analysis now to study your heart rate and use that
26:05
Speaker 1: to better understand how arrhythmia happens through math. So there's
26:12
Speaker 1: the especially with natural systems. That's kind of like the
26:16
Speaker 1: biggest contribution that um fractal geometry is produced so far,
26:20
Speaker 1: I think, aside from c g I is what medical
26:24
Speaker 1: uh well, just that that whole understanding that was first
26:28
Speaker 1: really kind of um voiced by Lewis Fry Richardson with
26:32
Speaker 1: the coastline that there's, um, there are natural systems out
26:37
Speaker 1: there that we can't really that we're not quite paying
26:40
Speaker 1: attention to, we don't really know how to deal with that.
26:43
Speaker 1: We're trying to apply something like Euclidean geometry to something
26:47
Speaker 1: that you can't really use that for um. That that's
26:51
Speaker 1: what fractal geometry is really contributed so far, is to
26:53
Speaker 1: basically say, hey, there's a lot of natural systems out
26:56
Speaker 1: here that are self similar and recursive and now that
27:00
Speaker 1: we kind of see in the fractal world, we see
27:03
Speaker 1: them everywhere, and we have a better understanding of them.
27:06
Speaker 1: And one of the best examples of that, I thought
27:09
Speaker 1: was figuring out how larger animals use less energy and
27:14
Speaker 1: smaller animals they use energy more efficiently. And um, this
27:18
Speaker 1: is a kind of a biological paradox for a really
27:21
Speaker 1: long time, and these guys figured it out using I guess,
27:24
Speaker 1: kind of the um same kind of insight that fractal
27:28
Speaker 1: geometry has. That if you take genes and genes are
27:33
Speaker 1: the mathematical formula or the equivalent of a mathematical formula,
27:38
Speaker 1: and you UH feed in uh these genetic processes, what
27:43
Speaker 1: it's going to put out is this self similar recursive
27:49
Speaker 1: pattern to where the bigger the organism is, the more
27:53
Speaker 1: this thing goes and goes and goes, the less energy
27:56
Speaker 1: it's going to use because there's more of it and
27:59
Speaker 1: it doesn't require very much energy to produce past a
28:01
Speaker 1: certain point. So if you have a very small animal,
28:04
Speaker 1: it's using a lot of energy to do these things
28:06
Speaker 1: to carry this out. But there's that economy of scale
28:09
Speaker 1: because you're still using a relatively simple formula, your genetic code,
28:14
Speaker 1: right UM, to carry out a very complex, seemingly complex
28:19
Speaker 1: um system, which is your organs or you as an organism.
28:24
Speaker 1: So in the end, an elephant uses less energy than
28:26
Speaker 1: a mouse, Yes, because they're both using the same formula,
28:30
Speaker 1: the same input. And then eventually you reach a point
28:33
Speaker 1: where it just gets easier and easier and easier to
28:37
Speaker 1: to use something simple to create a complex system. I
28:40
Speaker 1: love it too. Uh. I got one more thing. You
28:43
Speaker 1: heard this guy Jason Paget, Huh, this is pretty crazy. UM.
28:47
Speaker 1: This guy, like nine years ago, I think UM, was
28:52
Speaker 1: mugged in Tacoma, Washington, got hit in the back of
28:55
Speaker 1: the head really hard, knocked him out, and he acquired UM,
29:01
Speaker 1: a form of synesthesia in which he sees fractals from
29:05
Speaker 1: being hit in the head and UM basically it's an
29:08
Speaker 1: acquired savant savantasm, which is pretty rare to acquire this.
29:13
Speaker 1: Later on, UM, and this guy hated math, and his
29:18
Speaker 1: family used to make fun of him, he said, because
29:20
Speaker 1: he was the worst at pictionary. Uh. I couldn't draw
29:23
Speaker 1: a thing, couldn't draw a lick. Now this guy can
29:26
Speaker 1: draw reportedly mathematically correct fractals by hand, and he's the
29:33
Speaker 1: only person on earth that can do this. And you
29:36
Speaker 1: should see these things. They're like, you know, a huge
29:40
Speaker 1: you know, two by two fractal that looks like it
29:43
Speaker 1: was plotted by like a supercomputer. And this guy does
29:46
Speaker 1: these by hand now out of nowhere because he got
29:49
Speaker 1: hit on the head. That's pretty amazing. Yeah, it's crazy.
29:51
Speaker 1: He got him in the fractal center. Huh. Did that's
29:54
Speaker 1: strange that we would have like that ability latent in
29:58
Speaker 1: us you know. Yeah, Well they studied his brain of course, um,
30:01
Speaker 1: and they found that the two areas that lit up
30:04
Speaker 1: in the left hemisphere were the areas that control exact
30:07
Speaker 1: math and mental imagery. So they dont have it. And he's,
30:12
Speaker 1: you know, he's fine with it, although he says that
30:14
Speaker 1: he's a bit obsessive about it because he's it's one
30:17
Speaker 1: of those deals where everywhere he looks now he sees fractals.
30:20
Speaker 1: Oh yeah, well I got the impression that people who
30:23
Speaker 1: are who are fractal geometers have the same thing. Yeah,
30:27
Speaker 1: you know, they're like, look at that cloud. I I
30:29
Speaker 1: can figure out how to describe it completely. Yeah with math, Yeah,
30:33
Speaker 1: it's crazy. Um. And then it's everywhere canopies of the trees. Like.
30:36
Speaker 1: I got that impression as well that once you start
30:38
Speaker 1: seeing fractals in natural systems, like then everything becomes um,
30:43
Speaker 1: fractals and a lot simpler to understand. I realized today
30:46
Speaker 1: that I have always doodled in fractals. Yeah yeah, because
30:50
Speaker 1: I can't really draw, so whenever I doodle, it's like
30:52
Speaker 1: it's always been um little fractal shapes, Like I would
30:57
Speaker 1: draw some kind of geometric shape, then split off from
31:00
Speaker 1: that and make it smaller, and in the end they're
31:03
Speaker 1: sort of like fractals. Oh, your fractal tree that you
31:05
Speaker 1: showed me, it's pretty awesome. So you got anything else?
31:10
Speaker 1: Uh No, I would strongly urge you to read this
31:13
Speaker 1: article a few more times and then maybe go off
31:16
Speaker 1: and read some more about fractals, because we definitely have
31:18
Speaker 1: not covered all of it. I'll watch that Nova documentary. Yeah,
31:22
Speaker 1: good stuff. What is it chasing the hidden? To mention?
31:25
Speaker 1: Is that what it's called? Diould call it chasing the dragon? Well,
31:28
Speaker 1: there's the dragon curve fractal. It's pretty boss, that's right,
31:31
Speaker 1: it is. UM. So you want to type fractals in
31:35
Speaker 1: the search bar how stuff works dot com to start,
31:38
Speaker 1: and that will bring up this very very good article.
31:41
Speaker 1: And I said search bar, which means it's time for
31:43
Speaker 1: listening to ma'am Josh. I'm gonna call this, uh, don't
31:48
Speaker 1: eat your peanuts around me, jerk. Yeah. Remember when the
31:51
Speaker 1: Air Traffic Control remarked that I never heard the announcement that, uh,
31:56
Speaker 1: no one can eat peanuts on the plane. Yeah. I've
31:58
Speaker 1: flown a lot in my life and I've never heard
32:00
Speaker 1: that before. So Ian Hammer writes in on the Air
32:04
Speaker 1: Traffic Control episode, you were talking about peanuts being completely
32:07
Speaker 1: absent on some flights, And as a person that is
32:11
Speaker 1: really allergic to peanuts, I can shed some light. My
32:14
Speaker 1: allergy is bad enough to wear. The smell of peanuts,
32:17
Speaker 1: which is really just the presence of peanut molecules in
32:19
Speaker 1: the air, will cause me to get itchy and swollen. Uh.
32:22
Speaker 1: In the case that I am in contact with a peanut,
32:25
Speaker 1: have the superpower of becoming a balloon, and I'll swell
32:28
Speaker 1: up to the point where I will be dead in
32:29
Speaker 1: a matter of minutes. I can delay the anaphylactic shock
32:33
Speaker 1: for ten minutes, give or take with an injection of epinephrin,
32:36
Speaker 1: and this will only work twice, I think. So um,
32:42
Speaker 1: if I do have reaction, I have twenty minutes plus
32:44
Speaker 1: the fifteen minutes I have before normal anaphylactic shock would
32:48
Speaker 1: kill me. There really is in a way to save
32:50
Speaker 1: me in that instance, unless I can be administered the
32:53
Speaker 1: proper treatment that you can get only at a hospital,
32:56
Speaker 1: because you can imagine when a plane is at thirty
32:58
Speaker 1: feet there's not much can be done and to get
33:01
Speaker 1: me to a hospital within that thirty five minute time frame.
33:04
Speaker 1: So flying can be a pretty scary thing when someone
33:06
Speaker 1: near you. Besides that they really want a peanut buttercup.
33:09
Speaker 1: People do this sometimes and it's a real pain to
33:11
Speaker 1: have to deal with. I just wanted to give you
33:13
Speaker 1: guys an overview of peanut allergy sufferers when it comes
33:16
Speaker 1: to flying. Keep up the incredible work. Look forward to
33:19
Speaker 1: seeing a TV pilot Ian Hammer. So incredible, is right.
33:23
Speaker 1: If we were insensitive to that, then all apologies. He
33:28
Speaker 1: didn't indicate that, but I think we weren't. I just
33:30
Speaker 1: remember being surprised. Yeah, I was surprised, but and I
33:33
Speaker 1: knew allergies could get bad, but man, that I think
33:36
Speaker 1: on the plane, I was like, what I've known about
33:38
Speaker 1: this since I saw an episode of Freaks and Geeks
33:40
Speaker 1: wherein one of the characters almost died because like some
33:43
Speaker 1: bully at school, like you gave him some peanuts. Oh yeah,
33:47
Speaker 1: was that it was the Martin Star character, the analog
33:51
Speaker 1: to Paul from Wonder Years, Okay, which was I can't
33:58
Speaker 1: remember something, illok freaks some Yeah, it's good good. Um,
34:03
Speaker 1: well let's see allergen. How about a practice story if
34:07
Speaker 1: you know something about fractals that we don't, or can
34:09
Speaker 1: correct us or explain it better than we did, which
34:12
Speaker 1: I'm not sure that that's much of a long shot. Um,
34:16
Speaker 1: we want to hear about it. You can tweet to
34:17
Speaker 1: us at s Y s K podcast. You can visit
34:20
Speaker 1: us on Facebook at Facebook dot com slash stuff you
34:23
Speaker 1: Should Know, or send us an email at Stuff Podcast
34:27
Speaker 1: at Discovery dot com. For more on this and thousands
34:35
Speaker 1: of other topics, visit how Stuff works dot com. Brought
34:45
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34:49
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