WEBVTT - SYSK Selects: Fractals - Whoa 0:00:00.920 --> 0:00:04.040 How do folks, Charles W. Chuck Bryant here in the corral, 0:00:04.480 --> 0:00:06.200 and I'm gonna last so up a Stuff you Should 0:00:06.200 --> 0:00:09.240 Know select for you from June seventh, two thousand twelve. 0:00:09.880 --> 0:00:13.600 Fractals Colin Whoa, this is a tough one for me. 0:00:13.800 --> 0:00:16.360 I'm not gonna lie. Fractals is one of the toughest 0:00:16.360 --> 0:00:19.239 episodes I've ever had to learn and research. And that's 0:00:19.239 --> 0:00:25.439 where we're gonna revisit it right here, right now. Welcome 0:00:25.480 --> 0:00:27.720 to Stuff you Should Know, a production of My Heart 0:00:27.800 --> 0:00:36.320 Radios How Stuff Works. Hey, and welcome to the podcast. 0:00:36.400 --> 0:00:40.120 I'm Josh Clark, hanging on by my fingernails with me 0:00:40.200 --> 0:00:42.920 as always as Charles W. Chuck Bryant, doing much the 0:00:42.960 --> 0:00:47.160 same as we are about to start speaking on stuff 0:00:47.159 --> 0:00:52.479 you should know about. Fractals. Yea, more math theoretical, Matt 0:00:52.840 --> 0:00:57.000 even Yeah, a new branch of geometry. It's non Euclidean 0:00:58.400 --> 0:01:02.240 since you brought it up, Okay, very new. Euclidean geometry 0:01:02.360 --> 0:01:09.160 was like three B C and fractals are so there's 0:01:09.360 --> 0:01:11.160 a little bit of a gap there. There is a 0:01:11.200 --> 0:01:13.880 little bit of a gap and uh, there's a lot 0:01:13.920 --> 0:01:19.760 of animosity among the Euclideans towards Fractillians. They need to 0:01:19.800 --> 0:01:22.120 loosen up and look at some of those far out pictures. 0:01:22.800 --> 0:01:25.280 I know, you know it's funny. Did you watch um, 0:01:25.400 --> 0:01:27.800 did you watch that one doc on? Yeah? Okay, did 0:01:27.800 --> 0:01:31.200 you see the other? The Arthur C. Clark one. It 0:01:31.280 --> 0:01:33.920 was made in like maybe eight s eighty seven and 0:01:33.959 --> 0:01:38.240 it had nothing but like um delicate sound of thunder 0:01:38.360 --> 0:01:40.720 rip off music going on the whole time. It was 0:01:40.800 --> 0:01:43.880 really really trippy. Well, I posted a picture I don't 0:01:43.880 --> 0:01:45.320 know if you saw today on the stuff you should 0:01:45.319 --> 0:01:49.520 know all of the of the Mandel brought set. Its 0:01:49.560 --> 0:01:52.320 beautiful it is and it's very cool. And I didn't 0:01:52.320 --> 0:01:54.560 even say what it was. I just posted it, and 0:01:54.600 --> 0:01:57.680 like I'd say, about half the people were like, very cool, man, 0:01:57.720 --> 0:01:59.400 this is rad I love the Mantal brought set like 0:01:59.640 --> 0:02:02.960 fractill talk about fractals. And then the other half were like, 0:02:03.480 --> 0:02:05.480 well you guys tripping out like what you did a 0:02:05.480 --> 0:02:09.200 grateful dead day. That's actually math, believe it or not. 0:02:09.400 --> 0:02:11.600 But it does look very it's very tied eye in 0:02:11.680 --> 0:02:14.240 nature and that's why the hippies like it. Plus also, 0:02:14.240 --> 0:02:16.760 I mean, if you've ever seen a fractal play out 0:02:16.800 --> 0:02:22.320 on a computer screen. Yeah. Um, so we are talking 0:02:22.320 --> 0:02:24.680 about fractals. I don't I don't necessarily want to give 0:02:24.680 --> 0:02:28.760 a disclaimer. Chuck and I are not theoretical mathematicians. We're 0:02:28.760 --> 0:02:33.600 not even like normal mathematicians. I balanced my checkbook my 0:02:33.760 --> 0:02:36.239 hand just to keep that little part of my brain going. 0:02:36.400 --> 0:02:39.120 So I don't like forget how to add and subtract 0:02:39.400 --> 0:02:42.240 later on in life. I make myself do that, and 0:02:42.280 --> 0:02:46.760 I don't let myself jump ahead. I show my work. Yeah. Um, 0:02:46.800 --> 0:02:50.000 and that's about the extent of math in my life normally. See, 0:02:50.040 --> 0:02:52.200 I was the kid in math that when they said 0:02:52.200 --> 0:02:54.520 you're not allowed to use calculators, I would go, like, 0:02:55.200 --> 0:02:58.400 there are calculators in life, so why can't we use them. Yeah, 0:02:58.520 --> 0:03:01.280 Like they made calculators so we didn't have to do maths, right. 0:03:01.320 --> 0:03:03.160 But at the same time, I find that shoddy because 0:03:03.160 --> 0:03:08.120 it's like, you're not you're not You're just circumventing learning something, 0:03:08.240 --> 0:03:10.880 and it's like the calculators there to support you after 0:03:10.960 --> 0:03:14.320 you know what you're doing. I disagree. Well, I think 0:03:14.320 --> 0:03:18.480 this is a pretty prime example of like going around 0:03:19.480 --> 0:03:23.920 to get to the end. So when when I was 0:03:23.960 --> 0:03:26.240 researching this, I was like, Okay, well, they don't really 0:03:26.280 --> 0:03:27.760 know what they're doing with this stuff yet, so we 0:03:27.800 --> 0:03:30.240 can just totally be like, well it's it's there, anything 0:03:30.280 --> 0:03:32.359 you wanted to be and nothing at all. And then 0:03:32.440 --> 0:03:35.480 like I started looking a little more deeply into I'm like, oh, no, 0:03:35.640 --> 0:03:38.400 they do kind of know what they're doing. We really 0:03:38.400 --> 0:03:40.040 don't know what we're talking about. So I feel like 0:03:40.080 --> 0:03:43.080 I have, just from researching this, a little bit, um 0:03:43.280 --> 0:03:47.520 something of a grasp of what fractals are, a little 0:03:47.560 --> 0:03:49.760 bit For those of you who who don't know what 0:03:49.800 --> 0:03:52.320 we're talking about, like, take a second to um look 0:03:52.360 --> 0:03:56.040 up just typing fractal and search images on your favorite 0:03:56.040 --> 0:03:59.440 search engine and you'll be like, oh, yes, of course 0:03:59.480 --> 0:04:01.920 it's a fractal um And that's what we're going to 0:04:01.960 --> 0:04:07.440 talk about, because fractal fractals are a new field, like 0:04:07.480 --> 0:04:10.040 we said, in geometry, and they do have use and 0:04:10.080 --> 0:04:13.800 they have usefulness that I think people haven't even considered yet. 0:04:14.360 --> 0:04:16.520 But the the stuff that they have figured out how 0:04:16.560 --> 0:04:19.039 to use it for is pretty amazing stuff. Can I 0:04:19.080 --> 0:04:21.200 say what a fractal is at least so people know 0:04:21.640 --> 0:04:24.000 they should clear it all up? It is a geometric 0:04:24.040 --> 0:04:26.719 shape that is self similar through infinite iterations in a 0:04:26.760 --> 0:04:30.000 recursive pattern and through infinite detail exactly. So there you 0:04:30.040 --> 0:04:32.200 have it. Boom, Do we need to even continue? No? 0:04:32.360 --> 0:04:35.840 But um, and that sounds like really that put me off, 0:04:36.360 --> 0:04:38.599 Like this article was pretty well done by a guy 0:04:38.680 --> 0:04:41.039 named Craig Haggett. I don't know who that it is, freelancer. 0:04:41.040 --> 0:04:44.520 I guess um, it's a pretty well done article. But 0:04:44.560 --> 0:04:46.800 that a sentence like that can put a person off 0:04:46.800 --> 0:04:49.240 pretty easy. And he even put it, you know, he 0:04:49.360 --> 0:04:51.159 made a joke about it, like, oh, you know that, 0:04:51.200 --> 0:04:54.040 you get it, you know whatever. But um, when you 0:04:54.080 --> 0:04:56.640 think about it, if you take that apart, one of 0:04:56.680 --> 0:05:01.760 the hallmarks of fractal fractals, um is that they are 0:05:02.360 --> 0:05:06.880 a very complex result from a very simple system. And 0:05:06.920 --> 0:05:09.920 there's like basically three hallmarks two fractals that you just 0:05:09.960 --> 0:05:15.479 pointed out right. There is um self similarity, which is 0:05:16.360 --> 0:05:20.160 if you if you cut a chunk, like a microscopic 0:05:20.200 --> 0:05:23.840 piece of a fractal off and compare it to the 0:05:23.839 --> 0:05:27.320 whole fractal, it's going to be virtually the same. Yeah, 0:05:27.440 --> 0:05:30.159 like or a fern. And the cool thing about fractals 0:05:30.200 --> 0:05:33.800 is is to me the coolest thing is that fractals. 0:05:35.960 --> 0:05:38.000 The point they made in the Nova documentary is that 0:05:38.400 --> 0:05:41.719 all of our math up until they discovered fractals and 0:05:41.760 --> 0:05:46.679 described practicals was based on things that we basically created 0:05:46.720 --> 0:05:52.839 and built. Like all geometry, right, Euclidean geometry, you have length, width, 0:05:53.279 --> 0:05:56.719 and height, which should view the three dimensions, right, yes, 0:05:56.800 --> 0:06:00.640 for like pyramids and buildings and combs and all those things. 0:06:00.720 --> 0:06:02.960 And you it's extremely useful and we've done quite a 0:06:02.960 --> 0:06:07.400 bit with this. But what Euclidean geometry, as far as 0:06:07.440 --> 0:06:13.839 the fractal geometrists or geometers um insist, failed at is 0:06:13.920 --> 0:06:17.279 when they said, okay, look at that mountain. That's a cone. 0:06:17.320 --> 0:06:21.039 It's an imperfect cone, it's a rough cone, but it's 0:06:21.040 --> 0:06:25.159 a cone shape, right, So yeah, Euclidean geometry holds sway. 0:06:25.279 --> 0:06:29.880 What the fractal geometers say is, yeah, you could say 0:06:29.880 --> 0:06:31.679 that it's a cone, but if you tried to measure 0:06:31.720 --> 0:06:33.760 and describe it as such, you're not going to come 0:06:33.839 --> 0:06:38.240 up with a very descriptive, a very um detailed description 0:06:38.720 --> 0:06:43.120 of that mountain. So what's the point What fractal geometry 0:06:43.160 --> 0:06:46.240 does is it says we're going to describe that mountain 0:06:46.560 --> 0:06:50.760 in every little craig and peak possible. And so what 0:06:50.839 --> 0:06:55.480 you have is the fractal dimension, which exists in conjunction 0:06:55.520 --> 0:06:59.160 with length, widthin height. And what the fractal dimension describes 0:06:59.279 --> 0:07:03.040 is the complex city of the object that exists within 0:07:03.080 --> 0:07:07.159 those three dimensions as well. That's right. So finishing my point, 0:07:07.560 --> 0:07:10.560 the cool thing about fractals is that everything that we 0:07:10.600 --> 0:07:13.600 had done previously in geometry were because of things we've built. 0:07:13.960 --> 0:07:16.760 Practicals help describe things that were have been here since 0:07:16.800 --> 0:07:20.760 the beginning of time in nature, and one of the 0:07:20.760 --> 0:07:24.600 truest examples of that is the fern. Right with self similarity. 0:07:24.680 --> 0:07:27.640 You take a little snippet off of a fern, although 0:07:27.640 --> 0:07:30.280 you shouldn't do that. Let's just look at it. Uh, 0:07:30.320 --> 0:07:32.720 it's gonna look the same as the larger part of 0:07:32.720 --> 0:07:35.440 the fern, and then the whole fern itself very self 0:07:35.480 --> 0:07:39.720 similar but not necessarily exact. No, it can be. There 0:07:39.800 --> 0:07:42.720 is a form of self similarity that is exact and precise, 0:07:42.760 --> 0:07:47.280 but in nature that's rare, if not just completely not found. Right, 0:07:47.320 --> 0:07:50.000 that's right. So you've got self similarity, which is the 0:07:50.160 --> 0:07:53.040 smaller part is virtually the same or looks the same, 0:07:53.160 --> 0:07:56.880 or structured the same as the whole UM. And this 0:07:57.000 --> 0:08:02.280 process of self similarity UM going larger smaller in scale 0:08:02.720 --> 0:08:07.720 is called recursiveness, right, And recursiveness is UM. Like you 0:08:07.760 --> 0:08:10.320 know those paintings where it's like a guy I think 0:08:10.360 --> 0:08:13.520 Stephen Colbert, the one that he gave to the Smithsonian 0:08:13.680 --> 0:08:16.880 has recursiveness in it, where it's a man in a 0:08:16.880 --> 0:08:20.280 painting standing in front of like a mantle, and above 0:08:20.320 --> 0:08:23.200 the mantle is the painting that you're looking at, and 0:08:23.240 --> 0:08:24.840 then it goes on and on and on and on 0:08:24.920 --> 0:08:28.720 and on anything that's infinitely repeating, right, same with if 0:08:28.760 --> 0:08:31.480 you're in a dressing room and there's a mirror on 0:08:31.520 --> 0:08:34.640 either side of the wall, you just keep going on infinitely. 0:08:34.640 --> 0:08:41.400 It's recursiveness and with fractals the recursiveness of self similarity. Right. 0:08:41.800 --> 0:08:45.400 So there's two two traits. UM is produced through this 0:08:45.440 --> 0:08:48.640 thing called iteration, that's right. And that's where you say, 0:08:48.679 --> 0:08:52.720 here's the whole I'm gonna put it into this formula, 0:08:53.280 --> 0:08:59.480 and the formula has has the formula. The output of 0:08:59.520 --> 0:09:04.760 the formula produces the input for the next round of 0:09:04.840 --> 0:09:08.400 that same formula. It's a loop exactly, so it's self 0:09:08.400 --> 0:09:12.720 sustaining and it can go on infinitely recursion. Right. That's right. 0:09:13.200 --> 0:09:15.520 So what we've just come up with is a fractal 0:09:15.559 --> 0:09:19.240 is anything that has a self similar structure and it's 0:09:19.559 --> 0:09:24.800 recursive through iteration. That's right. Okay, So um A, really 0:09:25.320 --> 0:09:29.120 I came upon this kind of easy, one easier explanation 0:09:29.200 --> 0:09:32.360 of a fractal from Ben wal Mandel brought site. He died, 0:09:32.360 --> 0:09:35.400 by the way in two. He seemed like a pretty 0:09:35.400 --> 0:09:40.400 good guy. He was definitely thinking different. Um. And the 0:09:40.440 --> 0:09:43.880 way that Mandel brought described a really easy way to 0:09:43.960 --> 0:09:46.080 think of a fractal is um. There's this thing called 0:09:46.120 --> 0:09:50.800 the Serpinsky gasket, and you take a triangle and you 0:09:50.840 --> 0:09:54.040 can combine them into a bunch of little triangles and 0:09:54.120 --> 0:10:00.280 spaces triangular spaces that form a larger triangle. Right, So 0:10:00.840 --> 0:10:04.839 that that one initial solid triangle is called the initiator, 0:10:04.880 --> 0:10:08.160 that's the original shape, and then all those other triangles 0:10:08.200 --> 0:10:12.160 combine that form that larger triangle or a self similar 0:10:12.240 --> 0:10:15.360 version of that larger triangle to the original triangle. That's 0:10:15.360 --> 0:10:21.160 called generator. Right. So the formula for creating a fractal 0:10:21.480 --> 0:10:24.560 would be to go into that generator, the version that 0:10:24.600 --> 0:10:27.280 has all the little smaller triangles that make up a 0:10:27.360 --> 0:10:31.000 larger whole triangle. And say, all the ones that look 0:10:31.080 --> 0:10:35.000 like the initiator, the original just solid black triangle, take 0:10:35.040 --> 0:10:38.400 that out and swap it with the generator version, and 0:10:38.440 --> 0:10:43.280 all of a sudden you have one that's exponentially more detailed. 0:10:43.720 --> 0:10:46.640 There's more to it, And that's a fractal. That's all 0:10:46.679 --> 0:10:48.960 there is to it. You know what else is a fractal? 0:10:49.160 --> 0:10:53.120 What the coastline? Yeah, that was a big one. Lewis 0:10:53.120 --> 0:10:57.800 Fry Richardson was an English mathematician early twenty century, and 0:10:57.840 --> 0:11:01.000 he very brilliantly said, you know what, if you take 0:11:01.080 --> 0:11:04.000 a yardstick and you measured the coastline of England, you're 0:11:04.040 --> 0:11:07.160 gonna get a number. If you take a one ft 0:11:07.240 --> 0:11:11.000 ruler and measure the coastline, you're gonna get a different number. 0:11:11.240 --> 0:11:15.120 If you take a one inch ruler and measure the coastline, 0:11:15.160 --> 0:11:18.600 you're gonna get a different number. And it's basically infinite 0:11:18.679 --> 0:11:22.920 in that the smaller you go with your your unit 0:11:23.000 --> 0:11:26.520 of measure or your tool is the larger number you're 0:11:26.520 --> 0:11:31.520 gonna get. Because the coastline is so infinitely varied in 0:11:31.559 --> 0:11:34.160 its little nooks and crannies, right exactly It's a very 0:11:34.160 --> 0:11:36.320 cool way of thinking about it. There's a second part 0:11:36.360 --> 0:11:39.520 of that to Chuck, is that so depending on the you, 0:11:40.320 --> 0:11:42.840 what you're using, the measure, the tool you're using, the measure, 0:11:43.360 --> 0:11:46.680 the number, the perimeter of that coastline could go on infinitely, 0:11:47.120 --> 0:11:49.720 but it still contains the same finite amount of space 0:11:49.760 --> 0:11:52.920 within its paradox. That is a big time paradox because 0:11:52.960 --> 0:11:55.600 things aren't supposed to be infinite and finite at the 0:11:55.600 --> 0:11:59.520 same time, right right, Um and uh Lewis Fry Richardson 0:12:00.280 --> 0:12:04.360 he basically established in that coming up with that paradox, 0:12:05.400 --> 0:12:08.960 this kind of revolution and thought that fractal geometry is 0:12:09.000 --> 0:12:12.440 based on that. You can have the infinite mixed with 0:12:12.480 --> 0:12:16.880 the finite. You can get it from pretty simple formulas 0:12:16.920 --> 0:12:23.160 that create very increasingly complex systems, right Um. And Fry 0:12:23.280 --> 0:12:25.839 wasn't the He wasn't He was the first guy to 0:12:25.920 --> 0:12:28.080 really kind of put forth this idea of thought, but 0:12:28.080 --> 0:12:30.600 he wasn't the first one to notice this paradox. Yeah, 0:12:30.679 --> 0:12:33.840 and before people even knew they were fractals, there were 0:12:33.880 --> 0:12:37.240 there were artists like da Vinci that saw this pattern 0:12:37.280 --> 0:12:39.760 and tree branches that was um I know in the 0:12:39.800 --> 0:12:43.679 Nova documentary and the article, they point out the uh 0:12:43.920 --> 0:12:51.960 Katsu Chica Hokusai Japanese artists created the Great Wave off Kanagawa, 0:12:52.559 --> 0:12:55.720 and uh those are fractals. It's a it's ocean waves 0:12:55.720 --> 0:12:58.000 breaking and at the top of the crest of the 0:12:58.000 --> 0:13:01.040 waves are a little self similar or waves breaking off 0:13:01.080 --> 0:13:03.960 into smaller and smaller self similar versions. And that's a 0:13:04.120 --> 0:13:06.920 natural fractal, or in this case, it's a depiction of one. 0:13:07.040 --> 0:13:09.400 So they were you know, early African and Nabajo artists 0:13:09.440 --> 0:13:12.520 were doing this and they didn't realize that they were 0:13:12.640 --> 0:13:15.000 fractals and that there were fractals all around us. No, 0:13:15.120 --> 0:13:19.000 they just saw crystals in a snowflake or another good one, yeah, exactly. Um, 0:13:19.040 --> 0:13:21.360 they were just they saw that there was what they 0:13:21.400 --> 0:13:24.560 were looking at was a repeating pattern that was self 0:13:24.600 --> 0:13:29.680 similar and recursive. Right, yeah, that's it. That's a fractal, right. Yeah. 0:13:29.720 --> 0:13:33.079 And and Ben Wha Mandel brought was the first one 0:13:33.120 --> 0:13:35.839 to say, you know what, we can we can use 0:13:35.960 --> 0:13:38.920 math equations to actually apply to this. And he was 0:13:38.920 --> 0:13:41.600 a big star for a while, and then they sort 0:13:41.600 --> 0:13:44.199 of turned on him and said, you know what, this 0:13:44.280 --> 0:13:48.280 is all cool and trippy looking, but it's useless. Right, 0:13:48.360 --> 0:13:52.000 and he said, oh yeah, screw you guys, watch this 0:13:52.120 --> 0:13:56.560 and he wrote another book which started to uh give 0:13:56.600 --> 0:14:02.240 some practical applications which are pretty exciting. UM. So the 0:14:02.280 --> 0:14:05.360 whole thing, the whole principle that is based on UM 0:14:05.520 --> 0:14:08.560 is that you can take a formula and plug in 0:14:09.160 --> 0:14:13.760 a very simple UM, well, a relatively simple formula like 0:14:13.800 --> 0:14:17.040 mantle Brod's formula. Will take that one. For example, his 0:14:17.080 --> 0:14:23.520 is um ZED goes to ZED squared plus c. Right, 0:14:24.440 --> 0:14:27.840 that's what it's called. If you're in England, zed, we 0:14:27.920 --> 0:14:34.680 say z Z. Well, anyway, Zed goes to which is 0:14:34.760 --> 0:14:37.560 and the goes to is the key right here. This 0:14:37.640 --> 0:14:41.040 is what makes it fractal goes to means that um, 0:14:41.040 --> 0:14:43.440 it's an error. It's an equal sign. It looks like 0:14:43.440 --> 0:14:46.280 an equal sign with a part of an arrow pointing 0:14:46.800 --> 0:14:50.360 towards ZED, the other point pointing towards the rest of 0:14:50.400 --> 0:14:54.520 the formula, which means that the the there's that feedback 0:14:54.520 --> 0:14:56.640 loop where it's like, okay, once you have the number 0:14:56.960 --> 0:15:00.000 that this punches out, you have, you feed it back 0:15:00.040 --> 0:15:01.920 can and you'll get another number and knows, just keep 0:15:01.920 --> 0:15:04.600 going and going and going, and every time, remember you're 0:15:04.640 --> 0:15:12.000 swapping out the original the initiator for the the detailed 0:15:13.040 --> 0:15:18.480 version the generator, and it's just getting exponentially more complex 0:15:18.600 --> 0:15:22.640 with just that one iteration of that very simple formula. 0:15:23.920 --> 0:15:27.440 UM and Mandel brought set Uh. This is the one 0:15:27.480 --> 0:15:30.320 that's like it's probably the most famous one. That's the 0:15:30.320 --> 0:15:33.080 one that the Deadheads like because it's like this crazy 0:15:33.320 --> 0:15:37.200 juxtaposition between like black and like different colors and everything. 0:15:38.280 --> 0:15:42.640 And with his formula, two things happen with the number 0:15:42.880 --> 0:15:46.480 that you put in. It either goes towards zero or 0:15:46.520 --> 0:15:49.440 it shoots off to the infinite. And what they did 0:15:49.760 --> 0:15:53.240 for this for the the Mandel brought set fractals was 0:15:53.440 --> 0:15:57.480 they assigned a color to a number based on how 0:15:57.560 --> 0:16:01.680 quickly it goes off to towards infinity. Right, so let's 0:16:01.680 --> 0:16:04.120 say that you have like four, If you plug four 0:16:04.160 --> 0:16:07.920 into this and in ten generations, it'll it'll become an 0:16:07.920 --> 0:16:12.200 infinite number. UM. Then say that that would be grouped 0:16:12.200 --> 0:16:15.960 into a blue color like ten generations blue, eight generations 0:16:16.040 --> 0:16:20.920 is red, ninety generations is orange. See what I'm saying. UM. 0:16:21.000 --> 0:16:23.760 And then the other direction, like say if you put 0:16:23.800 --> 0:16:25.920 in four point two or something like that, it'll go 0:16:26.040 --> 0:16:29.160 towards zero and any number that eventually will go towards 0:16:29.240 --> 0:16:33.040 zero is represented as black. So what you have then, 0:16:33.320 --> 0:16:36.920 is this really intricate depending on where you're zooming in 0:16:37.040 --> 0:16:41.240 or out on the fractal, this intricate change of colors, 0:16:41.240 --> 0:16:43.960 and what you're really just seeing our numbers that are 0:16:44.080 --> 0:16:47.360 plots on a plane, and that's your fractal, and then 0:16:47.360 --> 0:16:51.120 the black parts are numbers that will eventually be be zero. Right, 0:16:51.160 --> 0:16:55.200 And most of the mental mental brought set is black. Yeah, 0:16:55.520 --> 0:16:58.640 but if you zoom in, like that's the whole point. 0:16:58.720 --> 0:17:01.560 You zoom in on one of those little uh what 0:17:01.640 --> 0:17:05.320 do we even call those little spikes? Uh? I guess 0:17:05.359 --> 0:17:07.640 you could call it a plot. A plot, and it's 0:17:07.680 --> 0:17:10.720 gonna look like what you just saw. And the Nova 0:17:10.800 --> 0:17:13.240 documentary is very cool when they zoom in on these, 0:17:13.440 --> 0:17:16.159 it's sort of mind blowing. Yeah, it is very I 0:17:16.280 --> 0:17:19.200 strongly recommend watching that because they explain it way better 0:17:19.240 --> 0:17:21.240 than us. Well, it helps to see it for sure, 0:17:21.320 --> 0:17:24.160 Oh yeah, big time. So um or draw it as 0:17:24.240 --> 0:17:27.960 I have done. It's a pretty nice little fract Yeah. 0:17:53.000 --> 0:17:55.520 So we've talked about fractals, We talked about the Mandel 0:17:55.560 --> 0:17:58.359 brought set, we talked about where they started to come 0:17:58.400 --> 0:18:05.600 from um and the the idea. Remember Lewis fried Richardson, 0:18:05.640 --> 0:18:09.439 he was talking about measuring the coastline and going off 0:18:09.480 --> 0:18:12.560 into the infinite, but still containing a finite amount um. 0:18:12.720 --> 0:18:15.800 A guy came after him named Helga von Coke. He 0:18:15.880 --> 0:18:18.000 came up with a Coke snowflake, which is pretty cool. 0:18:18.000 --> 0:18:20.879 If you take a straight line, or you take a triangle, 0:18:21.520 --> 0:18:23.720 and then on each side of the triangle in the 0:18:23.760 --> 0:18:28.119 middle you bust out the middle into another triangular hump. 0:18:28.680 --> 0:18:30.399 You do that over and over and over again. It 0:18:30.440 --> 0:18:33.120 goes off into infinity. Although it contains a finite amount 0:18:33.160 --> 0:18:36.359 of space. The perimeter goes off to the infinite. A 0:18:36.400 --> 0:18:40.200 guy named Georg Cantor came up with the cancer set, 0:18:40.480 --> 0:18:42.439 which is you just take a straight line and you 0:18:42.520 --> 0:18:44.520 take the middle out of it, and then for each 0:18:44.520 --> 0:18:46.320 of those two lines that produces, you do the same 0:18:46.320 --> 0:18:48.320 thing and it just keeps going on and on and 0:18:48.440 --> 0:18:51.080 rather than going to nothingness like you're like, well, if 0:18:51.080 --> 0:18:53.760 you take a six inch line, eventually you're gonna bust 0:18:53.760 --> 0:18:56.560 it down and nothingness again. That doesn't happen. They found 0:18:56.560 --> 0:18:59.000 that it goes off to the infinite. So they realized 0:18:59.520 --> 0:19:03.000 Ben Wall mantel Brought was plugging all these into computers, 0:19:03.040 --> 0:19:06.439 because that's what it took people realize this, Like George 0:19:06.480 --> 0:19:09.080 Cantor um Man I hope that's how you say his 0:19:09.240 --> 0:19:12.560 first name. He was he was working in the eighteen eighties, 0:19:13.160 --> 0:19:16.239 Um Gaston Julio came up with the Julia sets for 0:19:16.560 --> 0:19:19.480 producing a repeating pattern using feedback loop. All these guys 0:19:19.480 --> 0:19:23.560 were like nineteenth century early twentieth century mathematicians and it 0:19:23.600 --> 0:19:27.760 was strictly theoretical until the late seventies when guys like 0:19:27.800 --> 0:19:31.360 Mantel Brought who worked at IBM, started feeding these things 0:19:31.440 --> 0:19:35.399 into these new fangled computers and seeing the results like 0:19:35.440 --> 0:19:38.680 this fractals like the mantel Brought set that he saw right, 0:19:39.800 --> 0:19:45.240 So Um, almost immediately there was a practical use for 0:19:45.800 --> 0:19:51.280 fractals that came in the form of c g I. Yeah. 0:19:51.359 --> 0:19:54.360 They interviewed that one guy in the documentary um who 0:19:54.720 --> 0:19:58.520 worked on the first c g I shot in motion 0:19:58.560 --> 0:20:01.520 picture history, which was Star Trek to the Wrath of 0:20:01.600 --> 0:20:05.399 con and Uh. He was tasked with making a c 0:20:05.560 --> 0:20:10.439 g I uh land surface like mountain range and pretty 0:20:10.440 --> 0:20:12.280 mind blowing with it. Yeah, and he did. I mean, 0:20:12.800 --> 0:20:14.399 now you look back and it kind of looks silly, 0:20:14.440 --> 0:20:18.640 but at the time it was completely revolutionary. And once 0:20:18.680 --> 0:20:21.080 he learned about fractals in the geometry and the math 0:20:21.119 --> 0:20:23.560 of fractals, it was pretty easy for him, and he 0:20:23.600 --> 0:20:25.239 made it seem like he was like, oh, well, this 0:20:25.320 --> 0:20:26.960 is the key, this is how you do it right. 0:20:27.119 --> 0:20:29.879 So well, and it is kind of easy, especially if 0:20:29.880 --> 0:20:32.280 you know what you're doing with computer programming and math, 0:20:32.800 --> 0:20:36.159 because what you're basically doing to create a fractal generator 0:20:36.680 --> 0:20:40.439 is teaching your computer to to do something within a 0:20:40.520 --> 0:20:44.200 certain formula. That's your fractal formula, right, And so what 0:20:44.280 --> 0:20:47.399 Lauren Carpenter, the guy who created the the Star Trek 0:20:47.440 --> 0:20:50.480 to landscape for the first c G all c g 0:20:50.680 --> 0:20:53.720 I shot ever, what he basically did was created a 0:20:53.720 --> 0:20:56.480 computer program that said, hey, computer, I'm gonna give you 0:20:56.560 --> 0:20:58.600 a bunch of triangles. Because I think that was the 0:20:58.680 --> 0:21:01.960 earliest stuff he was working with. Um, I'm gonna give 0:21:01.960 --> 0:21:04.399 you a bunch of triangles, and I want you to 0:21:04.440 --> 0:21:08.760 take those triangles and generate a new fractal set from it, right, 0:21:09.480 --> 0:21:10.879 And then I want you to do it again and 0:21:10.880 --> 0:21:13.760 again and again, and then every third time I want 0:21:13.760 --> 0:21:18.399 you to start turning them forty degrees, so it's going 0:21:18.440 --> 0:21:21.520 to change the pattern slightly, and then all of a 0:21:21.560 --> 0:21:24.640 sudden you have these infinite variations. The reason why when 0:21:24.640 --> 0:21:26.359 you go back and look at that shot that it 0:21:26.480 --> 0:21:30.600 still looks kind of you know today, is because the 0:21:30.600 --> 0:21:33.119 computer he was working at didn't have the computing power 0:21:33.160 --> 0:21:37.080 to do that many times. Now we have higher computer 0:21:37.280 --> 0:21:40.119 computing power, and so what we're doing is telling our 0:21:40.160 --> 0:21:43.040 computers to keep going and going and going, swapping out 0:21:43.119 --> 0:21:47.160 that initiator, that one single black triangle everywhere it can 0:21:47.200 --> 0:21:50.040 find it in this pattern, this pattern of triangles in 0:21:50.080 --> 0:21:53.159 the fractal with a brand new fractal. So it's just 0:21:53.240 --> 0:21:55.640 creating more and more and more and more fractals, which 0:21:55.640 --> 0:21:58.600 creates a finer and finer and finer resolution, which makes 0:21:58.600 --> 0:22:01.560 something look all the more real. Yeah, like the part 0:22:01.600 --> 0:22:04.560 in the doc about the Star Wars, I was making 0:22:04.560 --> 0:22:08.040 the lava splashing. It's amazing, Yes, it was because they 0:22:08.080 --> 0:22:10.280 showed the first one they did it looks kind of plain, 0:22:10.840 --> 0:22:13.520 and then once you fed it through this infinite feedback loop, 0:22:14.000 --> 0:22:20.160 it just like shattered and and and uh, fractured, not fractaled, 0:22:20.760 --> 0:22:23.280 although I want to say fractaled off and just look 0:22:23.359 --> 0:22:25.840 more detailed, more detailed, more detailed, until it looked like 0:22:26.080 --> 0:22:28.720 lava splashing. Right, it's pretty amazing. Well, that's where the 0:22:28.720 --> 0:22:31.520 word fractal comes from. Is um Mandel brought coined in 0:22:32.840 --> 0:22:37.440 to say, to indicate how the things fracture off and 0:22:37.520 --> 0:22:41.720 they form irregular patterns. Um, you can create a fractal 0:22:41.800 --> 0:22:47.480 that that is regularly repeating, but it doesn't look as natural. 0:22:48.680 --> 0:22:52.600 And with like say, if you're creating lava, you've got 0:22:52.600 --> 0:22:55.080 to have that one rule that like every third generation 0:22:55.640 --> 0:22:59.000 kicks forty degrees or whatever the rule is. That just 0:22:59.080 --> 0:23:01.680 kind of throws a little bit of dissimilarity and too 0:23:01.720 --> 0:23:04.560 because if something is too self similar, it's not going 0:23:04.600 --> 0:23:06.679 to look right. It's not gonna look natural, it's not 0:23:06.680 --> 0:23:09.880 gonna look real, which kind of leads you to think, chuck. 0:23:09.920 --> 0:23:13.760 Then that there is a an application for studying natural 0:23:13.800 --> 0:23:19.440 phenomenon using fractals, right, while there are I guess all kinds, Um, 0:23:20.119 --> 0:23:24.240 well this isn't so much natural. But the documentary interviewed 0:23:24.280 --> 0:23:28.479 Nathan Cohen who was a ham radio operator and his 0:23:28.600 --> 0:23:31.560 landlord said, dude, you can't have that huge antenna hanging 0:23:31.560 --> 0:23:34.919 out of your apartment so he started bending wires a 0:23:35.000 --> 0:23:39.679 straight wire into essentially a fractal and found that on 0:23:39.720 --> 0:23:43.879 the very first go it got better reception, um, merely 0:23:43.960 --> 0:23:46.320 by the fact that it was bent in that way 0:23:46.720 --> 0:23:50.959 and it was self similar. So he eventually used that 0:23:51.720 --> 0:23:54.560 two I hope make a lot of money. I got 0:23:54.600 --> 0:23:57.320 the impressing that he did, okay, um by applying that 0:23:57.359 --> 0:24:00.719