WEBVTT - Fractals: Whoa 0:00:00.320 --> 0:00:02.960 Brought to you by the reinvented two thousand twelve Camray. 0:00:03.200 --> 0:00:07.560 It's ready. Are you welcome to Stuff you Should Know 0:00:08.200 --> 0:00:16.400 from House Stuff Works dot Com. Hey, and welcome to 0:00:16.440 --> 0:00:20.040 the podcast. I'm Josh Clark, hanging on by my fingernails 0:00:20.520 --> 0:00:23.360 with me as always as Charles W. Chuck Bryant, doing 0:00:23.440 --> 0:00:26.960 much the same as we were about to start speaking 0:00:27.480 --> 0:00:32.879 on stuff you should know about fractals, more math, theoretical 0:00:33.000 --> 0:00:37.200 man even, Yeah, a new branch of geometry. It's non 0:00:37.240 --> 0:00:42.520 Euclidean since you brought it up, okay, very new Euclidean 0:00:42.520 --> 0:00:50.560 geometry was like, and fractals are. So there's a little 0:00:50.560 --> 0:00:52.440 bit of a gap there. There is a little bit 0:00:52.479 --> 0:00:55.520 of a gap. And uh, there's a lot of animosity 0:00:55.560 --> 0:01:01.160 among the Euclideans towards Fractillians. They need to loosen up 0:01:01.200 --> 0:01:03.840 and look at some of those far out pictures. I know, 0:01:04.040 --> 0:01:06.520 you know it's funny. Did you watch um, did you 0:01:06.520 --> 0:01:08.920 watch that one doc on? Yeah? Okay, did you see 0:01:08.920 --> 0:01:12.440 the other the Arthur C. Clark one. It was made 0:01:12.440 --> 0:01:15.119 in like maybe eighties, six eighty seven, and it had 0:01:15.200 --> 0:01:19.640 nothing but like um delicate sound of thunder rip off 0:01:19.760 --> 0:01:23.440 music going on the whole time. It was really really trippy. Well, 0:01:23.520 --> 0:01:25.120 I posted a picture I don't know if you saw 0:01:25.120 --> 0:01:28.160 today on the stuff, you should know all of the 0:01:28.240 --> 0:01:31.480 of the Mandel brought set. It's beautiful, it is and 0:01:31.520 --> 0:01:33.840 it's very cool. And I didn't even say what it was. 0:01:33.880 --> 0:01:37.039 I just posted it, and like I'd say, about half 0:01:37.040 --> 0:01:39.160 the people were like, very cool, man, this is rattle 0:01:39.160 --> 0:01:42.399 of the Mantal brought set, like fractals, talk about fractals. 0:01:42.520 --> 0:01:44.880 And then the other half were like, well, you guys 0:01:44.920 --> 0:01:48.720 tripping out like what you did, grateful dead day. That 0:01:48.880 --> 0:01:51.000 is actually math, believe or not. But it does look 0:01:51.080 --> 0:01:53.680 very it's very tie dye in nature, and that's why 0:01:53.720 --> 0:01:55.680 the hippies like it. Plus also, I mean, if you've 0:01:55.680 --> 0:01:58.680 ever seen a fractal play out on the computer screen, 0:01:58.760 --> 0:02:04.080 like yeah, um, so we are talking about fractals. I 0:02:04.400 --> 0:02:06.760 don't necessarily want to give a disclaimer. Chuck and I 0:02:06.800 --> 0:02:12.000 are not theoretical mathematicians. We're not even like normal mathematicians. 0:02:12.720 --> 0:02:15.560 I balanced my checkbook my hand just to keep that 0:02:15.600 --> 0:02:17.880 little part of my brain going. So I don't like 0:02:17.960 --> 0:02:21.040 forget how to add and subtract later on in life. 0:02:21.080 --> 0:02:23.880 I make myself to that, and I don't let myself 0:02:23.919 --> 0:02:27.959 jump ahead. I show my work. Yeah. Um, and that's 0:02:27.960 --> 0:02:30.840 about the extent of math and my life normally. See, 0:02:30.840 --> 0:02:33.040 I was the kid in math that when they said 0:02:33.040 --> 0:02:35.320 you're not allowed to use calculators, I would go like, 0:02:36.040 --> 0:02:39.200 there are calculators in life, so why can't we use them. Yeah, 0:02:39.320 --> 0:02:42.120 Like they made calculators so we didn't have to do maths, right, 0:02:42.120 --> 0:02:44.000 But at the same time, I find that shoddy because 0:02:44.000 --> 0:02:48.960 it's like you're not you're not You're just circumventing learning something, 0:02:49.040 --> 0:02:51.720 and it's like the calculators there to support you after 0:02:51.800 --> 0:02:55.120 you know what you're doing. I disagree. Well, I think 0:02:55.160 --> 0:02:59.280 this is a pretty prime example of like going around 0:03:00.280 --> 0:03:04.720 to get to the end. So when when I was 0:03:04.760 --> 0:03:07.079 researching this, I was like, Okay, well, they don't really 0:03:07.080 --> 0:03:08.560 know what they're doing with this stuff yet, so we 0:03:08.600 --> 0:03:11.080 can just totally be like, well it's it's there anything 0:03:11.080 --> 0:03:13.200 you wanted to be and nothing at all. And then 0:03:13.240 --> 0:03:16.280 like I started looking a little more deeply into I'm like, oh, no, 0:03:16.480 --> 0:03:19.160 they do kind of know what they're doing. We really 0:03:19.240 --> 0:03:20.880 do know what we're talking about. So I feel like 0:03:20.880 --> 0:03:23.919 I have, just from researching this a little bit um, 0:03:24.080 --> 0:03:29.080 something of a grasp of what fractals are at. For 0:03:29.120 --> 0:03:31.440 those of you who who don't know what we're talking about, like, 0:03:31.520 --> 0:03:34.440 take a second to um, look up just typing fractal 0:03:34.720 --> 0:03:38.960 and search images on your favorite search engine and you'll 0:03:39.000 --> 0:03:41.640 be like, oh, yes, of course it's a fractal, um 0:03:41.720 --> 0:03:45.320 And that's what we're going to talk about, because fractal 0:03:45.960 --> 0:03:49.520 fractals are a new field, like we said, in geometry, 0:03:49.560 --> 0:03:52.200 and they do have use and they have usefulness that 0:03:52.280 --> 0:03:55.840 I think people haven't even considered yet. But the the 0:03:55.920 --> 0:03:57.760 stuff that they have figured out how to use it 0:03:57.800 --> 0:04:00.760 for is pretty amazing stuff. Can what if fractal is 0:04:01.200 --> 0:04:03.400 at least so people know this should clear it all up. 0:04:04.000 --> 0:04:06.360 It is a geometric shape that is self similar through 0:04:06.360 --> 0:04:10.160 infinite iterations in a recursive pattern and through infinite detail exactly. 0:04:10.440 --> 0:04:12.040 So there you have it. Boom. Do we need to 0:04:12.040 --> 0:04:15.280 even continue? No? But um, And that sounds like really 0:04:15.600 --> 0:04:18.599 that put me off, Like this article was pretty well 0:04:18.600 --> 0:04:20.800 done by a guy named Craig Haggett. I don't know 0:04:20.800 --> 0:04:24.240 who that is, freelancer, I guess, um, And it's a 0:04:24.240 --> 0:04:26.520 pretty well done article. But that a sentence like that 0:04:26.600 --> 0:04:29.320 can put a person off pretty easy, and he even 0:04:29.360 --> 0:04:31.320 put it, you know, he made a joke about it like, 0:04:31.360 --> 0:04:33.040 oh you know that, you get it, you know whatever. 0:04:33.680 --> 0:04:36.000 But um, when you think about it, if you take 0:04:36.040 --> 0:04:41.680 that apart, one of the hallmarks of fractal fractals um 0:04:41.800 --> 0:04:45.480 is that they are a very complex result from a 0:04:45.600 --> 0:04:49.720 very simple system. And there's like basically three hallmarks two 0:04:49.720 --> 0:04:53.400 fractals that you just pointed out right. There is um 0:04:53.520 --> 0:04:58.960 self similarity, which is if you if you cut a 0:04:59.120 --> 0:05:03.640 chunk like a microscopic piece of a fractal off and 0:05:03.720 --> 0:05:06.440 compare it to the whole fractal, it's going to be 0:05:06.560 --> 0:05:09.760 virtually the same, yeah, like or a fern. And the 0:05:09.800 --> 0:05:13.440 cool thing about practicals is is, to me, the coolest 0:05:13.440 --> 0:05:17.599 thing is that practicals. The point they made in the 0:05:17.600 --> 0:05:20.839 Nova documentary is that all of our math up until 0:05:21.040 --> 0:05:25.839 they discovered fractals and described practicals, was based on things 0:05:25.880 --> 0:05:30.680 that we've basically created and built. Like all geometry, right 0:05:30.720 --> 0:05:35.560 Euclidean geometry. You have length, width, and height, which which 0:05:35.560 --> 0:05:38.520 should be the three dimensions, right, yes, for like pyramids 0:05:38.520 --> 0:05:42.080 and buildings, cones and all those things. And you it's 0:05:42.160 --> 0:05:44.240 extremely useful and we've done quite a bit with this. 0:05:45.200 --> 0:05:49.880 But what Euclidean geometry, as far as the fractal geometrists 0:05:49.960 --> 0:05:56.200 or geometers um insist fail That is when they said, okay, 0:05:56.240 --> 0:05:59.320 look at that mountain, that's a cone. It's an imperfect cone, 0:05:59.400 --> 0:06:03.039 it's a rough cone, but it's a cone shape, right, 0:06:03.080 --> 0:06:07.720 So yeah, Clidean geometry holds sway. What the fractal geometers 0:06:07.760 --> 0:06:11.400 say is, yeah, you could say that it's a cone, 0:06:11.440 --> 0:06:13.520 but if you tried to measure and describe it as such, 0:06:13.640 --> 0:06:16.400 you're not going to come up with a very descriptive, 0:06:16.600 --> 0:06:21.960 a very um detailed description of that mountain. So what's 0:06:22.000 --> 0:06:25.440 the point. What fractal geometry does is it says we're 0:06:25.480 --> 0:06:28.600 going to describe that mountain in every little craig and 0:06:28.680 --> 0:06:33.960 peak possible. And so what you have is the fractal dimension, 0:06:34.480 --> 0:06:38.039 which exists in conjunction with length, widthin height. And what 0:06:38.120 --> 0:06:42.920 the fractal dimension describes is the complexity of the object 0:06:42.960 --> 0:06:47.520 that exists within those three dimensions as well. So, finishing 0:06:47.520 --> 0:06:51.080 my point, the cool thing about practicals is that everything 0:06:51.120 --> 0:06:53.720 that we had done previously in geometry were because of 0:06:53.800 --> 0:06:56.920 things we built. Practicals help describe things that were have 0:06:57.040 --> 0:07:00.720 been here since the beginning of time in nature, and 0:07:01.240 --> 0:07:03.560 one of the truest examples of that is the fern. 0:07:03.839 --> 0:07:07.400 Right with self similarity, you take a little snippet off 0:07:07.400 --> 0:07:09.360 of a fern, all that you shouldn't do that, let's 0:07:09.360 --> 0:07:12.600 just look at it. Uh, it's gonna look the same 0:07:12.640 --> 0:07:14.800 as the larger part of the fern, and then the 0:07:14.840 --> 0:07:19.320 whole fern itself very self similar but not necessarily exact. No, 0:07:19.600 --> 0:07:22.000 it can be. There is a form of self similarity 0:07:22.040 --> 0:07:25.120 that is exact and precise, but in nature that's rare, 0:07:25.160 --> 0:07:29.040 if not just completely not found. Right, that's right. So 0:07:29.200 --> 0:07:32.000 you've got self similarity, which is the smaller part is 0:07:32.320 --> 0:07:34.640 virtually the same or looks the same or structured the 0:07:34.680 --> 0:07:38.640 same as the whole um. And this process of self 0:07:38.640 --> 0:07:45.840 similarity um going larger smaller in scale, it's called recursiveness, right, yeah, 0:07:46.120 --> 0:07:49.960 And recursiveness is um like you know those paintings where 0:07:50.000 --> 0:07:52.440 it's like a guy I think Stephen Colbert, the one 0:07:52.480 --> 0:07:55.800 that he gave to the Smithsonian has recursiveness in it, 0:07:56.040 --> 0:07:59.200 where it's a man in a painting standing in front 0:07:59.360 --> 0:08:02.440 of like mantle, and above the mantle is the painting 0:08:02.800 --> 0:08:04.920 that you're looking at, and then it goes on and 0:08:04.960 --> 0:08:08.760 on and on and on and on anything that's infinitely repeating, right, 0:08:08.880 --> 0:08:11.840 same with if you're in a dressing room and there's 0:08:11.840 --> 0:08:13.880 a mirror on either side of the wall, you just 0:08:13.960 --> 0:08:19.520 keep going on infinitely. It's recursiveness, and with fractals the 0:08:19.520 --> 0:08:24.200 recursiveness of self similarity. Right, So there's two two traits. 0:08:24.880 --> 0:08:27.840 Um is produced through this thing called iteration, that's right. 0:08:28.400 --> 0:08:32.080 And that's where you say, here's the whole I'm gonna 0:08:32.360 --> 0:08:36.640 put it into this formula, and the formula has has 0:08:38.520 --> 0:08:42.800 the formula. The output of the formula produces the input 0:08:43.559 --> 0:08:47.040 for the next round of that same formula. It's a 0:08:47.080 --> 0:08:50.640 loop exactly, so it's self sustaining and it can go 0:08:50.679 --> 0:08:55.280 on infinitely recursion. Right. That's right. So what we've just 0:08:55.320 --> 0:08:57.199 come up with is the fractal is anything that has 0:08:57.200 --> 0:09:04.079 a self similar structure and it recursive through iteration. That's okay. 0:09:04.160 --> 0:09:07.760 So um A, really I came upon this kind of 0:09:07.800 --> 0:09:11.640 easy one easier explanation of a fractal from Ben wal 0:09:11.720 --> 0:09:13.800 Mandel brought site. He died, by the way in two 0:09:15.400 --> 0:09:18.000 he seemed like a pretty good guy. He was definitely 0:09:18.240 --> 0:09:22.920 thinking different um. And the way that Mandel brought described 0:09:23.440 --> 0:09:26.120 A really easy way to think of a fractal is um. 0:09:26.160 --> 0:09:29.840 There's this thing called the Serpentsky gasket. And you take 0:09:29.840 --> 0:09:33.840 a triangle and you can combine them into a bunch 0:09:33.880 --> 0:09:38.600 of little triangles and spaces, triangular spaces that form a 0:09:38.720 --> 0:09:44.320 larger triangle. Right, So that that one initial solid triangle 0:09:44.679 --> 0:09:47.720 is called the initiator, that's the original shape. And then 0:09:47.800 --> 0:09:51.079 all those other triangles combine that form that larger triangle 0:09:51.760 --> 0:09:55.080 or a self similar version of that larger triangle, the 0:09:55.080 --> 0:10:00.600 original triangle. That's called a generator. Right. So the formula 0:10:00.679 --> 0:10:04.239 for creating a fractal would be to go into that generator, 0:10:04.679 --> 0:10:07.640 the version that has all the little smaller triangles and 0:10:07.679 --> 0:10:11.160 make up a larger whole triangle. And say, all the 0:10:11.200 --> 0:10:14.240 ones that look like the initiator, the original just solid 0:10:14.240 --> 0:10:17.360 black triangle, take that out and swap it with the 0:10:17.440 --> 0:10:20.520 generator version, and all of a sudden you have one 0:10:20.760 --> 0:10:26.480 that's exponentially more detailed. There's more to it, And that's 0:10:26.520 --> 0:10:28.880 a fractal. That's all there is to it. You know 0:10:28.920 --> 0:10:32.560 what else is a fractal? What the coastline? Yeah, that 0:10:32.640 --> 0:10:35.320 was a big one. Lewis fried Richardson was an English 0:10:35.360 --> 0:10:40.680 mathematician early twenty century, and he very brilliantly said, you 0:10:40.760 --> 0:10:43.320 know what, if you take a yardstick and you measured 0:10:43.320 --> 0:10:46.400 the coastline of England, you're gonna get a number. If 0:10:46.400 --> 0:10:50.560 you take a one ft ruler and measure the coastline, 0:10:50.559 --> 0:10:53.040 you're gonna get a different number. If you take a 0:10:53.120 --> 0:10:56.480 one inch ruler and measure the coastline, you're gonna get 0:10:56.520 --> 0:11:00.640 a different number. And it's basically infinite in that the 0:11:00.679 --> 0:11:04.800 smaller you go with your your unit of measure or 0:11:04.840 --> 0:11:08.240 your tool is the larger number you're gonna get, because 0:11:09.120 --> 0:11:13.080 the coastline is so infinitely varied in its little nooks 0:11:13.120 --> 0:11:15.400 and crannies, right exactly. It's a very cool way of 0:11:15.440 --> 0:11:18.040 thinking about it. There's a second part of that too, Chuck. 0:11:18.240 --> 0:11:21.840 Is that so depending on the you, what you're using, 0:11:21.840 --> 0:11:24.720 the measure, the tool you're using the measure, the number 0:11:24.920 --> 0:11:28.040 the perimeter of that coastline could go on infinitely, but 0:11:28.120 --> 0:11:31.840 it still contains the same finite amount of space within paradox. 0:11:31.960 --> 0:11:34.920 That is a big time paradox because things aren't supposed 0:11:34.920 --> 0:11:37.520 to be infinite and finite at the same time, right 0:11:38.000 --> 0:11:43.360 Um and uh Lewis Fry Richardson. He basically established in 0:11:43.520 --> 0:11:46.760 that coming up with that paradox, the this kind of 0:11:46.800 --> 0:11:51.040 revolution and thought that fractal geometry is based on that 0:11:51.160 --> 0:11:54.360 you can have the infinite mixed with the finite, and 0:11:54.480 --> 0:11:58.240 you can get it from pretty simple formulas that create 0:11:58.679 --> 0:12:04.440 very increasingly complex systems, right, Um, And Fry wasn't the 0:12:04.679 --> 0:12:07.120 He wasn't He was the first guy to really kind 0:12:07.160 --> 0:12:09.200 of put forth this idea of thought, but he wasn't 0:12:09.240 --> 0:12:12.760 the first one to notice this paradox. Yeah, and before 0:12:12.760 --> 0:12:15.000 people even knew there were fractals, there were there were 0:12:15.120 --> 0:12:18.960 artists like Da Vinci that saw this pattern and tree branches. 0:12:19.080 --> 0:12:21.559 That was um. I know. In the Nova documentary and 0:12:21.600 --> 0:12:27.559 the article they point out the uh Catsu Chica Hokusai 0:12:29.400 --> 0:12:34.199 Japanese artists created the Great Wave off Kanagawa and uh 0:12:34.240 --> 0:12:37.400 those are fractals. It's a it's ocean waves breaking and 0:12:37.440 --> 0:12:39.800 at the top of the crest of the waves are 0:12:39.920 --> 0:12:42.960 little self similar waves breaking off into smaller and smaller 0:12:43.160 --> 0:12:46.200 self similar versions. And that's a natural fractal, or in 0:12:46.200 --> 0:12:48.360 this case, it's a depiction of one. So they were 0:12:48.400 --> 0:12:50.760 you know, early African and Navajo artists were doing this 0:12:50.880 --> 0:12:54.400 and they didn't realize that they were fractals and there 0:12:54.400 --> 0:12:57.520 were fractals all around us. No, they just saw crystals 0:12:57.520 --> 0:12:59.800 in a snowflake or another good one, Yeah, exactly. Um. 0:12:59.800 --> 0:13:02.200 They were just they saw that there was what they 0:13:02.200 --> 0:13:05.400 were looking at was a repeating pattern that was self 0:13:05.440 --> 0:13:08.680 similar and recursive. Right, yeah, that's it. That's a fractal. 0:13:09.440 --> 0:13:13.400 Right yeah. And and Ben Wha mandel Brought was the 0:13:13.400 --> 0:13:16.240 first one to say, you know what, we can we 0:13:16.240 --> 0:13:19.360 can use math equations to actually apply to this. And 0:13:19.480 --> 0:13:21.360 he was a big star for a while. And then 0:13:22.000 --> 0:13:24.400 they sort of turned on him and said, you know what, 0:13:24.840 --> 0:13:28.240 this is all cool and trippy looking, but it's useless, 0:13:28.960 --> 0:13:32.520 right And he said, oh yeah, screw you guys. Watch 0:13:32.640 --> 0:13:36.800 this And he wrote another book which started to uh 0:13:37.160 --> 0:13:42.240 give some practical applications which are pretty exciting. UM. So 0:13:42.960 --> 0:13:45.080 the whole thing, the whole principle that this is based 0:13:45.120 --> 0:13:48.560 on UM is that you can take a formula and 0:13:48.720 --> 0:13:54.120 plug in a very simple UM, well, a relatively simple 0:13:54.160 --> 0:13:57.160 formula like mantel Brought's formula. Will take that one. For example, 0:13:57.600 --> 0:14:04.280 his is um Z goes to zed squared plus c. Right, 0:14:05.240 --> 0:14:08.600 that's what it's called. If you're in England, z we 0:14:08.679 --> 0:14:15.480 say z z Well, anyway zed goes to which is 0:14:15.559 --> 0:14:18.320 and the goes to is the key right here, this 0:14:18.400 --> 0:14:21.840 is what makes it fractal. Goes to means that um, 0:14:21.840 --> 0:14:24.240 it's an error. It's an equal sign. It looks like 0:14:24.240 --> 0:14:27.080 an equal sign with an part of an arrow pointing 0:14:27.600 --> 0:14:31.160 towards ZED, the other point pointing toward the rest of 0:14:31.200 --> 0:14:35.320 the formula, which means that the the there's that feedback 0:14:35.320 --> 0:14:37.440 loop where it's like, okay, once you have the number 0:14:37.760 --> 0:14:40.840 that this punches out, you have you feed it back 0:14:40.840 --> 0:14:42.880 in and you'll get another number and just keep going 0:14:42.920 --> 0:14:45.920 and going and going. And every time, remember you're swapping 0:14:45.920 --> 0:14:54.160 out the original the initiator for the the detailed version 0:14:54.280 --> 0:14:59.520 the generator, and it's just getting exponentially more complex with 0:14:59.600 --> 0:15:05.000 just the one iteration of that's very simple formula UM 0:15:05.040 --> 0:15:08.520 and Mandel brought set uh. This is the one that's 0:15:08.600 --> 0:15:11.280 like it's probably the most famous one. That's the one 0:15:11.320 --> 0:15:15.000 that the Deadheads like because it's like this crazy juxtaposition 0:15:15.040 --> 0:15:19.280 between like black and like different colors and everything. And 0:15:19.480 --> 0:15:23.800 with his formula, two things happen with the number that 0:15:23.840 --> 0:15:27.400 you put in. It either goes towards zero, or it 0:15:27.440 --> 0:15:30.880 shoots off to the infinite. And what they did for this, 0:15:31.080 --> 0:15:35.040 for the the Mandel brought set fractals was they assigned 0:15:35.280 --> 0:15:39.240 a color to a number based on how quickly it 0:15:39.280 --> 0:15:42.840 goes off to towards infinity. Right, So let's say that 0:15:42.880 --> 0:15:45.360 you have like four, If you plug four into this 0:15:45.800 --> 0:15:50.800 and in ten generations, it'll it'll become an infinite number. Um. 0:15:50.920 --> 0:15:53.640 Then say that that would be grouped into a blue 0:15:53.640 --> 0:15:57.840 color like ten generations blue, eight generations is red, ninety 0:15:57.920 --> 0:16:02.120 generations is orange. See what I'm saying, um. And then 0:16:02.680 --> 0:16:04.880 the other direction, like say if you put in four 0:16:04.920 --> 0:16:07.480 point two or something like that, it'll go towards zero. 0:16:08.040 --> 0:16:10.840 And any number that eventually will go towards zero is 0:16:10.960 --> 0:16:14.360 represented as black. So what you have then is this 0:16:14.560 --> 0:16:18.200 really intricate depending on where you're zooming in or out 0:16:18.360 --> 0:16:22.280 on the fractal, this intricate change of colors, and what 0:16:22.320 --> 0:16:25.640 you're really just seeing our numbers that are plots on 0:16:25.680 --> 0:16:28.480 a plane, and that's your fractal, and then the black 0:16:28.520 --> 0:16:31.920 parts are numbers that will eventually be be zero. Right, 0:16:31.960 --> 0:16:36.040 And most of the mental mental brought set is black. Yeah, 0:16:36.320 --> 0:16:39.440 but if you zoom in like that's the whole point 0:16:39.520 --> 0:16:42.400 you zoom in on one of those little uh what 0:16:42.440 --> 0:16:46.120 do we even call those little spikes? Uh? I guess 0:16:46.160 --> 0:16:48.440 you could call it a plot. A plot, and it's 0:16:48.480 --> 0:16:51.200 gonna look like what you just saw. And that The 0:16:51.280 --> 0:16:53.760 Nova documentary is very cool when they zoom in on 0:16:53.840 --> 0:16:56.400 these and it's sort of mind blowing. Yeah, it is 0:16:56.520 --> 0:16:59.360 very I strongly recommend watching that because they explain it 0:16:59.440 --> 0:17:01.680 way better than us. Well it helps to see it 0:17:01.720 --> 0:17:07.840 for sure. So um, it's a pretty nice little friend, 0:17:09.560 --> 0:17:13.960 um chuck. So we've talked about fractals, we talked about 0:17:13.960 --> 0:17:16.879 the Mandel brought set, we talked about where they started 0:17:16.920 --> 0:17:23.800 to come from, UM, and the the idea. Remember Lewis 0:17:23.800 --> 0:17:27.920 fried Richardson, he was talking about measuring the coastline and 0:17:27.960 --> 0:17:30.320 going off into the infinite but still containing a finite 0:17:30.359 --> 0:17:34.000 amount UM. A guy came after him named Helga von Coke. 0:17:34.640 --> 0:17:36.880 He came up with a Coke snowflake, which is pretty cool. 0:17:36.920 --> 0:17:39.800 If you take a straight line, or you take a triangle, 0:17:40.440 --> 0:17:42.639 and then on each side of the triangle in the 0:17:42.640 --> 0:17:47.040 middle you bust out the middle into another triangular hump. 0:17:47.560 --> 0:17:49.320 You do that over and over and over again. It 0:17:49.359 --> 0:17:52.040 goes off into infinity. Although it contains a finite amount 0:17:52.080 --> 0:17:55.280 of space, the perimeter goes off to the infinite. A 0:17:55.320 --> 0:17:59.120 guy named Georg Cantor came up with the Cancer set, 0:17:59.400 --> 0:18:01.600 which is just take a straight line and you take 0:18:01.640 --> 0:18:03.520 the middle out of it, and then for each of 0:18:03.520 --> 0:18:05.400 those two lines that produces, you do the same thing 0:18:05.440 --> 0:18:07.560 and it just keeps going on and on and rather 0:18:07.640 --> 0:18:10.080 than going to nothingness like you're like, well, if you 0:18:10.119 --> 0:18:12.760 take a six inch line, eventually you're gonna bust it 0:18:12.760 --> 0:18:15.560 down and nothingness again, that doesn't happen. They found that 0:18:15.600 --> 0:18:18.640 it goes off to the infinite. So they realized ben 0:18:18.720 --> 0:18:22.160 Wa Mantel brought was plugging all these into computers. Because 0:18:22.240 --> 0:18:25.800 that's what it took. People realize it's like George Cantor 0:18:26.280 --> 0:18:28.680 um Man, I hope that's how you say his first name. 0:18:28.960 --> 0:18:32.359 He was he was working in the eighteen eighties. Um 0:18:32.720 --> 0:18:35.920 Gaston Julio came up with the Julius sets for producing 0:18:35.920 --> 0:18:38.520 a repeating pattern using feedback loop. All these guys were 0:18:38.560 --> 0:18:42.600 like nineteenth century early twentieth century mathematicians, and it was 0:18:42.720 --> 0:18:47.040 strictly theoretical until the late seventies, when guys like Mantel 0:18:47.040 --> 0:18:50.760 brought who worked at IBM started feeding these things into 0:18:51.040 --> 0:18:54.520 these new fangled computers and seeing the results like this, 0:18:54.760 --> 0:18:57.600 fractals like the mantel brought set that he saw right, 0:18:58.720 --> 0:19:04.159 so um, almost immediately there was a practical use for 0:19:04.720 --> 0:19:10.240 fractals that came in the form of c g I. Yeah, 0:19:10.280 --> 0:19:13.320 they interviewed that one guy and the documentary um who 0:19:13.640 --> 0:19:17.439 worked on the first c g I shot in motion 0:19:17.480 --> 0:19:20.439 picture history, which was Star Trek to the Wrath of 0:19:20.520 --> 0:19:24.320 con and uh. He was tasked with making a c 0:19:24.480 --> 0:19:29.320 g I uh land surface like mountain range and pretty 0:19:29.359 --> 0:19:31.200 mind blowing with it. Yeah, and he did. I mean, 0:19:31.680 --> 0:19:33.320 now you look back and it kind of looks silly, 0:19:33.359 --> 0:19:37.560 but at the time it was completely revolutionary. And once 0:19:37.600 --> 0:19:40.000 he learned about fractals in the geometry and the math 0:19:40.040 --> 0:19:42.480 of practicals, it was pretty easy for him. And he 0:19:42.520 --> 0:19:44.280 made it seem like he's like, oh, well, this is 0:19:44.320 --> 0:19:46.920 the key, this is how you do it right. So well, 0:19:47.160 --> 0:19:49.040 and it is kind of easy, especially if you know 0:19:49.080 --> 0:19:52.159 what you're doing with computer programming and math, because what 0:19:52.200 --> 0:19:56.120 you're basically doing to create a fractal generator is teaching 0:19:56.119 --> 0:20:00.399 your computer to to do something within a certain formula 0:20:00.480 --> 0:20:03.960 that's a fractal formula, right, and so what Lauren Carpenter, 0:20:04.000 --> 0:20:07.360 the guy who created them the star Trek to landscape 0:20:07.400 --> 0:20:10.240 for the first c G all c g I shot. Ever, 0:20:11.119 --> 0:20:14.560 what he basically did was created a computer program that said, hey, computer, 0:20:14.800 --> 0:20:16.760 I'm gonna give you a bunch of triangles. Because I 0:20:16.800 --> 0:20:20.240 think that was the earliest stuff he was working with. Um, 0:20:20.320 --> 0:20:22.800 I'm gonna give you a bunch of triangles, and I 0:20:22.880 --> 0:20:26.120 want you to take those triangles and generate a new 0:20:26.240 --> 0:20:28.960 fractal set from it, right, And then I want you 0:20:29.000 --> 0:20:31.120 to do it again and again and again, and then 0:20:31.200 --> 0:20:35.240 every third time I want you to start turning them 0:20:35.520 --> 0:20:39.520 forty degrees. So that's going to change the pattern slightly, 0:20:39.920 --> 0:20:42.159 and then all of a sudden you have these infinite variations. 0:20:42.560 --> 0:20:44.520 The reason why when you go back and look at 0:20:44.520 --> 0:20:48.440 that shot that it still looks kind of you know today, 0:20:48.960 --> 0:20:51.159 is because the computer he was working at didn't have 0:20:51.160 --> 0:20:54.679 the computing power to do that many times. Now we 0:20:54.760 --> 0:20:58.320 have higher computer computing power, and so what we're doing 0:20:58.400 --> 0:21:00.920 is telling our computers to keep going and going and going, 0:21:01.200 --> 0:21:05.800 swapping out the initiator that one single black triangle everywhere 0:21:05.800 --> 0:21:08.359 it can find it in this pattern. This pattern of 0:21:08.400 --> 0:21:11.679 triangles in the fractal with a brand new fractal. So 0:21:11.720 --> 0:21:14.320 it's just creating more and more and more and more fractals, 0:21:14.320 --> 0:21:17.200 which creates a finer and finer and finer resolution, which 0:21:17.240 --> 0:21:20.200 makes something look all the more realistic. Yeah, like the 0:21:20.240 --> 0:21:23.560 part in the doc about the Star Wars's making the 0:21:23.640 --> 0:21:27.280 lava splashing, it's amazing. Yes, it was because they showed 0:21:27.280 --> 0:21:29.200 the first one that he did. It looks kind of plain, 0:21:29.760 --> 0:21:32.439 and then once you fed it through this infinite feedback loop, 0:21:32.920 --> 0:21:38.960 it just like shattered and and and uh, fractured, not fractal, 0:21:39.680 --> 0:21:42.200 although I want to say fractal off and just look 0:21:42.280 --> 0:21:44.760 more detailed, more detailed, more detailed, until it looked like 0:21:45.000 --> 0:21:47.639 lava splashing, right, it's pretty amazing. Well, that's where the 0:21:47.640 --> 0:21:50.440 word fractal comes from. Is um Mandel brought coined in 0:21:51.720 --> 0:21:56.360 to say, to indicate how the things fracture off and 0:21:56.400 --> 0:22:00.640 they form irregular patterns. Um, you can create to fractal 0:22:00.720 --> 0:22:06.400 that that is regularly repeating, but it doesn't look as natural. 0:22:07.600 --> 0:22:11.280 And with like say, if you're creating lava, right, you've 0:22:11.320 --> 0:22:13.440 got to have that one rule that like every third 0:22:13.480 --> 0:22:17.720 generation kicks forty degrees or whatever. The rule is that 0:22:17.840 --> 0:22:20.639 just kind of throws a little bit of dissimilarity into it, 0:22:20.640 --> 0:22:23.600 because if something's too self similar, it's not going to 0:22:23.680 --> 0:22:25.840 look right. It's not gonna look natural, it's not gonna 0:22:25.840 --> 0:22:28.800 look real, which kind of leads you to think, chuck, 0:22:28.840 --> 0:22:32.679 then that there is a an application for studying natural 0:22:32.720 --> 0:22:37.520 phenomenon using fractals, right, while there are I guess all 0:22:37.600 --> 0:22:41.760 kinds um, well, this isn't so much natural. But the 0:22:42.080 --> 0:22:46.280 documentary interviewed Nathan Cohen who was a ham radio operator, 0:22:46.520 --> 0:22:49.440 and his landlord said, dude, you can't have that huge 0:22:49.480 --> 0:22:53.119 antenna hanging out of your apartment. So he started bending 0:22:53.160 --> 0:22:58.280 wires a straight wire into essentially a fractal and found 0:22:58.320 --> 0:23:00.880 that on the very first go it got better reception 0:23:01.800 --> 0:23:04.800 um merely by the fact that it was bent in 0:23:04.840 --> 0:23:08.760 that way and it was self similar. So he eventually 0:23:09.480 --> 0:23:12.639 used that two I hope make a lot of money. 0:23:13.160 --> 0:23:15.720 I got the imperson that he did, okay, um by 0:23:15.720 --> 0:23:18.880 applying that technology to cell phones um, and the way 0:23:18.920 --> 0:23:20.680 that they describe it as all the different things a 0:23:20.720 --> 0:23:22.919 cell phone can do, if you were to have a 0:23:22.960 --> 0:23:25.560 different antenna for each one of those functions, it would 0:23:25.600 --> 0:23:28.680 be like carrying around a little porcupine. So what cell 0:23:28.720 --> 0:23:33.080 phones now are based on is a fractal design called 0:23:33.680 --> 0:23:39.600 Manger sponge Minger sponge and uh, it's basically a box fractal. 0:23:39.840 --> 0:23:42.240 And if you crack up in your little cell phone, 0:23:42.280 --> 0:23:44.080