1 00:00:00,920 --> 00:00:04,040 Speaker 1: How do folks, Charles W. Chuck Bryant here in the corral, 2 00:00:04,480 --> 00:00:06,200 Speaker 1: and I'm gonna last so up a Stuff you Should 3 00:00:06,200 --> 00:00:09,240 Speaker 1: Know select for you from June seventh, two thousand twelve. 4 00:00:09,880 --> 00:00:13,600 Speaker 1: Fractals Colin Whoa, this is a tough one for me. 5 00:00:13,800 --> 00:00:16,360 Speaker 1: I'm not gonna lie. Fractals is one of the toughest 6 00:00:16,360 --> 00:00:19,239 Speaker 1: episodes I've ever had to learn and research. And that's 7 00:00:19,239 --> 00:00:25,439 Speaker 1: where we're gonna revisit it right here, right now. Welcome 8 00:00:25,480 --> 00:00:27,720 Speaker 1: to Stuff you Should Know, a production of My Heart 9 00:00:27,800 --> 00:00:36,320 Speaker 1: Radios How Stuff Works. Hey, and welcome to the podcast. 10 00:00:36,400 --> 00:00:40,120 Speaker 1: I'm Josh Clark, hanging on by my fingernails with me 11 00:00:40,200 --> 00:00:42,920 Speaker 1: as always as Charles W. Chuck Bryant, doing much the 12 00:00:42,960 --> 00:00:47,160 Speaker 1: same as we are about to start speaking on stuff 13 00:00:47,159 --> 00:00:52,479 Speaker 1: you should know about. Fractals. Yea, more math theoretical, Matt 14 00:00:52,840 --> 00:00:57,000 Speaker 1: even Yeah, a new branch of geometry. It's non Euclidean 15 00:00:58,400 --> 00:01:02,240 Speaker 1: since you brought it up, Okay, very new. Euclidean geometry 16 00:01:02,360 --> 00:01:09,160 Speaker 1: was like three B C and fractals are so there's 17 00:01:09,360 --> 00:01:11,160 Speaker 1: a little bit of a gap there. There is a 18 00:01:11,200 --> 00:01:13,880 Speaker 1: little bit of a gap and uh, there's a lot 19 00:01:13,920 --> 00:01:19,760 Speaker 1: of animosity among the Euclideans towards Fractillians. They need to 20 00:01:19,800 --> 00:01:22,120 Speaker 1: loosen up and look at some of those far out pictures. 21 00:01:22,800 --> 00:01:25,280 Speaker 1: I know, you know it's funny. Did you watch um, 22 00:01:25,400 --> 00:01:27,800 Speaker 1: did you watch that one doc on? Yeah? Okay, did 23 00:01:27,800 --> 00:01:31,200 Speaker 1: you see the other? The Arthur C. Clark one. It 24 00:01:31,280 --> 00:01:33,920 Speaker 1: was made in like maybe eight s eighty seven and 25 00:01:33,959 --> 00:01:38,240 Speaker 1: it had nothing but like um delicate sound of thunder 26 00:01:38,360 --> 00:01:40,720 Speaker 1: rip off music going on the whole time. It was 27 00:01:40,800 --> 00:01:43,880 Speaker 1: really really trippy. Well, I posted a picture I don't 28 00:01:43,880 --> 00:01:45,320 Speaker 1: know if you saw today on the stuff you should 29 00:01:45,319 --> 00:01:49,520 Speaker 1: know all of the of the Mandel brought set. Its 30 00:01:49,560 --> 00:01:52,320 Speaker 1: beautiful it is and it's very cool. And I didn't 31 00:01:52,320 --> 00:01:54,560 Speaker 1: even say what it was. I just posted it, and 32 00:01:54,600 --> 00:01:57,680 Speaker 1: like I'd say, about half the people were like, very cool, man, 33 00:01:57,720 --> 00:01:59,400 Speaker 1: this is rad I love the Mantal brought set like 34 00:01:59,640 --> 00:02:02,960 Speaker 1: fractill talk about fractals. And then the other half were like, 35 00:02:03,480 --> 00:02:05,480 Speaker 1: well you guys tripping out like what you did a 36 00:02:05,480 --> 00:02:09,200 Speaker 1: grateful dead day. That's actually math, believe it or not. 37 00:02:09,400 --> 00:02:11,600 Speaker 1: But it does look very it's very tied eye in 38 00:02:11,680 --> 00:02:14,240 Speaker 1: nature and that's why the hippies like it. Plus also, 39 00:02:14,240 --> 00:02:16,760 Speaker 1: I mean, if you've ever seen a fractal play out 40 00:02:16,800 --> 00:02:22,320 Speaker 1: on a computer screen. Yeah. Um, so we are talking 41 00:02:22,320 --> 00:02:24,680 Speaker 1: about fractals. I don't I don't necessarily want to give 42 00:02:24,680 --> 00:02:28,760 Speaker 1: a disclaimer. Chuck and I are not theoretical mathematicians. We're 43 00:02:28,760 --> 00:02:33,600 Speaker 1: not even like normal mathematicians. I balanced my checkbook my 44 00:02:33,760 --> 00:02:36,239 Speaker 1: hand just to keep that little part of my brain going. 45 00:02:36,400 --> 00:02:39,120 Speaker 1: So I don't like forget how to add and subtract 46 00:02:39,400 --> 00:02:42,240 Speaker 1: later on in life. I make myself do that, and 47 00:02:42,280 --> 00:02:46,760 Speaker 1: I don't let myself jump ahead. I show my work. Yeah. Um, 48 00:02:46,800 --> 00:02:50,000 Speaker 1: and that's about the extent of math in my life normally. See, 49 00:02:50,040 --> 00:02:52,200 Speaker 1: I was the kid in math that when they said 50 00:02:52,200 --> 00:02:54,520 Speaker 1: you're not allowed to use calculators, I would go, like, 51 00:02:55,200 --> 00:02:58,400 Speaker 1: there are calculators in life, so why can't we use them. Yeah, 52 00:02:58,520 --> 00:03:01,280 Speaker 1: Like they made calculators so we didn't have to do maths, right. 53 00:03:01,320 --> 00:03:03,160 Speaker 1: But at the same time, I find that shoddy because 54 00:03:03,160 --> 00:03:08,120 Speaker 1: it's like, you're not you're not You're just circumventing learning something, 55 00:03:08,240 --> 00:03:10,880 Speaker 1: and it's like the calculators there to support you after 56 00:03:10,960 --> 00:03:14,320 Speaker 1: you know what you're doing. I disagree. Well, I think 57 00:03:14,320 --> 00:03:18,480 Speaker 1: this is a pretty prime example of like going around 58 00:03:19,480 --> 00:03:23,920 Speaker 1: to get to the end. So when when I was 59 00:03:23,960 --> 00:03:26,240 Speaker 1: researching this, I was like, Okay, well, they don't really 60 00:03:26,280 --> 00:03:27,760 Speaker 1: know what they're doing with this stuff yet, so we 61 00:03:27,800 --> 00:03:30,240 Speaker 1: can just totally be like, well it's it's there, anything 62 00:03:30,280 --> 00:03:32,359 Speaker 1: you wanted to be and nothing at all. And then 63 00:03:32,440 --> 00:03:35,480 Speaker 1: like I started looking a little more deeply into I'm like, oh, no, 64 00:03:35,640 --> 00:03:38,400 Speaker 1: they do kind of know what they're doing. We really 65 00:03:38,400 --> 00:03:40,040 Speaker 1: don't know what we're talking about. So I feel like 66 00:03:40,080 --> 00:03:43,080 Speaker 1: I have, just from researching this, a little bit, um 67 00:03:43,280 --> 00:03:47,520 Speaker 1: something of a grasp of what fractals are, a little 68 00:03:47,560 --> 00:03:49,760 Speaker 1: bit For those of you who who don't know what 69 00:03:49,800 --> 00:03:52,320 Speaker 1: we're talking about, like, take a second to um look 70 00:03:52,360 --> 00:03:56,040 Speaker 1: up just typing fractal and search images on your favorite 71 00:03:56,040 --> 00:03:59,440 Speaker 1: search engine and you'll be like, oh, yes, of course 72 00:03:59,480 --> 00:04:01,920 Speaker 1: it's a fractal um And that's what we're going to 73 00:04:01,960 --> 00:04:07,440 Speaker 1: talk about, because fractal fractals are a new field, like 74 00:04:07,480 --> 00:04:10,040 Speaker 1: we said, in geometry, and they do have use and 75 00:04:10,080 --> 00:04:13,800 Speaker 1: they have usefulness that I think people haven't even considered yet. 76 00:04:14,360 --> 00:04:16,520 Speaker 1: But the the stuff that they have figured out how 77 00:04:16,560 --> 00:04:19,039 Speaker 1: to use it for is pretty amazing stuff. Can I 78 00:04:19,080 --> 00:04:21,200 Speaker 1: say what a fractal is at least so people know 79 00:04:21,640 --> 00:04:24,000 Speaker 1: they should clear it all up? It is a geometric 80 00:04:24,040 --> 00:04:26,719 Speaker 1: shape that is self similar through infinite iterations in a 81 00:04:26,760 --> 00:04:30,000 Speaker 1: recursive pattern and through infinite detail exactly. So there you 82 00:04:30,040 --> 00:04:32,200 Speaker 1: have it. Boom, Do we need to even continue? No? 83 00:04:32,360 --> 00:04:35,840 Speaker 1: But um, and that sounds like really that put me off, 84 00:04:36,360 --> 00:04:38,599 Speaker 1: Like this article was pretty well done by a guy 85 00:04:38,680 --> 00:04:41,039 Speaker 1: named Craig Haggett. I don't know who that it is, freelancer. 86 00:04:41,040 --> 00:04:44,520 Speaker 1: I guess um, it's a pretty well done article. But 87 00:04:44,560 --> 00:04:46,800 Speaker 1: that a sentence like that can put a person off 88 00:04:46,800 --> 00:04:49,240 Speaker 1: pretty easy. And he even put it, you know, he 89 00:04:49,360 --> 00:04:51,159 Speaker 1: made a joke about it, like, oh, you know that, 90 00:04:51,200 --> 00:04:54,040 Speaker 1: you get it, you know whatever. But um, when you 91 00:04:54,080 --> 00:04:56,640 Speaker 1: think about it, if you take that apart, one of 92 00:04:56,680 --> 00:05:01,760 Speaker 1: the hallmarks of fractal fractals, um is that they are 93 00:05:02,360 --> 00:05:06,880 Speaker 1: a very complex result from a very simple system. And 94 00:05:06,920 --> 00:05:09,920 Speaker 1: there's like basically three hallmarks two fractals that you just 95 00:05:09,960 --> 00:05:15,479 Speaker 1: pointed out right. There is um self similarity, which is 96 00:05:16,360 --> 00:05:20,160 Speaker 1: if you if you cut a chunk, like a microscopic 97 00:05:20,200 --> 00:05:23,840 Speaker 1: piece of a fractal off and compare it to the 98 00:05:23,839 --> 00:05:27,320 Speaker 1: whole fractal, it's going to be virtually the same. Yeah, 99 00:05:27,440 --> 00:05:30,159 Speaker 1: like or a fern. And the cool thing about fractals 100 00:05:30,200 --> 00:05:33,800 Speaker 1: is is to me the coolest thing is that fractals. 101 00:05:35,960 --> 00:05:38,000 Speaker 1: The point they made in the Nova documentary is that 102 00:05:38,400 --> 00:05:41,719 Speaker 1: all of our math up until they discovered fractals and 103 00:05:41,760 --> 00:05:46,679 Speaker 1: described practicals was based on things that we basically created 104 00:05:46,720 --> 00:05:52,839 Speaker 1: and built. Like all geometry, right, Euclidean geometry, you have length, width, 105 00:05:53,279 --> 00:05:56,719 Speaker 1: and height, which should view the three dimensions, right, yes, 106 00:05:56,800 --> 00:06:00,640 Speaker 1: for like pyramids and buildings and combs and all those things. 107 00:06:00,720 --> 00:06:02,960 Speaker 1: And you it's extremely useful and we've done quite a 108 00:06:02,960 --> 00:06:07,400 Speaker 1: bit with this. But what Euclidean geometry, as far as 109 00:06:07,440 --> 00:06:13,839 Speaker 1: the fractal geometrists or geometers um insist, failed at is 110 00:06:13,920 --> 00:06:17,279 Speaker 1: when they said, okay, look at that mountain. That's a cone. 111 00:06:17,320 --> 00:06:21,039 Speaker 1: It's an imperfect cone, it's a rough cone, but it's 112 00:06:21,040 --> 00:06:25,159 Speaker 1: a cone shape, right, So yeah, Euclidean geometry holds sway. 113 00:06:25,279 --> 00:06:29,880 Speaker 1: What the fractal geometers say is, yeah, you could say 114 00:06:29,880 --> 00:06:31,679 Speaker 1: that it's a cone, but if you tried to measure 115 00:06:31,720 --> 00:06:33,760 Speaker 1: and describe it as such, you're not going to come 116 00:06:33,839 --> 00:06:38,240 Speaker 1: up with a very descriptive, a very um detailed description 117 00:06:38,720 --> 00:06:43,120 Speaker 1: of that mountain. So what's the point What fractal geometry 118 00:06:43,160 --> 00:06:46,240 Speaker 1: does is it says we're going to describe that mountain 119 00:06:46,560 --> 00:06:50,760 Speaker 1: in every little craig and peak possible. And so what 120 00:06:50,839 --> 00:06:55,480 Speaker 1: you have is the fractal dimension, which exists in conjunction 121 00:06:55,520 --> 00:06:59,160 Speaker 1: with length, widthin height. And what the fractal dimension describes 122 00:06:59,279 --> 00:07:03,040 Speaker 1: is the complex city of the object that exists within 123 00:07:03,080 --> 00:07:07,159 Speaker 1: those three dimensions as well. That's right. So finishing my point, 124 00:07:07,560 --> 00:07:10,560 Speaker 1: the cool thing about fractals is that everything that we 125 00:07:10,600 --> 00:07:13,600 Speaker 1: had done previously in geometry were because of things we've built. 126 00:07:13,960 --> 00:07:16,760 Speaker 1: Practicals help describe things that were have been here since 127 00:07:16,800 --> 00:07:20,760 Speaker 1: the beginning of time in nature, and one of the 128 00:07:20,760 --> 00:07:24,600 Speaker 1: truest examples of that is the fern. Right with self similarity. 129 00:07:24,680 --> 00:07:27,640 Speaker 1: You take a little snippet off of a fern, although 130 00:07:27,640 --> 00:07:30,280 Speaker 1: you shouldn't do that. Let's just look at it. Uh, 131 00:07:30,320 --> 00:07:32,720 Speaker 1: it's gonna look the same as the larger part of 132 00:07:32,720 --> 00:07:35,440 Speaker 1: the fern, and then the whole fern itself very self 133 00:07:35,480 --> 00:07:39,720 Speaker 1: similar but not necessarily exact. No, it can be. There 134 00:07:39,800 --> 00:07:42,720 Speaker 1: is a form of self similarity that is exact and precise, 135 00:07:42,760 --> 00:07:47,280 Speaker 1: but in nature that's rare, if not just completely not found. Right, 136 00:07:47,320 --> 00:07:50,000 Speaker 1: that's right. So you've got self similarity, which is the 137 00:07:50,160 --> 00:07:53,040 Speaker 1: smaller part is virtually the same or looks the same, 138 00:07:53,160 --> 00:07:56,880 Speaker 1: or structured the same as the whole UM. And this 139 00:07:57,000 --> 00:08:02,280 Speaker 1: process of self similarity UM going larger smaller in scale 140 00:08:02,720 --> 00:08:07,720 Speaker 1: is called recursiveness, right, And recursiveness is UM. Like you 141 00:08:07,760 --> 00:08:10,320 Speaker 1: know those paintings where it's like a guy I think 142 00:08:10,360 --> 00:08:13,520 Speaker 1: Stephen Colbert, the one that he gave to the Smithsonian 143 00:08:13,680 --> 00:08:16,880 Speaker 1: has recursiveness in it, where it's a man in a 144 00:08:16,880 --> 00:08:20,280 Speaker 1: painting standing in front of like a mantle, and above 145 00:08:20,320 --> 00:08:23,200 Speaker 1: the mantle is the painting that you're looking at, and 146 00:08:23,240 --> 00:08:24,840 Speaker 1: then it goes on and on and on and on 147 00:08:24,920 --> 00:08:28,720 Speaker 1: and on anything that's infinitely repeating, right, same with if 148 00:08:28,760 --> 00:08:31,480 Speaker 1: you're in a dressing room and there's a mirror on 149 00:08:31,520 --> 00:08:34,640 Speaker 1: either side of the wall, you just keep going on infinitely. 150 00:08:34,640 --> 00:08:41,400 Speaker 1: It's recursiveness and with fractals the recursiveness of self similarity. Right. 151 00:08:41,800 --> 00:08:45,400 Speaker 1: So there's two two traits. UM is produced through this 152 00:08:45,440 --> 00:08:48,640 Speaker 1: thing called iteration, that's right. And that's where you say, 153 00:08:48,679 --> 00:08:52,720 Speaker 1: here's the whole I'm gonna put it into this formula, 154 00:08:53,280 --> 00:08:59,480 Speaker 1: and the formula has has the formula. The output of 155 00:08:59,520 --> 00:09:04,760 Speaker 1: the formula produces the input for the next round of 156 00:09:04,840 --> 00:09:08,400 Speaker 1: that same formula. It's a loop exactly, so it's self 157 00:09:08,400 --> 00:09:12,720 Speaker 1: sustaining and it can go on infinitely recursion. Right. That's right. 158 00:09:13,200 --> 00:09:15,520 Speaker 1: So what we've just come up with is a fractal 159 00:09:15,559 --> 00:09:19,240 Speaker 1: is anything that has a self similar structure and it's 160 00:09:19,559 --> 00:09:24,800 Speaker 1: recursive through iteration. That's right. Okay, So um A, really 161 00:09:25,320 --> 00:09:29,120 Speaker 1: I came upon this kind of easy, one easier explanation 162 00:09:29,200 --> 00:09:32,360 Speaker 1: of a fractal from Ben wal Mandel brought site. He died, 163 00:09:32,360 --> 00:09:35,400 Speaker 1: by the way in two. He seemed like a pretty 164 00:09:35,400 --> 00:09:40,400 Speaker 1: good guy. He was definitely thinking different. Um. And the 165 00:09:40,440 --> 00:09:43,880 Speaker 1: way that Mandel brought described a really easy way to 166 00:09:43,960 --> 00:09:46,080 Speaker 1: think of a fractal is um. There's this thing called 167 00:09:46,120 --> 00:09:50,800 Speaker 1: the Serpinsky gasket, and you take a triangle and you 168 00:09:50,840 --> 00:09:54,040 Speaker 1: can combine them into a bunch of little triangles and 169 00:09:54,120 --> 00:10:00,280 Speaker 1: spaces triangular spaces that form a larger triangle. Right, So 170 00:10:00,840 --> 00:10:04,839 Speaker 1: that that one initial solid triangle is called the initiator, 171 00:10:04,880 --> 00:10:08,160 Speaker 1: that's the original shape, and then all those other triangles 172 00:10:08,200 --> 00:10:12,160 Speaker 1: combine that form that larger triangle or a self similar 173 00:10:12,240 --> 00:10:15,360 Speaker 1: version of that larger triangle to the original triangle. That's 174 00:10:15,360 --> 00:10:21,160 Speaker 1: called generator. Right. So the formula for creating a fractal 175 00:10:21,480 --> 00:10:24,560 Speaker 1: would be to go into that generator, the version that 176 00:10:24,600 --> 00:10:27,280 Speaker 1: has all the little smaller triangles that make up a 177 00:10:27,360 --> 00:10:31,000 Speaker 1: larger whole triangle. And say, all the ones that look 178 00:10:31,080 --> 00:10:35,000 Speaker 1: like the initiator, the original just solid black triangle, take 179 00:10:35,040 --> 00:10:38,400 Speaker 1: that out and swap it with the generator version, and 180 00:10:38,440 --> 00:10:43,280 Speaker 1: all of a sudden you have one that's exponentially more detailed. 181 00:10:43,720 --> 00:10:46,640 Speaker 1: There's more to it, And that's a fractal. That's all 182 00:10:46,679 --> 00:10:48,960 Speaker 1: there is to it. You know what else is a fractal? 183 00:10:49,160 --> 00:10:53,120 Speaker 1: What the coastline? Yeah, that was a big one. Lewis 184 00:10:53,120 --> 00:10:57,800 Speaker 1: Fry Richardson was an English mathematician early twenty century, and 185 00:10:57,840 --> 00:11:01,000 Speaker 1: he very brilliantly said, you know what, if you take 186 00:11:01,080 --> 00:11:04,000 Speaker 1: a yardstick and you measured the coastline of England, you're 187 00:11:04,040 --> 00:11:07,160 Speaker 1: gonna get a number. If you take a one ft 188 00:11:07,240 --> 00:11:11,000 Speaker 1: ruler and measure the coastline, you're gonna get a different number. 189 00:11:11,240 --> 00:11:15,120 Speaker 1: If you take a one inch ruler and measure the coastline, 190 00:11:15,160 --> 00:11:18,600 Speaker 1: you're gonna get a different number. And it's basically infinite 191 00:11:18,679 --> 00:11:22,920 Speaker 1: in that the smaller you go with your your unit 192 00:11:23,000 --> 00:11:26,520 Speaker 1: of measure or your tool is the larger number you're 193 00:11:26,520 --> 00:11:31,520 Speaker 1: gonna get. Because the coastline is so infinitely varied in 194 00:11:31,559 --> 00:11:34,160 Speaker 1: its little nooks and crannies, right exactly It's a very 195 00:11:34,160 --> 00:11:36,320 Speaker 1: cool way of thinking about it. There's a second part 196 00:11:36,360 --> 00:11:39,520 Speaker 1: of that to Chuck, is that so depending on the you, 197 00:11:40,320 --> 00:11:42,840 Speaker 1: what you're using, the measure, the tool you're using, the measure, 198 00:11:43,360 --> 00:11:46,680 Speaker 1: the number, the perimeter of that coastline could go on infinitely, 199 00:11:47,120 --> 00:11:49,720 Speaker 1: but it still contains the same finite amount of space 200 00:11:49,760 --> 00:11:52,920 Speaker 1: within its paradox. That is a big time paradox because 201 00:11:52,960 --> 00:11:55,600 Speaker 1: things aren't supposed to be infinite and finite at the 202 00:11:55,600 --> 00:11:59,520 Speaker 1: same time, right right, Um and uh Lewis Fry Richardson 203 00:12:00,280 --> 00:12:04,360 Speaker 1: he basically established in that coming up with that paradox, 204 00:12:05,400 --> 00:12:08,960 Speaker 1: this kind of revolution and thought that fractal geometry is 205 00:12:09,000 --> 00:12:12,440 Speaker 1: based on that. You can have the infinite mixed with 206 00:12:12,480 --> 00:12:16,880 Speaker 1: the finite. You can get it from pretty simple formulas 207 00:12:16,920 --> 00:12:23,160 Speaker 1: that create very increasingly complex systems, right Um. And Fry 208 00:12:23,280 --> 00:12:25,839 Speaker 1: wasn't the He wasn't He was the first guy to 209 00:12:25,920 --> 00:12:28,080 Speaker 1: really kind of put forth this idea of thought, but 210 00:12:28,080 --> 00:12:30,600 Speaker 1: he wasn't the first one to notice this paradox. Yeah, 211 00:12:30,679 --> 00:12:33,840 Speaker 1: and before people even knew they were fractals, there were 212 00:12:33,880 --> 00:12:37,240 Speaker 1: there were artists like da Vinci that saw this pattern 213 00:12:37,280 --> 00:12:39,760 Speaker 1: and tree branches that was um I know in the 214 00:12:39,800 --> 00:12:43,679 Speaker 1: Nova documentary and the article, they point out the uh 215 00:12:43,920 --> 00:12:51,960 Speaker 1: Katsu Chica Hokusai Japanese artists created the Great Wave off Kanagawa, 216 00:12:52,559 --> 00:12:55,720 Speaker 1: and uh those are fractals. It's a it's ocean waves 217 00:12:55,720 --> 00:12:58,000 Speaker 1: breaking and at the top of the crest of the 218 00:12:58,000 --> 00:13:01,040 Speaker 1: waves are a little self similar or waves breaking off 219 00:13:01,080 --> 00:13:03,960 Speaker 1: into smaller and smaller self similar versions. And that's a 220 00:13:04,120 --> 00:13:06,920 Speaker 1: natural fractal, or in this case, it's a depiction of one. 221 00:13:07,040 --> 00:13:09,400 Speaker 1: So they were you know, early African and Nabajo artists 222 00:13:09,440 --> 00:13:12,520 Speaker 1: were doing this and they didn't realize that they were 223 00:13:12,640 --> 00:13:15,000 Speaker 1: fractals and that there were fractals all around us. No, 224 00:13:15,120 --> 00:13:19,000 Speaker 1: they just saw crystals in a snowflake or another good one, yeah, exactly. Um, 225 00:13:19,040 --> 00:13:21,360 Speaker 1: they were just they saw that there was what they 226 00:13:21,400 --> 00:13:24,560 Speaker 1: were looking at was a repeating pattern that was self 227 00:13:24,600 --> 00:13:29,680 Speaker 1: similar and recursive. Right, yeah, that's it. That's a fractal, right. Yeah. 228 00:13:29,720 --> 00:13:33,079 Speaker 1: And and Ben Wha Mandel brought was the first one 229 00:13:33,120 --> 00:13:35,839 Speaker 1: to say, you know what, we can we can use 230 00:13:35,960 --> 00:13:38,920 Speaker 1: math equations to actually apply to this. And he was 231 00:13:38,920 --> 00:13:41,600 Speaker 1: a big star for a while, and then they sort 232 00:13:41,600 --> 00:13:44,199 Speaker 1: of turned on him and said, you know what, this 233 00:13:44,280 --> 00:13:48,280 Speaker 1: is all cool and trippy looking, but it's useless. Right, 234 00:13:48,360 --> 00:13:52,000 Speaker 1: and he said, oh yeah, screw you guys, watch this 235 00:13:52,120 --> 00:13:56,560 Speaker 1: and he wrote another book which started to uh give 236 00:13:56,600 --> 00:14:02,240 Speaker 1: some practical applications which are pretty exciting. UM. So the 237 00:14:02,280 --> 00:14:05,360 Speaker 1: whole thing, the whole principle that is based on UM 238 00:14:05,520 --> 00:14:08,560 Speaker 1: is that you can take a formula and plug in 239 00:14:09,160 --> 00:14:13,760 Speaker 1: a very simple UM, well, a relatively simple formula like 240 00:14:13,800 --> 00:14:17,040 Speaker 1: mantle Brod's formula. Will take that one. For example, his 241 00:14:17,080 --> 00:14:23,520 Speaker 1: is um ZED goes to ZED squared plus c. Right, 242 00:14:24,440 --> 00:14:27,840 Speaker 1: that's what it's called. If you're in England, zed, we 243 00:14:27,920 --> 00:14:34,680 Speaker 1: say z Z. Well, anyway, Zed goes to which is 244 00:14:34,760 --> 00:14:37,560 Speaker 1: and the goes to is the key right here. This 245 00:14:37,640 --> 00:14:41,040 Speaker 1: is what makes it fractal goes to means that um, 246 00:14:41,040 --> 00:14:43,440 Speaker 1: it's an error. It's an equal sign. It looks like 247 00:14:43,440 --> 00:14:46,280 Speaker 1: an equal sign with a part of an arrow pointing 248 00:14:46,800 --> 00:14:50,360 Speaker 1: towards ZED, the other point pointing towards the rest of 249 00:14:50,400 --> 00:14:54,520 Speaker 1: the formula, which means that the the there's that feedback 250 00:14:54,520 --> 00:14:56,640 Speaker 1: loop where it's like, okay, once you have the number 251 00:14:56,960 --> 00:15:00,000 Speaker 1: that this punches out, you have, you feed it back 252 00:15:00,040 --> 00:15:01,920 Speaker 1: can and you'll get another number and knows, just keep 253 00:15:01,920 --> 00:15:04,600 Speaker 1: going and going and going, and every time, remember you're 254 00:15:04,640 --> 00:15:12,000 Speaker 1: swapping out the original the initiator for the the detailed 255 00:15:13,040 --> 00:15:18,480 Speaker 1: version the generator, and it's just getting exponentially more complex 256 00:15:18,600 --> 00:15:22,640 Speaker 1: with just that one iteration of that very simple formula. 257 00:15:23,920 --> 00:15:27,440 Speaker 1: UM and Mandel brought set Uh. This is the one 258 00:15:27,480 --> 00:15:30,320 Speaker 1: that's like it's probably the most famous one. That's the 259 00:15:30,320 --> 00:15:33,080 Speaker 1: one that the Deadheads like because it's like this crazy 260 00:15:33,320 --> 00:15:37,200 Speaker 1: juxtaposition between like black and like different colors and everything. 261 00:15:38,280 --> 00:15:42,640 Speaker 1: And with his formula, two things happen with the number 262 00:15:42,880 --> 00:15:46,480 Speaker 1: that you put in. It either goes towards zero or 263 00:15:46,520 --> 00:15:49,440 Speaker 1: it shoots off to the infinite. And what they did 264 00:15:49,760 --> 00:15:53,240 Speaker 1: for this for the the Mandel brought set fractals was 265 00:15:53,440 --> 00:15:57,480 Speaker 1: they assigned a color to a number based on how 266 00:15:57,560 --> 00:16:01,680 Speaker 1: quickly it goes off to towards infinity. Right, so let's 267 00:16:01,680 --> 00:16:04,120 Speaker 1: say that you have like four, If you plug four 268 00:16:04,160 --> 00:16:07,920 Speaker 1: into this and in ten generations, it'll it'll become an 269 00:16:07,920 --> 00:16:12,200 Speaker 1: infinite number. UM. Then say that that would be grouped 270 00:16:12,200 --> 00:16:15,960 Speaker 1: into a blue color like ten generations blue, eight generations 271 00:16:16,040 --> 00:16:20,920 Speaker 1: is red, ninety generations is orange. See what I'm saying. UM. 272 00:16:21,000 --> 00:16:23,760 Speaker 1: And then the other direction, like say if you put 273 00:16:23,800 --> 00:16:25,920 Speaker 1: in four point two or something like that, it'll go 274 00:16:26,040 --> 00:16:29,160 Speaker 1: towards zero and any number that eventually will go towards 275 00:16:29,240 --> 00:16:33,040 Speaker 1: zero is represented as black. So what you have then, 276 00:16:33,320 --> 00:16:36,920 Speaker 1: is this really intricate depending on where you're zooming in 277 00:16:37,040 --> 00:16:41,240 Speaker 1: or out on the fractal, this intricate change of colors, 278 00:16:41,240 --> 00:16:43,960 Speaker 1: and what you're really just seeing our numbers that are 279 00:16:44,080 --> 00:16:47,360 Speaker 1: plots on a plane, and that's your fractal, and then 280 00:16:47,360 --> 00:16:51,120 Speaker 1: the black parts are numbers that will eventually be be zero. Right, 281 00:16:51,160 --> 00:16:55,200 Speaker 1: And most of the mental mental brought set is black. Yeah, 282 00:16:55,520 --> 00:16:58,640 Speaker 1: but if you zoom in, like that's the whole point. 283 00:16:58,720 --> 00:17:01,560 Speaker 1: You zoom in on one of those little uh what 284 00:17:01,640 --> 00:17:05,320 Speaker 1: do we even call those little spikes? Uh? I guess 285 00:17:05,359 --> 00:17:07,640 Speaker 1: you could call it a plot. A plot, and it's 286 00:17:07,680 --> 00:17:10,720 Speaker 1: gonna look like what you just saw. And the Nova 287 00:17:10,800 --> 00:17:13,240 Speaker 1: documentary is very cool when they zoom in on these, 288 00:17:13,440 --> 00:17:16,159 Speaker 1: it's sort of mind blowing. Yeah, it is very I 289 00:17:16,280 --> 00:17:19,200 Speaker 1: strongly recommend watching that because they explain it way better 290 00:17:19,240 --> 00:17:21,240 Speaker 1: than us. Well, it helps to see it for sure, 291 00:17:21,320 --> 00:17:24,160 Speaker 1: Oh yeah, big time. So um or draw it as 292 00:17:24,240 --> 00:17:27,960 Speaker 1: I have done. It's a pretty nice little fract Yeah. 293 00:17:53,000 --> 00:17:55,520 Speaker 1: So we've talked about fractals, We talked about the Mandel 294 00:17:55,560 --> 00:17:58,359 Speaker 1: brought set, we talked about where they started to come 295 00:17:58,400 --> 00:18:05,600 Speaker 1: from um and the the idea. Remember Lewis fried Richardson, 296 00:18:05,640 --> 00:18:09,439 Speaker 1: he was talking about measuring the coastline and going off 297 00:18:09,480 --> 00:18:12,560 Speaker 1: into the infinite, but still containing a finite amount um. 298 00:18:12,720 --> 00:18:15,800 Speaker 1: A guy came after him named Helga von Coke. He 299 00:18:15,880 --> 00:18:18,000 Speaker 1: came up with a Coke snowflake, which is pretty cool. 300 00:18:18,000 --> 00:18:20,879 Speaker 1: If you take a straight line, or you take a triangle, 301 00:18:21,520 --> 00:18:23,720 Speaker 1: and then on each side of the triangle in the 302 00:18:23,760 --> 00:18:28,119 Speaker 1: middle you bust out the middle into another triangular hump. 303 00:18:28,680 --> 00:18:30,399 Speaker 1: You do that over and over and over again. It 304 00:18:30,440 --> 00:18:33,120 Speaker 1: goes off into infinity. Although it contains a finite amount 305 00:18:33,160 --> 00:18:36,359 Speaker 1: of space. The perimeter goes off to the infinite. A 306 00:18:36,400 --> 00:18:40,200 Speaker 1: guy named Georg Cantor came up with the cancer set, 307 00:18:40,480 --> 00:18:42,439 Speaker 1: which is you just take a straight line and you 308 00:18:42,520 --> 00:18:44,520 Speaker 1: take the middle out of it, and then for each 309 00:18:44,520 --> 00:18:46,320 Speaker 1: of those two lines that produces, you do the same 310 00:18:46,320 --> 00:18:48,320 Speaker 1: thing and it just keeps going on and on and 311 00:18:48,440 --> 00:18:51,080 Speaker 1: rather than going to nothingness like you're like, well, if 312 00:18:51,080 --> 00:18:53,760 Speaker 1: you take a six inch line, eventually you're gonna bust 313 00:18:53,760 --> 00:18:56,560 Speaker 1: it down and nothingness again. That doesn't happen. They found 314 00:18:56,560 --> 00:18:59,000 Speaker 1: that it goes off to the infinite. So they realized 315 00:18:59,520 --> 00:19:03,000 Speaker 1: Ben Wall mantel Brought was plugging all these into computers, 316 00:19:03,040 --> 00:19:06,439 Speaker 1: because that's what it took people realize this, Like George 317 00:19:06,480 --> 00:19:09,080 Speaker 1: Cantor um Man I hope that's how you say his 318 00:19:09,240 --> 00:19:12,560 Speaker 1: first name. He was he was working in the eighteen eighties, 319 00:19:13,160 --> 00:19:16,239 Speaker 1: Um Gaston Julio came up with the Julia sets for 320 00:19:16,560 --> 00:19:19,480 Speaker 1: producing a repeating pattern using feedback loop. All these guys 321 00:19:19,480 --> 00:19:23,560 Speaker 1: were like nineteenth century early twentieth century mathematicians and it 322 00:19:23,600 --> 00:19:27,760 Speaker 1: was strictly theoretical until the late seventies when guys like 323 00:19:27,800 --> 00:19:31,360 Speaker 1: Mantel Brought who worked at IBM, started feeding these things 324 00:19:31,440 --> 00:19:35,399 Speaker 1: into these new fangled computers and seeing the results like 325 00:19:35,440 --> 00:19:38,680 Speaker 1: this fractals like the mantel Brought set that he saw right, 326 00:19:39,800 --> 00:19:45,240 Speaker 1: So Um, almost immediately there was a practical use for 327 00:19:45,800 --> 00:19:51,280 Speaker 1: fractals that came in the form of c g I. Yeah. 328 00:19:51,359 --> 00:19:54,360 Speaker 1: They interviewed that one guy in the documentary um who 329 00:19:54,720 --> 00:19:58,520 Speaker 1: worked on the first c g I shot in motion 330 00:19:58,560 --> 00:20:01,520 Speaker 1: picture history, which was Star Trek to the Wrath of 331 00:20:01,600 --> 00:20:05,399 Speaker 1: con and Uh. He was tasked with making a c 332 00:20:05,560 --> 00:20:10,439 Speaker 1: g I uh land surface like mountain range and pretty 333 00:20:10,440 --> 00:20:12,280 Speaker 1: mind blowing with it. Yeah, and he did. I mean, 334 00:20:12,800 --> 00:20:14,399 Speaker 1: now you look back and it kind of looks silly, 335 00:20:14,440 --> 00:20:18,640 Speaker 1: but at the time it was completely revolutionary. And once 336 00:20:18,680 --> 00:20:21,080 Speaker 1: he learned about fractals in the geometry and the math 337 00:20:21,119 --> 00:20:23,560 Speaker 1: of fractals, it was pretty easy for him, and he 338 00:20:23,600 --> 00:20:25,239 Speaker 1: made it seem like he was like, oh, well, this 339 00:20:25,320 --> 00:20:26,960 Speaker 1: is the key, this is how you do it right. 340 00:20:27,119 --> 00:20:29,879 Speaker 1: So well, and it is kind of easy, especially if 341 00:20:29,880 --> 00:20:32,280 Speaker 1: you know what you're doing with computer programming and math, 342 00:20:32,800 --> 00:20:36,159 Speaker 1: because what you're basically doing to create a fractal generator 343 00:20:36,680 --> 00:20:40,439 Speaker 1: is teaching your computer to to do something within a 344 00:20:40,520 --> 00:20:44,200 Speaker 1: certain formula. That's your fractal formula, right, And so what 345 00:20:44,280 --> 00:20:47,399 Speaker 1: Lauren Carpenter, the guy who created the the Star Trek 346 00:20:47,440 --> 00:20:50,480 Speaker 1: to landscape for the first c G all c g 347 00:20:50,680 --> 00:20:53,720 Speaker 1: I shot ever, what he basically did was created a 348 00:20:53,720 --> 00:20:56,480 Speaker 1: computer program that said, hey, computer, I'm gonna give you 349 00:20:56,560 --> 00:20:58,600 Speaker 1: a bunch of triangles. Because I think that was the 350 00:20:58,680 --> 00:21:01,960 Speaker 1: earliest stuff he was working with. Um, I'm gonna give 351 00:21:01,960 --> 00:21:04,399 Speaker 1: you a bunch of triangles, and I want you to 352 00:21:04,440 --> 00:21:08,760 Speaker 1: take those triangles and generate a new fractal set from it, right, 353 00:21:09,480 --> 00:21:10,879 Speaker 1: And then I want you to do it again and 354 00:21:10,880 --> 00:21:13,760 Speaker 1: again and again, and then every third time I want 355 00:21:13,760 --> 00:21:18,399 Speaker 1: you to start turning them forty degrees, so it's going 356 00:21:18,440 --> 00:21:21,520 Speaker 1: to change the pattern slightly, and then all of a 357 00:21:21,560 --> 00:21:24,640 Speaker 1: sudden you have these infinite variations. The reason why when 358 00:21:24,640 --> 00:21:26,359 Speaker 1: you go back and look at that shot that it 359 00:21:26,480 --> 00:21:30,600 Speaker 1: still looks kind of you know today, is because the 360 00:21:30,600 --> 00:21:33,119 Speaker 1: computer he was working at didn't have the computing power 361 00:21:33,160 --> 00:21:37,080 Speaker 1: to do that many times. Now we have higher computer 362 00:21:37,280 --> 00:21:40,119 Speaker 1: computing power, and so what we're doing is telling our 363 00:21:40,160 --> 00:21:43,040 Speaker 1: computers to keep going and going and going, swapping out 364 00:21:43,119 --> 00:21:47,160 Speaker 1: that initiator, that one single black triangle everywhere it can 365 00:21:47,200 --> 00:21:50,040 Speaker 1: find it in this pattern, this pattern of triangles in 366 00:21:50,080 --> 00:21:53,159 Speaker 1: the fractal with a brand new fractal. So it's just 367 00:21:53,240 --> 00:21:55,640 Speaker 1: creating more and more and more and more fractals, which 368 00:21:55,640 --> 00:21:58,600 Speaker 1: creates a finer and finer and finer resolution, which makes 369 00:21:58,600 --> 00:22:01,560 Speaker 1: something look all the more real. Yeah, like the part 370 00:22:01,600 --> 00:22:04,560 Speaker 1: in the doc about the Star Wars, I was making 371 00:22:04,560 --> 00:22:08,040 Speaker 1: the lava splashing. It's amazing, Yes, it was because they 372 00:22:08,080 --> 00:22:10,280 Speaker 1: showed the first one they did it looks kind of plain, 373 00:22:10,840 --> 00:22:13,520 Speaker 1: and then once you fed it through this infinite feedback loop, 374 00:22:14,000 --> 00:22:20,160 Speaker 1: it just like shattered and and and uh, fractured, not fractaled, 375 00:22:20,760 --> 00:22:23,280 Speaker 1: although I want to say fractaled off and just look 376 00:22:23,359 --> 00:22:25,840 Speaker 1: more detailed, more detailed, more detailed, until it looked like 377 00:22:26,080 --> 00:22:28,720 Speaker 1: lava splashing. Right, it's pretty amazing. Well, that's where the 378 00:22:28,720 --> 00:22:31,520 Speaker 1: word fractal comes from. Is um Mandel brought coined in 379 00:22:32,840 --> 00:22:37,440 Speaker 1: to say, to indicate how the things fracture off and 380 00:22:37,520 --> 00:22:41,720 Speaker 1: they form irregular patterns. Um, you can create a fractal 381 00:22:41,800 --> 00:22:47,480 Speaker 1: that that is regularly repeating, but it doesn't look as natural. 382 00:22:48,680 --> 00:22:52,600 Speaker 1: And with like say, if you're creating lava, you've got 383 00:22:52,600 --> 00:22:55,080 Speaker 1: to have that one rule that like every third generation 384 00:22:55,640 --> 00:22:59,000 Speaker 1: kicks forty degrees or whatever the rule is. That just 385 00:22:59,080 --> 00:23:01,680 Speaker 1: kind of throws a little bit of dissimilarity and too 386 00:23:01,720 --> 00:23:04,560 Speaker 1: because if something is too self similar, it's not going 387 00:23:04,600 --> 00:23:06,679 Speaker 1: to look right. It's not gonna look natural, it's not 388 00:23:06,680 --> 00:23:09,880 Speaker 1: gonna look real, which kind of leads you to think, chuck. 389 00:23:09,920 --> 00:23:13,760 Speaker 1: Then that there is a an application for studying natural 390 00:23:13,800 --> 00:23:19,440 Speaker 1: phenomenon using fractals, right, while there are I guess all kinds, Um, 391 00:23:20,119 --> 00:23:24,240 Speaker 1: well this isn't so much natural. But the documentary interviewed 392 00:23:24,280 --> 00:23:28,479 Speaker 1: Nathan Cohen who was a ham radio operator and his 393 00:23:28,600 --> 00:23:31,560 Speaker 1: landlord said, dude, you can't have that huge antenna hanging 394 00:23:31,560 --> 00:23:34,919 Speaker 1: out of your apartment so he started bending wires a 395 00:23:35,000 --> 00:23:39,679 Speaker 1: straight wire into essentially a fractal and found that on 396 00:23:39,720 --> 00:23:43,879 Speaker 1: the very first go it got better reception, um, merely 397 00:23:43,960 --> 00:23:46,320 Speaker 1: by the fact that it was bent in that way 398 00:23:46,720 --> 00:23:50,959 Speaker 1: and it was self similar. So he eventually used that 399 00:23:51,720 --> 00:23:54,560 Speaker 1: two I hope make a lot of money. I got 400 00:23:54,600 --> 00:23:57,320 Speaker 1: the impressing that he did, okay, um by applying that 401 00:23:57,359 --> 00:24:00,719 Speaker 1: technology to cell phones. Um, and the way they describe 402 00:24:00,760 --> 00:24:02,520 Speaker 1: it as all the different things a cellphone can do, 403 00:24:03,119 --> 00:24:05,160 Speaker 1: if you were to have a different antenna for each 404 00:24:05,160 --> 00:24:07,400 Speaker 1: one of those functions, it would be like carrying around 405 00:24:07,400 --> 00:24:10,919 Speaker 1: a little porcupine. So what cell phones now are based 406 00:24:10,960 --> 00:24:17,280 Speaker 1: on is a fractal design called Manger sponge. Minger sponge, Yeah, 407 00:24:17,280 --> 00:24:20,680 Speaker 1: I think, man, and uh it's basically a box fractal. 408 00:24:20,920 --> 00:24:23,360 Speaker 1: And if you crack up in your little cell phone, 409 00:24:23,359 --> 00:24:25,160 Speaker 1: you're gonna see it wired that way. Yeah, You're going 410 00:24:25,200 --> 00:24:27,960 Speaker 1: to be looking at a fractal. It's a square, right, 411 00:24:28,040 --> 00:24:30,560 Speaker 1: and then within it are a bunch of little squares 412 00:24:31,160 --> 00:24:35,640 Speaker 1: in a recursive, self similar pattern. And you, friend, are 413 00:24:35,680 --> 00:24:39,720 Speaker 1: looking at a fractal. It's all around us. Yeah, Um, 414 00:24:39,760 --> 00:24:42,760 Speaker 1: it's also all around us in nature. There's uh in 415 00:24:42,800 --> 00:24:47,159 Speaker 1: that same uh documentary that NOVA program. There was a 416 00:24:47,200 --> 00:24:50,080 Speaker 1: team from I think University of Arizona. There's a team 417 00:24:50,119 --> 00:24:53,240 Speaker 1: of academics. Yeah, that was pretty cool. Who um, we're 418 00:24:53,280 --> 00:24:56,320 Speaker 1: trying to figure out if you predict the amount of 419 00:24:56,400 --> 00:25:01,119 Speaker 1: carbon capturing capacity an entire rainforest has just by measuring 420 00:25:01,680 --> 00:25:05,560 Speaker 1: UM and figuring out the self similar system that a 421 00:25:05,600 --> 00:25:11,080 Speaker 1: single tree in that rainforest UM has. That makes sense? Well, 422 00:25:11,600 --> 00:25:13,800 Speaker 1: it does, but it's kind of a leap. It's like, okay, 423 00:25:13,840 --> 00:25:17,680 Speaker 1: so as one tree does it follow the same system 424 00:25:17,680 --> 00:25:21,440 Speaker 1: that the whole rainforest does? And they apparently found that yes, 425 00:25:21,520 --> 00:25:25,520 Speaker 1: in fact it does, right, The same branching UH system 426 00:25:25,600 --> 00:25:30,080 Speaker 1: found in that tree is similar to the the growth 427 00:25:30,280 --> 00:26:01,680 Speaker 1: of the trees in the rainforest as a whole. Pretty cool. Yes, UM. 428 00:26:01,880 --> 00:26:05,240 Speaker 1: Tumors in the human body. UH. One of the keys 429 00:26:05,320 --> 00:26:08,600 Speaker 1: to getting rid of of cancer is or any kind 430 00:26:08,600 --> 00:26:11,399 Speaker 1: of tumors. Spotting these tumors early on. But with our 431 00:26:11,480 --> 00:26:13,919 Speaker 1: ultrasound technology you can only get so small and so 432 00:26:14,040 --> 00:26:18,880 Speaker 1: detailed that you can't see some of these natural fractals 433 00:26:18,880 --> 00:26:21,919 Speaker 1: that you know, your blood vessels are fractals essentially, just 434 00:26:21,960 --> 00:26:24,840 Speaker 1: like the branches of a tree are UM. So they 435 00:26:25,000 --> 00:26:30,520 Speaker 1: are now using geometry too. Now if I'm not sure 436 00:26:30,520 --> 00:26:32,520 Speaker 1: if I got this right, but I think it shows up. 437 00:26:33,040 --> 00:26:36,560 Speaker 1: It shows the flow of the blood because ultrasound can 438 00:26:36,560 --> 00:26:38,480 Speaker 1: pick that up through these fractals when they can't even 439 00:26:38,520 --> 00:26:43,560 Speaker 1: pick up the vessels themselves. Is that right, early earlier 440 00:26:43,640 --> 00:26:46,400 Speaker 1: tumor spotting, which right, well, for all intents of purposes, 441 00:26:46,400 --> 00:26:48,920 Speaker 1: they're looking at the vessels by finding the blood because 442 00:26:48,920 --> 00:26:51,399 Speaker 1: they see where it's flowing. But yeah, depending on the 443 00:26:51,840 --> 00:26:55,119 Speaker 1: pattern that it follows. If it follows like a like 444 00:26:55,160 --> 00:26:58,760 Speaker 1: a tree branching shape, it's healthy, right, yeah. And then 445 00:26:58,760 --> 00:27:01,400 Speaker 1: the tumors, all the veins are all bent and crooking, 446 00:27:01,440 --> 00:27:04,920 Speaker 1: going in all crazy directions. The read out of a heartbeat, yeah, 447 00:27:04,960 --> 00:27:07,480 Speaker 1: it's not consistent. It's a fractical yeah. So they use 448 00:27:07,560 --> 00:27:11,720 Speaker 1: fractal analysis now to study your heart rate and use 449 00:27:11,920 --> 00:27:17,800 Speaker 1: that to better understand how arrhythmia happens through math. So 450 00:27:18,040 --> 00:27:22,520 Speaker 1: there's the especially with natural systems. That's kind of like 451 00:27:22,560 --> 00:27:27,280 Speaker 1: the biggest contribution that UM Fractal geometry is produced so far, 452 00:27:27,480 --> 00:27:30,959 Speaker 1: I think, aside from c G I is what medical 453 00:27:31,119 --> 00:27:35,480 Speaker 1: uh well, just the that whole understanding that was first 454 00:27:35,560 --> 00:27:38,760 Speaker 1: really kind of um voiced by Lewis Fry Richardson with 455 00:27:38,800 --> 00:27:43,920 Speaker 1: the coastline that there's, um, there are natural systems out 456 00:27:43,960 --> 00:27:46,760 Speaker 1: there that we can't really that we're not quite paying 457 00:27:46,760 --> 00:27:50,040 Speaker 1: attention to, we don't really know how to deal with that. 458 00:27:50,080 --> 00:27:53,520 Speaker 1: We're trying to apply something like Euclidean geometry to something 459 00:27:53,560 --> 00:27:57,640 Speaker 1: that you can't really use that for um. That that's 460 00:27:57,640 --> 00:28:01,200 Speaker 1: what fractal geometry is really contributed so far as basically say, hey, 461 00:28:01,320 --> 00:28:03,880 Speaker 1: there's a lot of natural systems out here that are 462 00:28:03,920 --> 00:28:07,880 Speaker 1: self similar and recursive, and now that we kind of 463 00:28:07,960 --> 00:28:11,399 Speaker 1: see in the fractal world, we see them everywhere and 464 00:28:11,440 --> 00:28:13,760 Speaker 1: we have a better understanding of them. And one of 465 00:28:13,800 --> 00:28:17,240 Speaker 1: the best examples of that, I thought was figuring out 466 00:28:17,600 --> 00:28:22,359 Speaker 1: how larger animals use less energy than smaller animals. They 467 00:28:22,440 --> 00:28:25,840 Speaker 1: use energy more efficiently, and um, this is a kind 468 00:28:25,840 --> 00:28:28,719 Speaker 1: of a biological paradox for a really long time, and 469 00:28:28,760 --> 00:28:31,479 Speaker 1: these guys figured it out using I guess kind of 470 00:28:31,480 --> 00:28:35,840 Speaker 1: the um same kind of insight that fractal geometry has. 471 00:28:35,880 --> 00:28:40,600 Speaker 1: That if you take genes and genes are the mathematical 472 00:28:40,680 --> 00:28:45,680 Speaker 1: formula or the equivalent of a mathematical formula, and you 473 00:28:46,280 --> 00:28:50,640 Speaker 1: uh feed in uh, these genetic processes, what it's going 474 00:28:50,680 --> 00:28:56,680 Speaker 1: to put out. Is this self similar recursive pattern to 475 00:28:56,800 --> 00:29:00,920 Speaker 1: where the bigger the organism is, the more this thing 476 00:29:01,000 --> 00:29:03,360 Speaker 1: goes and goes and goes, the less energy it's going 477 00:29:03,400 --> 00:29:06,040 Speaker 1: to use because there's more of it and it doesn't 478 00:29:06,080 --> 00:29:08,960 Speaker 1: require very much energy to produce past a certain point. 479 00:29:09,360 --> 00:29:11,480 Speaker 1: So if you have a very small animal, it's using 480 00:29:11,480 --> 00:29:13,480 Speaker 1: a lot of energy to do these things to carry 481 00:29:13,520 --> 00:29:16,440 Speaker 1: this out. But there's that economy of scale because you're 482 00:29:16,480 --> 00:29:22,160 Speaker 1: still using a relatively simple formula your genetic code, right UM, 483 00:29:22,280 --> 00:29:27,320 Speaker 1: to carry out a very complex, seemingly complex UM system, 484 00:29:27,400 --> 00:29:31,000 Speaker 1: which is your organs or you as an organism. So 485 00:29:31,080 --> 00:29:34,080 Speaker 1: in the end, an elephant uses less energy than a mouse, yes, 486 00:29:34,120 --> 00:29:37,960 Speaker 1: because they're both using the same formula, the same input. 487 00:29:38,480 --> 00:29:40,800 Speaker 1: And then eventually you reach a point where it just 488 00:29:41,040 --> 00:29:44,800 Speaker 1: gets easier and easier and easier to to use something 489 00:29:44,840 --> 00:29:47,520 Speaker 1: simple to create a complex system. I love it. I 490 00:29:47,560 --> 00:29:50,440 Speaker 1: do too. Uh. I got one more thing. You heard 491 00:29:50,480 --> 00:29:54,000 Speaker 1: this guy, Jason Paget, Huh, this is pretty crazy. UM. 492 00:29:54,040 --> 00:29:58,680 Speaker 1: This guy like nine years ago, I think UM was 493 00:29:58,800 --> 00:30:02,160 Speaker 1: mugged and to come Washington got hit in the back 494 00:30:02,160 --> 00:30:05,600 Speaker 1: of the head really hard, knocked him out, and he 495 00:30:05,720 --> 00:30:10,480 Speaker 1: acquired UM a form of synesthesia in which he sees 496 00:30:10,520 --> 00:30:14,840 Speaker 1: fractals from being hit in the head. And um, basically 497 00:30:14,880 --> 00:30:19,200 Speaker 1: it's an acquired savant savantism, which is pretty rare to 498 00:30:19,240 --> 00:30:23,880 Speaker 1: acquire this later on. Um, and this guy hated math, 499 00:30:24,560 --> 00:30:26,720 Speaker 1: and his family used to make fun of him, he said, 500 00:30:26,760 --> 00:30:30,240 Speaker 1: because he was the worst at pictionary. Uh, I couldn't 501 00:30:30,280 --> 00:30:32,840 Speaker 1: draw a thing, couldn't draw a lick. Now, this guy 502 00:30:33,120 --> 00:30:40,160 Speaker 1: can draw reportedly mathematically correct fractals by hand, and he's 503 00:30:40,160 --> 00:30:42,760 Speaker 1: the only person on earth that can do this. And 504 00:30:42,800 --> 00:30:45,720 Speaker 1: you should see these things. They're like, you know, a 505 00:30:45,880 --> 00:30:50,120 Speaker 1: huge you know, two by two fractal that looks like 506 00:30:50,160 --> 00:30:52,880 Speaker 1: it was plotted by like a supercomputer. And this guy 507 00:30:53,000 --> 00:30:55,600 Speaker 1: does these by hand now out of nowhere because he 508 00:30:55,640 --> 00:30:58,160 Speaker 1: got hit on the head. That's pretty amazing. Yeah, it's crazy. 509 00:30:58,240 --> 00:31:00,840 Speaker 1: He got him in the fractal center. Huh he did. 510 00:31:01,000 --> 00:31:04,880 Speaker 1: That's strange that we would have like that ability latent 511 00:31:04,960 --> 00:31:07,280 Speaker 1: in us, you know. Yeah. Well, they studied his brain, 512 00:31:07,320 --> 00:31:10,000 Speaker 1: of course, UM, and they found that the two areas 513 00:31:10,120 --> 00:31:13,400 Speaker 1: that lit up in the left hemisphere were the areas 514 00:31:13,440 --> 00:31:16,600 Speaker 1: that control exact math and mental imagery. So they have 515 00:31:16,640 --> 00:31:20,240 Speaker 1: it well, and he's you know, he's fine with it, 516 00:31:20,320 --> 00:31:22,959 Speaker 1: although he says that he's a bit obsessive about it 517 00:31:22,960 --> 00:31:25,840 Speaker 1: because he's it's one of those deals where everywhere he 518 00:31:25,880 --> 00:31:28,480 Speaker 1: looks now he sees fractals. Oh yeah, Well, I got 519 00:31:28,480 --> 00:31:32,640 Speaker 1: the impression that people who are who are fractal geometers 520 00:31:32,640 --> 00:31:34,760 Speaker 1: have the same thing. Yeah, you know, they're like, click 521 00:31:34,760 --> 00:31:36,800 Speaker 1: at that cloud. I I can figure out how to 522 00:31:36,840 --> 00:31:40,880 Speaker 1: describe it completely. Yeah with math. Yeah, it's crazy, um. 523 00:31:40,920 --> 00:31:43,120 Speaker 1: And then it's everywhere canopies of the trees. Like. I 524 00:31:43,160 --> 00:31:45,480 Speaker 1: got that impression as well that once you start seeing 525 00:31:45,480 --> 00:31:50,280 Speaker 1: fractals in natural systems, like then everything becomes um fractals 526 00:31:50,280 --> 00:31:53,360 Speaker 1: and a lot simpler to understand. I realized today that 527 00:31:53,440 --> 00:31:56,600 Speaker 1: I have always doodled in fractals. Oh yeah, yeah, because 528 00:31:56,640 --> 00:31:59,000 Speaker 1: I can't really draw, so whenever I doodle, it's like 529 00:31:59,560 --> 00:32:03,520 Speaker 1: it's all aways been um little fractal shapes. Like I 530 00:32:03,520 --> 00:32:06,480 Speaker 1: would draw some kind of geometric shape, then split off 531 00:32:06,480 --> 00:32:08,840 Speaker 1: from that and make it smaller, and in the end 532 00:32:09,360 --> 00:32:11,880 Speaker 1: they're sort of like fractals. Oh your fractal tree that 533 00:32:11,960 --> 00:32:15,960 Speaker 1: you showed me, it's pretty awesome. So you got anything else? 534 00:32:16,640 --> 00:32:20,040 Speaker 1: Uh No, I would strongly urge you to read this 535 00:32:20,160 --> 00:32:22,960 Speaker 1: article a few more times. And then maybe go off 536 00:32:23,000 --> 00:32:25,280 Speaker 1: and read some more about fractals, because we definitely have 537 00:32:25,320 --> 00:32:28,360 Speaker 1: not covered all of it. I watched that Nova documentary. Yeah, 538 00:32:28,400 --> 00:32:31,080 Speaker 1: that's good stuff. What is it? Chasing the hidden dimentioned? 539 00:32:31,920 --> 00:32:33,760 Speaker 1: Is that what it's called? And you call it chasing 540 00:32:33,760 --> 00:32:37,360 Speaker 1: the dragon? Well, there's the dragon curve fractal. It's pretty boss, 541 00:32:37,400 --> 00:32:40,600 Speaker 1: That's right, it is boss. Um. So you want to 542 00:32:40,640 --> 00:32:44,040 Speaker 1: type fractals in the search bar how stuff works dot 543 00:32:44,040 --> 00:32:46,440 Speaker 1: com to start, and that will bring up this very 544 00:32:46,720 --> 00:32:49,520 Speaker 1: very good article. And I said search bar, which means 545 00:32:49,520 --> 00:32:54,600 Speaker 1: it's time for a listener mail. Josh, I'm gonna call this, uh, 546 00:32:55,000 --> 00:32:58,240 Speaker 1: don't eat your peanuts around me, jerk. Yeah. Remember when 547 00:32:58,280 --> 00:33:02,800 Speaker 1: the Air Traffic Control remark that never heard the announcement that, uh, 548 00:33:03,000 --> 00:33:05,400 Speaker 1: no one can eat peanuts on the plane. I've flown 549 00:33:05,440 --> 00:33:07,920 Speaker 1: a lot in my life and I've never heard that before. 550 00:33:08,680 --> 00:33:12,320 Speaker 1: So Ian Hammer writes in on the Air Traffic Control episode, 551 00:33:12,320 --> 00:33:15,720 Speaker 1: you were talking about peanuts being completely absent on some flights, 552 00:33:16,280 --> 00:33:18,800 Speaker 1: And as a person that is really allergic to peanuts, 553 00:33:18,880 --> 00:33:21,600 Speaker 1: I can shed some light. My allergy is bad enough 554 00:33:21,640 --> 00:33:24,360 Speaker 1: to wear the smell of peanuts, which is really just 555 00:33:24,480 --> 00:33:27,120 Speaker 1: the presence of peanut molecules in the air will cause 556 00:33:27,160 --> 00:33:29,640 Speaker 1: me to get itchy and swollen. Uh. In the case 557 00:33:29,680 --> 00:33:32,040 Speaker 1: that I am in contact with a peanut have the 558 00:33:32,080 --> 00:33:34,960 Speaker 1: superpower of becoming a balloon, and I'll swell up to 559 00:33:35,040 --> 00:33:36,720 Speaker 1: the point where I will be dead in a matter 560 00:33:36,760 --> 00:33:40,440 Speaker 1: of minutes. I can delay the anaphylactic shock for ten minutes, 561 00:33:40,440 --> 00:33:43,480 Speaker 1: give or take with an injection of epinephrin, and this 562 00:33:43,520 --> 00:33:48,760 Speaker 1: will only work twice twice in his life. I think, so, um, 563 00:33:48,800 --> 00:33:50,680 Speaker 1: if I do have a reaction, I have twenty minutes 564 00:33:50,720 --> 00:33:54,480 Speaker 1: plus the fifteen minutes I have before normal anaphylactic shock 565 00:33:54,560 --> 00:33:56,600 Speaker 1: would kill me. There really is in a way to 566 00:33:56,640 --> 00:33:59,880 Speaker 1: save me in that instance, unless I can be administered 567 00:33:59,880 --> 00:34:02,720 Speaker 1: the proper treatment that you can get only at a hospital. 568 00:34:02,800 --> 00:34:04,480 Speaker 1: Because you can imagine when a plane is at thirty 569 00:34:04,840 --> 00:34:07,760 Speaker 1: feet there's not much can be done to get me 570 00:34:07,840 --> 00:34:10,080 Speaker 1: to a hospital within that thirty five minute time frame. 571 00:34:10,920 --> 00:34:12,759 Speaker 1: So flying can be a pretty scary thing when someone 572 00:34:12,800 --> 00:34:15,520 Speaker 1: near you. Besides that they really want a peanut buttercup. 573 00:34:16,080 --> 00:34:17,960 Speaker 1: People do this sometimes and it's a real pain to 574 00:34:18,000 --> 00:34:19,920 Speaker 1: have to deal with. I just wanted to give you 575 00:34:19,920 --> 00:34:22,879 Speaker 1: guys an overview of peanut allergy sufferers when it comes 576 00:34:22,880 --> 00:34:26,080 Speaker 1: to flying. Keep up the incredible work. Look forward to 577 00:34:26,080 --> 00:34:29,960 Speaker 1: seeing a TV pilot Ian Hammer. So incredible, is right? 578 00:34:30,080 --> 00:34:34,759 Speaker 1: If we were insensitive to that, then all apologies. He 579 00:34:34,800 --> 00:34:37,040 Speaker 1: didn't indicate that, but I know we weren't. I just 580 00:34:37,080 --> 00:34:39,960 Speaker 1: remember being surprised. Yeah, I was surprised, but I knew 581 00:34:39,960 --> 00:34:43,440 Speaker 1: allergies could get bad. But man, that I think on 582 00:34:43,480 --> 00:34:45,640 Speaker 1: the plane, I was like, what I've known about this 583 00:34:45,680 --> 00:34:47,799 Speaker 1: since I saw an episode of Freaks and Geeks wherein 584 00:34:47,880 --> 00:34:50,880 Speaker 1: one of the characters almost died because like some bully 585 00:34:50,960 --> 00:34:54,640 Speaker 1: at school like gave him some peanuts. Oh yeah, was 586 00:34:54,680 --> 00:34:58,560 Speaker 1: that it was the Martin Star character, the analog to 587 00:34:58,719 --> 00:35:05,439 Speaker 1: Paul from Wonder Years, Okay, which was, Um, I can't 588 00:35:05,480 --> 00:35:07,719 Speaker 1: remember his name. I book for some weeks. Yeah, it's good, 589 00:35:07,840 --> 00:35:12,000 Speaker 1: good show. Um, well, let's see allergies. How about a 590 00:35:12,040 --> 00:35:15,600 Speaker 1: practice story if you know something about fractals that we don't, 591 00:35:15,760 --> 00:35:18,600 Speaker 1: or can correct us or explain it better than we did, 592 00:35:18,760 --> 00:35:22,640 Speaker 1: which I'm not sure that that's much of a long shot. Um, 593 00:35:22,680 --> 00:35:24,400 Speaker 1: we want to hear about it. You can tweet to 594 00:35:24,480 --> 00:35:27,279 Speaker 1: us at s Y s K Podcast. You can visit 595 00:35:27,360 --> 00:35:30,400 Speaker 1: us on Facebook at facebook dot com. Slash Stuff you 596 00:35:30,440 --> 00:35:32,759 Speaker 1: Should Know, or you can send us an email to 597 00:35:32,920 --> 00:35:38,960 Speaker 1: Stuff podcast at how stuff works dot com. Stuff you 598 00:35:38,960 --> 00:35:41,480 Speaker 1: Should Know is a production of iHeart Radio's How Stuff Works. 599 00:35:41,760 --> 00:35:43,719 Speaker 1: For more podcasts for my heart Radio, because at the 600 00:35:43,719 --> 00:35:46,440 Speaker 1: iHeart Radio app, Apple Podcasts, or wherever you listen to 601 00:35:46,480 --> 00:35:47,280 Speaker 1: your favorite shows.