Here's. The thing saving money with Geico was almost better than playing pick up basketball. Is always that guy who joined your game, he never passes the rock he instantly bricks theories and who can We have you and then put his hands up and say no foul, no foul, with Geico It's easy to switch and save on car insurance no need to fake an angel sprain because you're absolutely exhausted so which, in save with back it's almost better than sports, brought to you by the reinvented two thousand twelve Camry. It's ready for you, welcome to stop. You should know greenhouse gas networks. Hey look into the pockets of just Clark hanging on by my finger nails with me, as always is Charleston each upright through much the same,

about to start speaking. Instead, we should know about practice yea, more math, you're, ready, man, even a new geometry its non euclidean, since you brought it up very new you kidding. Geometry was like three hundred BC and fractals nineteen. Seventy five. Yet so this little bit of a gap there there is low, bit of a gap and there's a lot of animosity among the Ukrainians toward factor. Millions they need to loosen up and look at some of those far out pictures- and now here is funny. Did you watch? Did you watch that one dark on yeah? Ok, did you see the other the Arthur She Clark, one it was made in, like maybe eighty six, eighty seven and had nothing but like a delicate, sound of thunder. Often music, going on the whole time. It was really really pretty well

had a picture of you saw today on the stuff. You should know all of the idea of the Mandl brought said it's beautiful It is in his very cool and I'd eddying say what it was at his posted it, unlike I'd, say about half the people were like bearing oh man. This is rattle of the mental browser. Like fractals talk about practice, then the other half or like will you go driven out? I agree that grateful their day has actually math. We were not buy, it does look for it, tied I in nature, and how is why the hippies, like post, also mean if you ve ever seen a fractal play out on a computer screen, so we are talking about fractals either, not necessarily want to give a disclaimer. Chuck and I are not theoretical mathematicians we're not even like normal mathematicians. I balance my checkbook by hand keep that little part of my brain going. So I dont like forget how to add an subtract

later on in life. I make myself either and I dont want myself jump ahead. I show my work here and that's about it Ten of math and my life normally see I was he had a math that women you're not allowed to use calculators our guy, but there are calculators in life. So what can we use? Em, like they made calculator, so we didn't have to do my right, but at the same time find that shoddy, because it's like you're not you're, not you're, just circumventing learning something and it's like they Calculate- is there to support you after you know what you're doing discreet well, I think this is a pretty prime exam. Love like going around to get to the end. So when, when I was researching this, I was like ok really, no other deal with the stuff. Yes, this totally did. Likewise is anything you wanted to be a nothing at all and then like us, You were more deeply term like now. They do can know what they're doing there.

We really do need no time ass. I feel like I have this from researching this a little bit something a grasp of white fractals are again to a little bit. For those of you who don't know what we're talking about like take a second to look up just type in fractal and search images on your favorite search engine and you'll be like up. Yes, of course, it's a fractal and that's what we're going to talk about, because fractal fractals are a new field like we said in geometry, they do have use and they have usefulness there. I think people haven't even considered yet area, but the stuff they have figured out how to use force pretty amazing stuff Kennedy reckless at way so people now this cleared up is a GM metric shape that is self similar through infinite admirations intercourse a pattern and through infinity to exactly so there you have it boom. Do we need even continue? No but

in that sounds like really that put me off like this article is pretty well done by a guy named Craig Hague. It I don't know who that is freelancer. I guess yet it it's a pretty well then article, but that a sentence like that can put a person off pretty nature and even put it, you know you made a joke about it. Like all acknowledge you get it, you know whatever threat by when you think about it. If you take that a part, one of the hallmarks of fractal fractals is that there is a very complex result from a very simple system and there's like basically three hallmarks those that you just pointed out right. There is self similarity which is, if you, if you cut a chunk, I like a microscopic piece of a fractal off and compare it to the whole fractal. It's gonna be virtually the same yeah like or a fern, and the cool thing about practices is

me. The cool thing is that fractals appointment made Minerva documentary is that all of our math up until they discovered fractals and describe fractals was based on things that we basically created and built, like all geometry, right, euclidean geometry. You have links with in height with which the three dimensions right. Yes, really, pyramids and building the cute, I homes and other things, and you it's extremely useful. We dont quite a bit with this, but euclidean geometry. As far as the fractal geometry, wrists or geometers insist failed is when they said. Ok, look at that mountain, the account it's an imperfect com is a rough cone yeah, but its accounts. Right. So yet euclidean geometry hold sway what the fractal geometers say is yet it you could say that

calm. But if you tried to measure and describe it as such you're not going to come up with a very descriptive, a very detailed description of that mountain. So what's the point, what fractal geometry does is says: we're going to describe that mountain in little Craig and peak possible right, and so what you have is the fractal dimension, which exists in conjunction with length within height and what the fractal dimension describes. As the complexity of the object that exist within those three dimensions as well, the track soap finishing my point: the cool thing practice. Is that everything that we had done previously and geometry were because things we built practice, help described things that were have been here since the beginning of time, yeah in nature, and one of the truest examples of that is the first right with self similarity. You take a little snippet,

the fern, although you shouldn't do that, was just look at it. It's gonna look the same as the larger part of the first and then the whole fern itself very self, similar right, but not necessarily exact. Now, a camera There is a form of self. Similarly, that is exact and precise, but in nature that's rare, if not completely, not found right there, so you got self similarity which is the smaller part, is virtually the same or looks the same restructured the same as the whole and this process of self similarity going larger, smaller scale is covered, cursive ness I yet every cursive. This is like you know those paintings where it's like a guy. I think Stephen Colbert, the one that he gave to the Smithsonian, has recursive innocent, where it's a man in a painting,

standing in front of like a mantle and above the mantle, is the painting yeah you're looking at, and then it goes on and on and on and on and on. Yet anything this infinitely repeating right, the same with, if you're in a young, dressing room and there's a mere on either side of the wall. You just keep going on infinitely recursive ness and with fractals the recursive newness of self similarity right. So there's two two traits is produced through this thing called adoration, and that's where you say: here's the whole eminent put it into this formula and the formula has: has the formulate the output of the formula produces the input for the next round of that same formula to loop, exactly

so it's self sustaining and it can go on infinitely recursion right, that's right! So what we discover this fractals, anything that has a self similar structure and its recursive through iteration. That's right! Ok! So I'm a really I came upon. This can easy one easier explanation of a fact or from them, while Mandl brought sight, he died by the way into doesn't in Yahoo, sent hissing like a pretty good guy he was deafening, think indifferent and the way that men are brought described. Easy way to think of a fractals there's. This thing called the serpent gas get there and you take a triangle and you can combine them into a bunch little triangles and spaces triangular spaces. Yeah that form a larger triangle right, so that that one initial, solid trying

is called the initiators of the original shape right and then all those other triangles combine form that larger triangle, a self more version of that larger triangle. The original triangle- that's called generator right, so the formula for creating a so would be to go into that generator. The version that has all the little smaller triangles and make up a larger whole triangle and say all the ones that look like the initiators of the original, just solid black triangle. Take that out and swap it with the job, later version right and all of a sudden. You have one that exponentially more detailed, there's more to it and that's a fractal. That's all there is to it. You know what else is a fragile, because there's a big one. Louis right Richardson was the english mathematician early Twentyth century and he very currently said you know what, if you take a yardstick and

should the coast of England you're gonna get a number. He take a one foot ruler and met because line you're gonna get a different number. You take a one inch ruler and measured Fine you're gonna get a different number in its basically infinite in that, The smaller you go with your ear of measure or your tool is, larger number, you're gonna get because the coastline is so infinitely varied in its little nooks and crannies right. Exactly is very cool way of thinking about it. There is a second part, to check is that so depending on the youth and what the what you're, using the measure the to using the measure. Yet the number the perimeter of the coastline could go on infinitely, but it still contains the same finite amount of space within the paradox. That is a big time paradox, because things aren't supposed to be infinite and finite. At the same time, I write and Louis FRY Richardson. He basically

damn published in the coming up with that paradox. The this kind of revolution in thought that fractal geometry is based on that you can have the infinite mixed with the finite right. You can get it from pretty simple formulas that create very increasingly complex systems right yet and fry. Wasn't he wasn't that he was the first got a really put forth this idea of thought, but he was in the first one notices paradox yeah and am before. Believing you there were fractals there were. There were artists, like divinity they saw this pattern entreaty just was on and on the nose. Humanitarian article. They point out the cat. Soon she got hooker sigh Eighteen, twenty japanese artist created the great wave off Canna Gower and those are fractals. It's a bit ocean waves breaking and at the top of the crest of the waves,

our little self similar waves breaking off in a smaller and smaller self, similar versions and its neck. Or or in their faces a depiction of one. So You know early African and never harder for doing this, and they didn't realize that they were fractals in their fractals all around us. Now they just saw crystals in snowflake or another good one, the exact they were just they'd saw that there was what they were looking at was a repeating pattern that was self similar am recursive right. That's it that's all no these resolutions are very, very difficult to keep get more exercise save more money. What about this? We have a resolution that you can really work with stop wasting time going to the post office. That right, you stamped out, I'm instead because they bring all the services of the Eu S postal service right to your computer with yours business sinning invoices or packages

or an online seller shipping out products stamps that can handle it all with ease yank it. This was simply come. You get five cents off every first class, stamp in up to forty percent of priority mail. This right? U S posted twenty four seven for any letter any package, any class anywhere. You want to send it, there's no risk and our promo code, ass white, ass, gay you're, gonna, get this offer afore weak trial, plus free postage and digital scale and there are no long term commitments or contracts just go to stamp that come click on the microphone top of the page and type in s. Why, as K that stance, I come from a goat s. Why, as K stamps that come never go to the polls, office. Again right and in then why Mandl brought was the first one to say you know what we can. We can use math equations actually apply to this and he was a big. For a while, and then they

he turned on him and said you know what this is all cool and trip can, but it's useless. And he said, oh yeah- screw You guys watch and he wrote another book which started to give some practical applications ratchet pretty exciting yeah, I'm so the whole thing the whole principle is based on is that you can take a formula and plug in a very simple. I was a relatively simple formula: Meno brought for you you'll. Take that one, for example, his is Zed, goes to dead, squared plus see.

Right? That's what it's called, if you're in England that we see that put every ladys it's dead anyway, that goes to which is in the goal. To is the key right here that what makes it fractal goes to means there is an error. Is an equal silent, looks like an equal within a part of a narrow pointing towards Zed, yet the other point pointing towards the rest of their formula, which means that the the it there's that feedback loop words like ok, once you have the number that this punches out,

You have you feed it back in and you'll get another number noses keep going and going in going in every time. Remember you're, swapping out the original, the initiator for the the detailed version, the generator and it's just getting exponentially more complex with just that. One adoration of that very simple formula. The trend in men brought set- this is the one that's like it's probably the most famous one. That's one of the dead had like like this crazy juxtaposition, between like black and like different colors everything and with his formula to things happen with a number that you put in it either goes towards zero or she talked to the infinite and what they did for this for

They are men brought set fractals. Was they assigned a color to a number based on how quickly it goes off to toward infinity right? So, let's say that you have like for, if you plug for into this ten generations it all. It will become. An infinite number right then say that that would be grouped into a blue color like ten generations. Blue eight generations is red. Ninety generations is orange, it's sort of thing and then the other direction say if you put in four point two or something like that, it'll go towards zero by any number. That, eventually, will go towards zero is represented as black, so what you have, then, is this really intricate, depending on where you looming in or out on the fractal. This intricate change of colors, in what you really seeing our numbers that are plots on a plane

it's your fractal, then the black parts or numbers that will eventually be be zero right. Most of the men dollar mental brought set as black yeah. But if you zoom in. Like that's. The whole point is a man on one of those little. What do we call those four spikes? I guess you could call a plot, apply it and it's gonna look like what you just saw and it didn't, document, is very cool when they zoom in on these ants sort of my blowing yeah. It is very, I strongly recommend watching that cause. They explain it way better than us. Well, it helps to see a pressure area big time so onwards, as I have done, my father S. Will frankly there shock yes, so we talked about fractals. We talked about the mandl brought said we talked about where they certainly come from and.

That's the idea, remember Louis FRY Richardson. He was talking about measuring the coast going off into the infinite, but still retaining a finite about the guy came after him. Hell given Coke there. He came over the coke snowflake, which is pretty call. If you take a straight line. Are you take a triangle? on each side, the triangle in the middle you bust out the middle into another triangular hump. You do that over and over and over again echoes off into infinity. Although it contains a finite amount of space, the perimeter goes off to the infinite right away. Named York Canter came over the cancer set, which is used to take a straight line and you take the middle out of it and then free to those two lines that produces you. Do this thing in this keeps going on and on and rather than going to nothingness like you like. Well, if you take a six inch line right, eventually, you're gonna bust, a diet nothingness again that doesn't happen. They found that it goes off the internet, so they

I was very warm and brought. It was plugging all these into computers, because that's what it took the azure people realize it's like your canter of the treaty says first name he was the. He was working in the eighteen eighties. Guest on Julio came with the Julia sets for producing repeating pattern, using feedback, loop lace, casually nineteenth century early twentieth century mathematicians was strictly theoretical until the late Seventys, when guys like men about who work the IBM started. Feeding these things into these new fangled computers, and seeing the results like this fractals, like the man brought said that he saw right so almost immediately. There is a practical use for fractals that came in the form of sea gee. I yeah? They interview that one guy in the documentary who worked on the first CD

shot in motion picture history. Niche was STAR trek to the wrath of cod, and he was tasked with making a cgi land surface like mountain range and when he mine blowing was the any data mean. Now you look back and I can look silly, but at the time it was complete Revolutionary and once he and about fractals in the geometry in the math fractals, those pretty easy form of any made it seem like he's like. Oh, this is the key the site. You do it right, so why wasn It is quite easy, especially if you know what you're doing with computer programming and math, because what you are basically doing to create a fractal generator is teaching your computer to to do something within a certain formula that here fractal form

right and so what Lauren Carpenter, the guy, who created the M, the STAR Trek to landscape for the first see all see gee, I shot ever hear what he basically did was created computer program. That said, hey Computer, I want to give you a bunch of triangles cause. I think that was the early stuff is working with you. I'm gonna give you a bunch of trial. Goals, and I want you to take this triangles and generate a new fractal set from right now and you did it again and again and again, and then every third time. I want you to start turning M forty degrees. So it's going to change the pattern slightly and then all of a sudden, you hovels, infinite variations. The and why, when you go back and look at that shot that it still works, can you know today is because the computer he was working at didn't, have the computing power to do that many times. Yasser now we have higher costs computing power, and so what we are doing is telling our computers-

going and going in guy swapping. That initiated that one single black go everywhere. It can find it in this pattern. This pattern of triangles in the fractal with a brain new fractal So it's just creating more and more and more more fractals, which creates a finer and finer finer resolution, which makes something look all the more realistic yet like that part in that. Talk about the star wars, wafts, making the lava, splashing yeah the maize. Yes, it was because they shouted First, when they did is looks gonna play and then once you that, through this infinite feedback loop it just like shattered and in an fractured, not rattled, although I want to say fractal off and just look more detailed, more detailed, more detailed until it looked like lava, splashing Red Freemason, let's, where the word fractal comes from his mental brought, coined ninety seventy five to say it's a indicate how things fracture off and they form a regular patterns.

You can create a fractal that that is regularly repeating, but it doesnt work is natural in with like, save your creating lava right. You ve got that one rule that like every third generation it yeah kicks forty degrees, ever the rule is that just Kenneth throws a little bit this similarity into because of something to self similar, it's not going to look right. It's not gonna. Look natural that Kullak real right, which China leads. You to think Chuck, then that there is a an application for studying natural phenomenon using fractals right while there I guess, all kinds, while this isn't so much natural, but that the document interviewed Nathan Cohen, who was a ham radio operator and his landlord said. Do you can't have that huge antenna hang out of your apartment so he started bending wires a straight wire into

essentially fractal and on the very first go. It got better reception merely by the fact that it was bent in that way, but in itself similar so he eventually use that too. I hope make a lot of money. I got the impression I get by applying that technology to cell phones and the way to date, rabbit, is all the different things a cell phone can do. If you were to have a different antenna for each one of these functions, it would be like carrying around little porcupine So what cellphones now are based on is Don't design called major sponge linger sponge. I have mentioned and it's basically a box fractal, and if you crack open yourself, you're gonna, see a wire that yeah you're going to be looking at a fractal. It's a square right and then within it are a bunch of little squares in a of self similar pattern

you friend or looking at a fractal tolerant. Yet it's also all around us and nature theirs in that same documentary that Nova programme there is a team but the University of Arizona. There's a team of academics, yells critical, who were trying to figure out if you predict the amount of carbon capture and capacity in entire rainforests, has just by measuring and figuring out this self similar system that a single tree in that rain forests here has a mix it well, it does, but it's kind of a leap. It's like ok, so is one tree. Does it follow the same system that the whole rainforest does and they apparently found that? Yes, in fact, it does right. The same branching system founded that tree is similar to the degree

of the trees in the rain forests as a whole people. Yes, I'm tumors in the human body here, one of the keys to getting rid of cancer is our or any kind of tumor spotting assume of early on, but with our elder sounding gee, you can only get so small and so detailed that you can't see some These natural fractals it you know your blood vessels were fractals, essentially disliked the branches of a tree are So there are now using geometry too. Now, if I'm not sure, if I got there but I think it shows up. It shows the flow. Of the blood because alteration pick that up to these fractals, when they can, you can pick up the vessels themselves, Zara yeah early earlier tumor spotting

wait for all intents and purposes there looking at the vessels by finding the blood because they yet where its flowing, but yet, depending on the pattern that it follows. If it follows lichen and like a tree, branching shape right, it's healthy right now and then to resolve the veins, are obeying crooking, going all crazy directions. The read out of a heartbeat not consistent to fractal yeah, so these fractal analysis now to study your heart rate, and I use that to better understand how a read me happens through map, so there's the especially with natural systems, that's kind of like the biggest contribution that fractal geometries produced so far. I think, I'm aside from CD

is what medical le, while just that that whole understanding that was first really kind of voiced by Louis FRY Richardson with the coastline that there's there are natural systems out there that we can really. If there were not quite paying attention to write. Really know how to deal with their were trying to apply something like you, clytie and geometry, to something that you can't really use that for right, that that's what fractal, geometries really contributed so far is basically say: hey, there's a lot of natural systems out here that are self similar em, cursive and now that we kind of sea in the fractal world we see everywhere, and we have a better understanding of one of the best examples of that I thought was figuring out,

How larger animals use less energy and smaller animals? They use energy more efficiently, and this is kind of a biological paradox rail really long time, and these guys figured it out using. I guess, kind of the same kind of insight that frightful geometry has that if you take genes and genes or the mathematical formula or the equivalent of a mathematical formula and you feed in these genetic processes, waits gonna put out. Is this self similar recursive pattern near to where the bigger the organism is the more? This thing goes:

goes, the less energy is going to use because there's more of it and it doesn't require very much energy to produce passed a certain point, Sophia, very small animal it using a lot of energy to do these things to carry this out, but there's that economy of scale, because you're still using a relatively simple formula, you're genetic code right to carry out a very complex, seemingly complex system. Just your organs, are you, as an organism? Bright, said the end, an elephant use less energy than a mouse. Yes, because they're both using the same formula, the same input and then eventually reach a point where it just gets easier and easier and easier crazy to tell you something simple: to create a complex system alone I did it. I got one more thing. You heard this guy Jason Padgett. This is,

crazy. On this guy, like nine years ago, I think, was mugged into come. A Washington got hit in the back of the head, really hard knocked him out and he acquired a form of xenophobia in which he said Animals. Well, being hidden ahead too, and basically it's an acquired, savant savant ISM, which is pretty rare, to acquire this later on, and this guy hated math and his family to make fun of them. He said because he was the worst pensionary.

Draw thing to draw lick now. This guy can draw reportedly mathematically correct, fractals by hand well in his only personal on earth. It can do this holy cow and you should see these things there, like you know a huge. You know, two by two fragile that looks like it was plotted by like a supercomputer in the sky disease by hand now added nowhere because he got hit on the head. That's pretty amazing! Yes, crazy! He get him fractals

her head. That's strange that we would have liked that ability late Nana sooner yeah. Well, they studied his brain of course, and they found that the two areas that lit up in the left hemisphere were the areas, control, exact, math and mental imagery, and he's he's fine with. Although he says it is a bit obsessive about it, because he is wireless deals. Where everywhere he looks now, he sees fractal area. While I get the impression that people who are who are fractal geometers have the same thing here in other likely that cloud I can figure out how to describe it completely yet with math, yeah, crazy and then it's everywhere canopies of trees. Like I get the impression as well that what you are seeing fractals in natural systems like then everything becomes fractals alot simpler, don't understand. I realized today that I have always doodle than fractals. Oh yeah yeah,

it really draw. So whenever I doodle it's like it's always little fractal shapes like. I would draw some kind of geometric shape and split off from that make it smaller and, in the end, the sort of like fractals, oh you're, fractal tree. The issue is pretty here's the thing: saving money with Geico was almost better than playing pick up. Basketball. Is always that guy who joined your game He never passes the rock he instantly bricks theories and who can We have you and then put his hands up and say no foul, no foul with Geico it's easy to switch and save on car insurance no need to fake an angel sprang because you're absolutely exhausted. So which in save with Geiger. It's almost

better than sports. So you anything else. I would strongly urge you to read this article a few more times and then maybe go off and read some more about freckles, because we definitely not covered all the watch that nobody Documentary Ganz good stuff. What is it chasing? The hidden dimension is always come in Chicago, chasing a dragon, others, dragging her Franco's reports that his boss, so you wanna, take fractals in the search bar. How supports that com to start and that will bring at this very good article n. I said search bar time for listen, we call this don't eat. You that's around me number when the air traffic control. I remarked that never heard the announcement that no one can be financed from the blame. A flown a lot in my life. I've never heard that

so in human rights and on the air traffic Control episode, you're talking about peanuts being completely absent on flights and as a person that is really allergic peanuts. Yet some light. My algae is bad enough to wear the smell of peanuts, which is really just the presents a peanut molecules in air. What caused me to get itchy and swollen in the case that I am in contact with the superpower, having a balloon and swell up to the point where I will dead in a matter of minutes, I can delay the end of lack shock for ten minutes, give or take with an injection of Evan Efron, and this will only work twice by poison of life. I think so if you every action have twenty minutes plus the fifteen minutes. I have before normal and shock, would kill me either. In a way to save me in that instance, unless I can be administered the proper treatment that you can get only at heart,

You can imagine when plane thirty thousand feet. There's not much can be done to get me to a hospital with thirty five minute timeframe so find me pretty scary thing when someone near you, They really want a peanut butter cup. People do the sometimes in its real pain, to have to deal with I just want to give you guys an overview of peanut allergy sufferers when it comes to flying, keep up the incredible work, look forward to seeing the tv pilot and hammer so incredible is right. If we would arrive sensitive to that, then all apologies. He didn't is that what we want

memory really surprised, yell, surprise, but, and I knew ours could get bad man. I think on the flannels like what I've known about this, since I saw an episode of freezing geeks wearing one of the characters, almost died and kiss like some old school, like oh yeah, was that it was the star, the analogue Paul from wonder years, which was on oh C mon fact historic there. If you know of their rifles, that we don't or can correct this or explain it better than we did, which I am not sure that this much of a long shot, you want to hear about it. You can tweak to us it s, landscape, podcast. You can visit some facebook at Facebook, dot, com, slash, suddenly no horse innocent email at stuff package,

discovery that count for more on this and thousands of other topics how stuff works. Dot com brought you by the way Then two thousand twelve Camry. It's ready for you I dont think America has ever gone back to the way that it was before the DC sniper the gun. Most likely a skilled marksman fired six times in the course of sixteen. Our police say they have never had a crime. Quite like this. It is quite a mystery and then, as the DC sniper case, unfolded that terror boldly group. This was the most intense man Hunt in american law enforcement. History, listen to monster DC, sniper on the eye, hard radio, app apple podcast. Or wherever you get your packets.