November 30, 2019 • 35 mins
In the 1980s, IBM mathematician Benoit Mandelbrot gazed for the first time upon his famous fractal. What resulted was a revolution in math and geometry and our understanding of the infinite, not to mention how we see Star Trek II. Get blown away by fractals in this classic episode.
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Speaker 1 (00:00):
How do folks, Charles W. Chuck Bryant here in the corral,
and I'm gonna last so up a Stuff you Should
Know select for you from June seventh, two thousand twelve.
Fractals Colin Whoa, this is a tough one for me.
I'm not gonna lie. Fractals is one of the toughest
episodes I've ever had to learn and research. And that's
where we're gonna revisit it right here, right now. Welcome
(00:25):
to Stuff you Should Know, a production of My Heart
Radios How Stuff Works. Hey, and welcome to the podcast.
I'm Josh Clark, hanging on by my fingernails with me
as always as Charles W. Chuck Bryant, doing much the
same as we are about to start speaking on stuff
(00:47):
you should know about. Fractals. Yea, more math theoretical, Matt
even Yeah, a new branch of geometry. It's non Euclidean
since you brought it up, Okay, very new. Euclidean geometry
was like three B C and fractals are so there's
(01:09):
a little bit of a gap there. There is a
little bit of a gap and uh, there's a lot
of animosity among the Euclideans towards Fractillians. They need to
loosen up and look at some of those far out pictures.
I know, you know it's funny. Did you watch um,
did you watch that one doc on? Yeah? Okay, did
you see the other? The Arthur C. Clark one. It
(01:31):
was made in like maybe eight s eighty seven and
it had nothing but like um delicate sound of thunder
rip off music going on the whole time. It was
really really trippy. Well, I posted a picture I don't
know if you saw today on the stuff you should
know all of the of the Mandel brought set. Its
beautiful it is and it's very cool. And I didn't
(01:52):
even say what it was. I just posted it, and
like I'd say, about half the people were like, very cool, man,
this is rad I love the Mantal brought set like
fractill talk about fractals. And then the other half were like,
well you guys tripping out like what you did a
grateful dead day. That's actually math, believe it or not.
But it does look very it's very tied eye in
nature and that's why the hippies like it. Plus also,
(02:14):
I mean, if you've ever seen a fractal play out
on a computer screen. Yeah. Um, so we are talking
about fractals. I don't I don't necessarily want to give
a disclaimer. Chuck and I are not theoretical mathematicians. We're
not even like normal mathematicians. I balanced my checkbook my
hand just to keep that little part of my brain going.
(02:36):
So I don't like forget how to add and subtract
later on in life. I make myself do that, and
I don't let myself jump ahead. I show my work. Yeah. Um,
and that's about the extent of math in my life normally. See,
I was the kid in math that when they said
you're not allowed to use calculators, I would go, like,
there are calculators in life, so why can't we use them. Yeah,
(02:58):
Like they made calculators so we didn't have to do maths, right.
But at the same time, I find that shoddy because
it's like, you're not you're not You're just circumventing learning something,
and it's like the calculators there to support you after
you know what you're doing. I disagree. Well, I think
this is a pretty prime example of like going around
(03:19):
to get to the end. So when when I was
researching this, I was like, Okay, well, they don't really
know what they're doing with this stuff yet, so we
can just totally be like, well it's it's there, anything
you wanted to be and nothing at all. And then
like I started looking a little more deeply into I'm like, oh, no,
they do kind of know what they're doing. We really
don't know what we're talking about. So I feel like
(03:40):
I have, just from researching this, a little bit, um
something of a grasp of what fractals are, a little
bit For those of you who who don't know what
we're talking about, like, take a second to um look
up just typing fractal and search images on your favorite
search engine and you'll be like, oh, yes, of course
it's a fractal um And that's what we're going to
(04:01):
talk about, because fractal fractals are a new field, like
we said, in geometry, and they do have use and
they have usefulness that I think people haven't even considered yet.
But the the stuff that they have figured out how
to use it for is pretty amazing stuff. Can I
say what a fractal is at least so people know
they should clear it all up? It is a geometric
(04:24):
shape that is self similar through infinite iterations in a
recursive pattern and through infinite detail exactly. So there you
have it. Boom, Do we need to even continue? No?
But um, and that sounds like really that put me off,
Like this article was pretty well done by a guy
named Craig Haggett. I don't know who that it is, freelancer.
I guess um, it's a pretty well done article. But
(04:44):
that a sentence like that can put a person off
pretty easy. And he even put it, you know, he
made a joke about it, like, oh, you know that,
you get it, you know whatever. But um, when you
think about it, if you take that apart, one of
the hallmarks of fractal fractals, um is that they are
a very complex result from a very simple system. And
(05:06):
there's like basically three hallmarks two fractals that you just
pointed out right. There is um self similarity, which is
if you if you cut a chunk, like a microscopic
piece of a fractal off and compare it to the
whole fractal, it's going to be virtually the same. Yeah,
(05:27):
like or a fern. And the cool thing about fractals
is is to me the coolest thing is that fractals.
The point they made in the Nova documentary is that
all of our math up until they discovered fractals and
described practicals was based on things that we basically created
and built. Like all geometry, right, Euclidean geometry, you have length, width,
(05:53):
and height, which should view the three dimensions, right, yes,
for like pyramids and buildings and combs and all those things.
And you it's extremely useful and we've done quite a
bit with this. But what Euclidean geometry, as far as
the fractal geometrists or geometers um insist, failed at is
(06:13):
when they said, okay, look at that mountain. That's a cone.
It's an imperfect cone, it's a rough cone, but it's
a cone shape, right, So yeah, Euclidean geometry holds sway.
What the fractal geometers say is, yeah, you could say
that it's a cone, but if you tried to measure
and describe it as such, you're not going to come
up with a very descriptive, a very um detailed description
(06:38):
of that mountain. So what's the point What fractal geometry
does is it says we're going to describe that mountain
in every little craig and peak possible. And so what
you have is the fractal dimension, which exists in conjunction
with length, widthin height. And what the fractal dimension describes
(06:59):
is the complex city of the object that exists within
those three dimensions as well. That's right. So finishing my point,
the cool thing about fractals is that everything that we
had done previously in geometry were because of things we've built.
Practicals help describe things that were have been here since
the beginning of time in nature, and one of the
(07:20):
truest examples of that is the fern. Right with self similarity.
You take a little snippet off of a fern, although
you shouldn't do that. Let's just look at it. Uh,
it's gonna look the same as the larger part of
the fern, and then the whole fern itself very self
similar but not necessarily exact. No, it can be. There
is a form of self similarity that is exact and precise,
(07:42):
but in nature that's rare, if not just completely not found. Right,
that's right. So you've got self similarity, which is the
smaller part is virtually the same or looks the same,
or structured the same as the whole UM. And this
process of self similarity UM going larger smaller in scale
is called recursiveness, right, And recursiveness is UM. Like you
(08:07):
know those paintings where it's like a guy I think
Stephen Colbert, the one that he gave to the Smithsonian
has recursiveness in it, where it's a man in a
painting standing in front of like a mantle, and above
the mantle is the painting that you're looking at, and
then it goes on and on and on and on
and on anything that's infinitely repeating, right, same with if
(08:28):
you're in a dressing room and there's a mirror on
either side of the wall, you just keep going on infinitely.
It's recursiveness and with fractals the recursiveness of self similarity. Right.
So there's two two traits. UM is produced through this
thing called iteration, that's right. And that's where you say,
here's the whole I'm gonna put it into this formula,
(08:53):
and the formula has has the formula. The output of
the formula produces the input for the next round of
that same formula. It's a loop exactly, so it's self
sustaining and it can go on infinitely recursion. Right. That's right.
So what we've just come up with is a fractal
(09:15):
is anything that has a self similar structure and it's
recursive through iteration. That's right. Okay, So um A, really
I came upon this kind of easy, one easier explanation
of a fractal from Ben wal Mandel brought site. He died,
by the way in two. He seemed like a pretty
good guy. He was definitely thinking different. Um. And the
(09:40):
way that Mandel brought described a really easy way to
think of a fractal is um. There's this thing called
the Serpinsky gasket, and you take a triangle and you
can combine them into a bunch of little triangles and
spaces triangular spaces that form a larger triangle. Right, So
(10:00):
that that one initial solid triangle is called the initiator,
that's the original shape, and then all those other triangles
combine that form that larger triangle or a self similar
version of that larger triangle to the original triangle. That's
called generator. Right. So the formula for creating a fractal
(10:21):
would be to go into that generator, the version that
has all the little smaller triangles that make up a
larger whole triangle. And say, all the ones that look
like the initiator, the original just solid black triangle, take
that out and swap it with the generator version, and
all of a sudden you have one that's exponentially more detailed.
(10:43):
There's more to it, And that's a fractal. That's all
there is to it. You know what else is a fractal?
What the coastline? Yeah, that was a big one. Lewis
Fry Richardson was an English mathematician early twenty century, and
he very brilliantly said, you know what, if you take
a yardstick and you measured the coastline of England, you're
(11:04):
gonna get a number. If you take a one ft
ruler and measure the coastline, you're gonna get a different number.
If you take a one inch ruler and measure the coastline,
you're gonna get a different number. And it's basically infinite
in that the smaller you go with your your unit
of measure or your tool is the larger number you're
(11:26):
gonna get. Because the coastline is so infinitely varied in
its little nooks and crannies, right exactly It's a very
cool way of thinking about it. There's a second part
of that to Chuck, is that so depending on the you,
what you're using, the measure, the tool you're using, the measure,
the number, the perimeter of that coastline could go on infinitely,
(11:47):
but it still contains the same finite amount of space
within its paradox. That is a big time paradox because
things aren't supposed to be infinite and finite at the
same time, right right, Um and uh Lewis Fry Richardson
he basically established in that coming up with that paradox,
this kind of revolution and thought that fractal geometry is
(12:09):
based on that. You can have the infinite mixed with
the finite. You can get it from pretty simple formulas
that create very increasingly complex systems, right Um. And Fry
wasn't the He wasn't He was the first guy to
really kind of put forth this idea of thought, but
he wasn't the first one to notice this paradox. Yeah,
(12:30):
and before people even knew they were fractals, there were
there were artists like da Vinci that saw this pattern
and tree branches that was um I know in the
Nova documentary and the article, they point out the uh
Katsu Chica Hokusai Japanese artists created the Great Wave off Kanagawa,
(12:52):
and uh those are fractals. It's a it's ocean waves
breaking and at the top of the crest of the
waves are a little self similar or waves breaking off
into smaller and smaller self similar versions. And that's a
natural fractal, or in this case, it's a depiction of one.
So they were you know, early African and Nabajo artists
were doing this and they didn't realize that they were
(13:12):
fractals and that there were fractals all around us. No,
they just saw crystals in a snowflake or another good one, yeah, exactly. Um,
they were just they saw that there was what they
were looking at was a repeating pattern that was self
similar and recursive. Right, yeah, that's it. That's a fractal, right. Yeah.
And and Ben Wha Mandel brought was the first one
(13:33):
to say, you know what, we can we can use
math equations to actually apply to this. And he was
a big star for a while, and then they sort
of turned on him and said, you know what, this
is all cool and trippy looking, but it's useless. Right,
and he said, oh yeah, screw you guys, watch this
and he wrote another book which started to uh give
(13:56):
some practical applications which are pretty exciting. UM. So the
whole thing, the whole principle that is based on UM
is that you can take a formula and plug in
a very simple UM, well, a relatively simple formula like
mantle Brod's formula. Will take that one. For example, his
(14:17):
is um ZED goes to ZED squared plus c. Right,
that's what it's called. If you're in England, zed, we
say z Z. Well, anyway, Zed goes to which is
and the goes to is the key right here. This
(14:37):
is what makes it fractal goes to means that um,
it's an error. It's an equal sign. It looks like
an equal sign with a part of an arrow pointing
towards ZED, the other point pointing towards the rest of
the formula, which means that the the there's that feedback
loop where it's like, okay, once you have the number
that this punches out, you have, you feed it back
(15:00):
can and you'll get another number and knows, just keep
going and going and going, and 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 iteration of that very simple formula.
(15:23):
UM and Mandel brought set Uh. This is the one
that's like it's probably the most famous one. That's the
one that the Deadheads like because it's like this crazy
juxtaposition between like black and like different colors and everything.
And with his formula, two things happen with the number
that you put in. It either goes towards zero or
(15:46):
it shoots off to the infinite. And what they did
for this for the the Mandel brought set fractals was
they assigned a color to a number based on how
quickly it goes off to towards infinity. Right, so let's
say that you have like four, If you plug four
into this and in ten generations, it'll it'll become an
(16:07):
infinite number. UM. Then say that that would be grouped
into a blue color like ten generations blue, eight generations
is red, ninety generations is orange. See what I'm saying. UM.
And then the other direction, like say if you put
in four point two or something like that, it'll go
towards zero and any number that eventually will go towards
(16:29):
zero is represented as black. So what you have then,
is this really intricate depending on where you're zooming in
or out on the fractal, this intricate change of colors,
and what you're really just seeing our numbers that are
plots on a plane, and that's your fractal, and then
the black parts are numbers that will eventually be be zero. Right,
(16:51):
And most of the mental mental brought set is black. Yeah,
but if you zoom in, like that's the whole point.
You zoom in on one of those little uh what
do we even call those little spikes? Uh? I guess
you could call it a plot. A plot, and it's
gonna look like what you just saw. And the Nova
documentary is very cool when they zoom in on these,
(17:13):
it's sort of mind blowing. Yeah, it is very I
strongly recommend watching that because they explain it way better
than us. Well, it helps to see it for sure,
Oh yeah, big time. So um or draw it as
I have done. It's a pretty nice little fract Yeah.
(17:53):
So we've talked about fractals, We talked about the Mandel
brought set, we talked about where they started to come
from um and the the idea. Remember Lewis fried Richardson,
he was talking about measuring the coastline and going off
into the infinite, but still containing a finite amount um.
A guy came after him named Helga von Coke. He
(18:15):
came up with a Coke snowflake, which is pretty cool.
If you take a straight line, or you take a triangle,
and then on each side of the triangle in the
middle you bust out the middle into another triangular hump.
You do that over and over and over again. It
goes off into infinity. Although it contains a finite amount
of space. The perimeter goes off to the infinite. A
(18:36):
guy named Georg Cantor came up with the cancer set,
which is you just take a straight line and you
take the middle out of it, and then for each
of those two lines that produces, you do the same
thing and it just keeps going on and on and
rather than going to nothingness like you're like, well, if
you take a six inch line, eventually you're gonna bust
it down and nothingness again. That doesn't happen. They found
(18:56):
that it goes off to the infinite. So they realized
Ben Wall mantel Brought was plugging all these into computers,
because that's what it took people realize this, Like George
Cantor um Man I hope that's how you say his
first name. He was he was working in the eighteen eighties,
Um Gaston Julio came up with the Julia sets for
producing a repeating pattern using feedback loop. All these guys
(19:19):
were like nineteenth century early twentieth century mathematicians and it
was strictly theoretical until the late seventies when guys like
Mantel Brought who worked at IBM, started feeding these things
into these new fangled computers and seeing the results like
this fractals like the mantel Brought set that he saw right,
(19:39):
So Um, almost immediately there was a practical use for
fractals that came in the form of c g I. Yeah.
They interviewed that one guy in the documentary um who
worked on the first c g I shot in motion
picture history, which was Star Trek to the Wrath of
(20:01):
con and Uh. He was tasked with making a c
g I uh land surface like mountain range and pretty
mind blowing with it. Yeah, and he did. I mean,
now you look back and it kind of looks silly,
but at the time it was completely revolutionary. And once
he learned about fractals in the geometry and the math
of fractals, it was pretty easy for him, and he
(20:23):
made it seem like he was like, oh, well, this
is the key, this is how you do it right.
So well, and it is kind of easy, especially if
you know what you're doing with computer programming and math,
because what you're basically doing to create a fractal generator
is teaching your computer to to do something within a
certain formula. That's your fractal formula, right, And so what
(20:44):
Lauren Carpenter, the guy who created the the Star Trek
to landscape for the first c G all c g
I shot ever, what he basically did was created a
computer program that said, hey, computer, I'm gonna give you
a bunch of triangles. Because I think that was the
earliest stuff he was working with. Um, I'm gonna give
you a bunch of triangles, and I want you to
(21:04):
take those triangles and generate a new fractal set from it, right,
And then I want you to do it again and
again and again, and then every third time I want
you to start turning them forty degrees, so it's going
to change the pattern slightly, and then all of a
sudden you have these infinite variations. The reason why when
(21:24):
you go back and look at that shot that it
still looks kind of you know today, is because the
computer he was working at didn't have the computing power
to do that many times. Now we have higher computer
computing power, and so what we're doing is telling our
computers to keep going and going and going, swapping out
that initiator, that one single black triangle everywhere it can
(21:47):
find it in this pattern, this pattern of triangles in
the fractal with a brand new fractal. So it's just
creating more and more and more and more fractals, which
creates a finer and finer and finer resolution, which makes
something look all the more real. Yeah, like the part
in the doc about the Star Wars, I was making
the lava splashing. It's amazing, Yes, it was because they
(22:08):
showed the first one they did it looks kind of plain,
and then once you fed it through this infinite feedback loop,
it just like shattered and and and uh, fractured, not fractaled,
although I want to say fractaled off and just look
more detailed, more detailed, more detailed, until it looked like
lava splashing. Right, it's pretty amazing. Well, that's where the
(22:28):
word fractal comes from. Is um Mandel brought coined in
to say, to indicate how the things fracture off and
they form irregular patterns. Um, you can create a fractal
that that is regularly repeating, but it doesn't look as natural.
And with like say, if you're creating lava, you've got
(22:52):
to have that one rule that like every third generation
kicks forty degrees or whatever the rule is. That just
kind of throws a little bit of dissimilarity and too
because if something is too self similar, it's not going
to look right. It's not gonna look natural, it's not
gonna look real, which kind of leads you to think, chuck.
Then that there is a an application for studying natural
(23:13):
phenomenon using fractals, right, while there are I guess all kinds, Um,
well this isn't so much natural. But the documentary interviewed
Nathan Cohen who was a ham radio operator and his
landlord said, dude, you can't have that huge antenna hanging
out of your apartment so he started bending wires a
(23:35):
straight wire into essentially a fractal and found that on
the very first go it got better reception, um, merely
by the fact that it was bent in that way
and it was self similar. So he eventually used that
two I hope make a lot of money. I got
the impressing that he did, okay, um by applying that
(23:57):
technology to cell phones. Um, and the way they describe
it as all the different things a cellphone can do,
if you were to have a different antenna for each
one of those functions, it would be like carrying around
a little porcupine. So what cell phones now are based
on is a fractal design called Manger sponge. Minger sponge, Yeah,
I think, man, and uh it's basically a box fractal.
(24:20):
And if you crack up in your little cell phone,
you're gonna see it wired that way. 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 recursive, self similar pattern. And you, friend, are
looking at a fractal. It's all around us. Yeah, Um,
it's also all around us in nature. There's uh in
(24:42):
that same uh documentary that NOVA program. There was a
team from I think University of Arizona. There's a team
of academics. Yeah, that was pretty cool. Who um, we're
trying to figure out if you predict the amount of
carbon capturing capacity an entire rainforest has just by measuring
UM and figuring out the self similar system that a
(25:05):
single tree in that rainforest UM has. That makes sense? Well,
it does, but it's kind of a leap. It's like, okay,
so as 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 UH system
found in that tree is similar to the the growth
(25:30):
of the trees in the rainforest as a whole. Pretty cool. Yes, UM.
(26:01):
Tumors in the human body. UH. One of the keys
to getting rid of of cancer is or any kind
of tumors. Spotting these tumors early on. But with our
ultrasound technology you can only get so small and so
detailed that you can't see some of these natural fractals
that you know, your blood vessels are fractals essentially, just
(26:21):
like the branches of a tree are UM. So they
are now using geometry too. Now if I'm not sure
if I got this right, but I think it shows up.
It shows the flow of the blood because ultrasound can
pick that up through these fractals when they can't even
pick up the vessels themselves. Is that right, early earlier
(26:43):
tumor spotting, which right, well, for all intents of purposes,
they're looking at the vessels by finding the blood because
they see where it's flowing. But yeah, depending on the
pattern that it follows. If it follows like a like
a tree branching shape, it's healthy, right, yeah. And then
the tumors, all the veins are all bent and crooking,
going in all crazy directions. The read out of a heartbeat, yeah,
(27:04):
it's not consistent. It's a fractical yeah. So they use
fractal analysis now to study your heart rate and use
that to better understand how arrhythmia happens through math. So
there's the especially with natural systems. That's kind of like
the biggest contribution that UM Fractal geometry is produced so far,
(27:27):
I think, aside from c G I is what medical
uh well, just the that whole understanding that was first
really kind of um voiced by Lewis Fry Richardson with
the coastline that there's, um, there are natural systems out
there that we can't really that we're not quite paying
attention to, we don't really know how to deal with that.
(27:50):
We're trying to apply something like Euclidean geometry to something
that you can't really use that for um. That that's
what fractal geometry is really contributed so far as basically say, hey,
there's a lot of natural systems out here that are
self similar and recursive, and now that we kind of
see in the fractal world, we see them everywhere and
(28:11):
we have a better understanding of them. And one of
the best examples of that, I thought was figuring out
how larger animals use less energy than smaller animals. They
use energy more efficiently, and um, this is a kind
of a biological paradox for a really long time, and
these guys figured it out using I guess kind of
(28:31):
the um same kind of insight that fractal geometry has.
That if you take genes and genes are the mathematical
formula or the equivalent of a mathematical formula, and you
uh feed in uh, these genetic processes, what it's going
to put out. Is this self similar recursive pattern to
(28:56):
where the bigger the organism is, the more this thing
goes and goes and goes, the less energy it's going
to use because there's more of it and it doesn't
require very much energy to produce past a certain point.
So if you have a very small animal, it's 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 your genetic code, right UM,
(29:22):
to carry out a very complex, seemingly complex UM system,
which is your organs or you as an organism. So
in the end, an elephant uses less energy than a mouse, yes,
because they're both using the same formula, the same input.
And then eventually you reach a point where it just
gets easier and easier and easier to to use something
(29:44):
simple to create a complex system. I love it. I
do too. Uh. I got one more thing. You heard
this guy, Jason Paget, Huh, this is pretty crazy. UM.
This guy like nine years ago, I think UM was
mugged and to come Washington got hit in the back
of the head really hard, knocked him out, and he
(30:05):
acquired UM a form of synesthesia in which he sees
fractals from being hit in the head. And um, basically
it's an acquired savant savantism, which is pretty rare to
acquire this later on. Um, and this guy hated math,
and his family used to make fun of him, he said,
(30:26):
because he was the worst at pictionary. Uh, I couldn't
draw a thing, couldn't draw a lick. Now, this guy
can draw reportedly mathematically correct fractals by hand, and he's
the only person on earth that can do this. And
you should see these things. They're like, you know, a
huge you know, two by two fractal that looks like
(30:50):
it was plotted by like a supercomputer. And this guy
does these by hand now out of nowhere because he
got hit on the head. That's pretty amazing. Yeah, it's crazy.
He got him in the fractal center. Huh he did.
That's strange that we would have like that ability latent
in us, you know. Yeah. Well, they studied his brain,
of course, UM, and they found that the two areas
that lit up in the left hemisphere were the areas
(31:13):
that control exact math and mental imagery. So they have
it well, and he's you know, he's fine with it,
although he says that he's a bit obsessive about it
because he's it's one of those deals where everywhere he
looks now he sees fractals. Oh yeah, Well, I got
the impression that people who are who are fractal geometers
have the same thing. Yeah, you know, they're like, click
(31:34):
at that cloud. I I can figure out how to
describe it completely. Yeah with math. Yeah, it's crazy, um.
And then it's everywhere canopies of the trees. Like. I
got that impression as well that once you start seeing
fractals in natural systems, like then everything becomes um fractals
and a lot simpler to understand. I realized today that
I have always doodled in fractals. Oh yeah, yeah, because
(31:56):
I can't really draw, so whenever I doodle, it's like
it's all aways been um little fractal shapes. Like I
would draw some kind of geometric shape, then split off
from that and make it smaller, and in the end
they're sort of like fractals. Oh your fractal tree that
you showed me, it's pretty awesome. So you got anything else?
Uh No, I would strongly urge you to read this
(32:20):
article a few more times. And then maybe go off
and read some more about fractals, because we definitely have
not covered all of it. I watched that Nova documentary. Yeah,
that's good stuff. What is it? Chasing the hidden dimentioned?
Is that what it's called? And you call it chasing
the dragon? Well, there's the dragon curve fractal. It's pretty boss,
That's right, it is boss. Um. So you want to
(32:40):
type fractals in the search bar how stuff works dot
com to start, and that will bring up this very
very good article. And I said search bar, which means
it's time for a listener mail. Josh, I'm gonna call this, uh,
don't eat your peanuts around me, jerk. Yeah. Remember when
the Air Traffic Control remark that never heard the announcement that, uh,
(33:03):
no one can eat peanuts on the plane. I've flown
a lot in my life and I've never heard that before.
So Ian Hammer writes in on the Air Traffic Control episode,
you were talking about peanuts being completely absent on some flights,
And as a person that is really allergic to peanuts,
I can shed some light. My allergy is bad enough
to wear the smell of peanuts, which is really just
(33:24):
the presence of peanut molecules in the air will cause
me to get itchy and swollen. Uh. In the case
that I am in contact with a peanut have the
superpower of becoming a balloon, and I'll swell up to
the point where I will be dead in a matter
of minutes. I can delay the anaphylactic shock for ten minutes,
give or take with an injection of epinephrin, and this
will only work twice twice in his life. I think, so, um,
(33:48):
if I do have a reaction, I have twenty minutes
plus the fifteen minutes I have before normal anaphylactic shock
would kill me. There really is in a way to
save me in that instance, unless I can be administered
the proper treatment that you can get only at a hospital.
Because you can imagine when a plane is at thirty
feet there's not much can be done to get me
to a hospital within that thirty five minute time frame.
(34:10):
So flying can be a pretty scary thing when someone
near you. Besides that they really want a peanut buttercup.
People do this sometimes and it's a real pain to
have to deal with. I just wanted to give you
guys an overview of peanut allergy sufferers when it comes
to flying. Keep up the incredible work. Look forward to
seeing a TV pilot Ian Hammer. So incredible, is right?
If we were insensitive to that, then all apologies. He
(34:34):
didn't indicate that, but I know we weren't. I just
remember being surprised. Yeah, I was surprised, but I knew
allergies could get bad. But man, that I think on
the plane, I was like, what I've known about this
since I saw an episode of Freaks and Geeks wherein
one of the characters almost died because like some bully
at school like gave him some peanuts. Oh yeah, was
that it was the Martin Star character, the analog to
(34:58):
Paul from Wonder Years, Okay, which was, Um, I can't
remember his name. I book for some weeks. Yeah, it's good,
good show. Um, well, let's see allergies. How about a
practice story if you know something about fractals that we don't,
or can correct us or explain it better than we did,
(35:18):
which I'm not sure that that's much of a long shot. Um,
we want to hear about it. You can tweet to
us at s Y s K Podcast. You can visit
us on Facebook at facebook dot com. Slash Stuff you
Should Know, or you can send us an email to
Stuff podcast at how stuff works dot com. Stuff you
(35:38):
Should Know is a production of iHeart Radio's How Stuff Works.
For more podcasts for my heart Radio, because at the
iHeart Radio app, Apple Podcasts, or wherever you listen to
your favorite shows.
How do folks, Charles W. Chuck Bryant here in the corral,
and I'm gonna last so up a Stuff you Should
Know select for you from June seventh, two thousand twelve.
Fractals Colin Whoa, this is a tough one for me.
I'm not gonna lie. Fractals is one of the toughest
episodes I've ever had to learn and research. And that's
where we're gonna revisit it right here, right now. Welcome
(00:25):
to Stuff you Should Know, a production of My Heart
Radios How Stuff Works. Hey, and welcome to the podcast.
I'm Josh Clark, hanging on by my fingernails with me
as always as Charles W. Chuck Bryant, doing much the
same as we are about to start speaking on stuff
(00:47):
you should know about. Fractals. Yea, more math theoretical, Matt
even Yeah, a new branch of geometry. It's non Euclidean
since you brought it up, Okay, very new. Euclidean geometry
was like three B C and fractals are so there's
(01:09):
a little bit of a gap there. There is a
little bit of a gap and uh, there's a lot
of animosity among the Euclideans towards Fractillians. They need to
loosen up and look at some of those far out pictures.
I know, you know it's funny. Did you watch um,
did you watch that one doc on? Yeah? Okay, did
you see the other? The Arthur C. Clark one. It
(01:31):
was made in like maybe eight s eighty seven and
it had nothing but like um delicate sound of thunder
rip off music going on the whole time. It was
really really trippy. Well, I posted a picture I don't
know if you saw today on the stuff you should
know all of the of the Mandel brought set. Its
beautiful it is and it's very cool. And I didn't
(01:52):
even say what it was. I just posted it, and
like I'd say, about half the people were like, very cool, man,
this is rad I love the Mantal brought set like
fractill talk about fractals. And then the other half were like,
well you guys tripping out like what you did a
grateful dead day. That's actually math, believe it or not.
But it does look very it's very tied eye in
nature and that's why the hippies like it. Plus also,
(02:14):
I mean, if you've ever seen a fractal play out
on a computer screen. Yeah. Um, so we are talking
about fractals. I don't I don't necessarily want to give
a disclaimer. Chuck and I are not theoretical mathematicians. We're
not even like normal mathematicians. I balanced my checkbook my
hand just to keep that little part of my brain going.
(02:36):
So I don't like forget how to add and subtract
later on in life. I make myself do that, and
I don't let myself jump ahead. I show my work. Yeah. Um,
and that's about the extent of math in my life normally. See,
I was the kid in math that when they said
you're not allowed to use calculators, I would go, like,
there are calculators in life, so why can't we use them. Yeah,
(02:58):
Like they made calculators so we didn't have to do maths, right.
But at the same time, I find that shoddy because
it's like, you're not you're not You're just circumventing learning something,
and it's like the calculators there to support you after
you know what you're doing. I disagree. Well, I think
this is a pretty prime example of like going around
(03:19):
to get to the end. So when when I was
researching this, I was like, Okay, well, they don't really
know what they're doing with this stuff yet, so we
can just totally be like, well it's it's there, anything
you wanted to be and nothing at all. And then
like I started looking a little more deeply into I'm like, oh, no,
they do kind of know what they're doing. We really
don't know what we're talking about. So I feel like
(03:40):
I have, just from researching this, a little bit, um
something of a grasp of what fractals are, a little
bit For those of you who who don't know what
we're talking about, like, take a second to um look
up just typing fractal and search images on your favorite
search engine and you'll be like, oh, yes, of course
it's a fractal um And that's what we're going to
(04:01):
talk about, because fractal fractals are a new field, like
we said, in geometry, and they do have use and
they have usefulness that I think people haven't even considered yet.
But the the stuff that they have figured out how
to use it for is pretty amazing stuff. Can I
say what a fractal is at least so people know
they should clear it all up? It is a geometric
(04:24):
shape that is self similar through infinite iterations in a
recursive pattern and through infinite detail exactly. So there you
have it. Boom, Do we need to even continue? No?
But um, and that sounds like really that put me off,
Like this article was pretty well done by a guy
named Craig Haggett. I don't know who that it is, freelancer.
I guess um, it's a pretty well done article. But
(04:44):
that a sentence like that can put a person off
pretty easy. And he even put it, you know, he
made a joke about it, like, oh, you know that,
you get it, you know whatever. But um, when you
think about it, if you take that apart, one of
the hallmarks of fractal fractals, um is that they are
a very complex result from a very simple system. And
(05:06):
there's like basically three hallmarks two fractals that you just
pointed out right. There is um self similarity, which is
if you if you cut a chunk, like a microscopic
piece of a fractal off and compare it to the
whole fractal, it's going to be virtually the same. Yeah,
(05:27):
like or a fern. And the cool thing about fractals
is is to me the coolest thing is that fractals.
The point they made in the Nova documentary is that
all of our math up until they discovered fractals and
described practicals was based on things that we basically created
and built. Like all geometry, right, Euclidean geometry, you have length, width,
(05:53):
and height, which should view the three dimensions, right, yes,
for like pyramids and buildings and combs and all those things.
And you it's extremely useful and we've done quite a
bit with this. But what Euclidean geometry, as far as
the fractal geometrists or geometers um insist, failed at is
(06:13):
when they said, okay, look at that mountain. That's a cone.
It's an imperfect cone, it's a rough cone, but it's
a cone shape, right, So yeah, Euclidean geometry holds sway.
What the fractal geometers say is, yeah, you could say
that it's a cone, but if you tried to measure
and describe it as such, you're not going to come
up with a very descriptive, a very um detailed description
(06:38):
of that mountain. So what's the point What fractal geometry
does is it says we're going to describe that mountain
in every little craig and peak possible. And so what
you have is the fractal dimension, which exists in conjunction
with length, widthin height. And what the fractal dimension describes
(06:59):
is the complex city of the object that exists within
those three dimensions as well. That's right. So finishing my point,
the cool thing about fractals is that everything that we
had done previously in geometry were because of things we've built.
Practicals help describe things that were have been here since
the beginning of time in nature, and one of the
(07:20):
truest examples of that is the fern. Right with self similarity.
You take a little snippet off of a fern, although
you shouldn't do that. Let's just look at it. Uh,
it's gonna look the same as the larger part of
the fern, and then the whole fern itself very self
similar but not necessarily exact. No, it can be. There
is a form of self similarity that is exact and precise,
(07:42):
but in nature that's rare, if not just completely not found. Right,
that's right. So you've got self similarity, which is the
smaller part is virtually the same or looks the same,
or structured the same as the whole UM. And this
process of self similarity UM going larger smaller in scale
is called recursiveness, right, And recursiveness is UM. Like you
(08:07):
know those paintings where it's like a guy I think
Stephen Colbert, the one that he gave to the Smithsonian
has recursiveness in it, where it's a man in a
painting standing in front of like a mantle, and above
the mantle is the painting that you're looking at, and
then it goes on and on and on and on
and on anything that's infinitely repeating, right, same with if
(08:28):
you're in a dressing room and there's a mirror on
either side of the wall, you just keep going on infinitely.
It's recursiveness and with fractals the recursiveness of self similarity. Right.
So there's two two traits. UM is produced through this
thing called iteration, that's right. And that's where you say,
here's the whole I'm gonna put it into this formula,
(08:53):
and the formula has has the formula. The output of
the formula produces the input for the next round of
that same formula. It's a loop exactly, so it's self
sustaining and it can go on infinitely recursion. Right. That's right.
So what we've just come up with is a fractal
(09:15):
is anything that has a self similar structure and it's
recursive through iteration. That's right. Okay, So um A, really
I came upon this kind of easy, one easier explanation
of a fractal from Ben wal Mandel brought site. He died,
by the way in two. He seemed like a pretty
good guy. He was definitely thinking different. Um. And the
(09:40):
way that Mandel brought described a really easy way to
think of a fractal is um. There's this thing called
the Serpinsky gasket, and you take a triangle and you
can combine them into a bunch of little triangles and
spaces triangular spaces that form a larger triangle. Right, So
(10:00):
that that one initial solid triangle is called the initiator,
that's the original shape, and then all those other triangles
combine that form that larger triangle or a self similar
version of that larger triangle to the original triangle. That's
called generator. Right. So the formula for creating a fractal
(10:21):
would be to go into that generator, the version that
has all the little smaller triangles that make up a
larger whole triangle. And say, all the ones that look
like the initiator, the original just solid black triangle, take
that out and swap it with the generator version, and
all of a sudden you have one that's exponentially more detailed.
(10:43):
There's more to it, And that's a fractal. That's all
there is to it. You know what else is a fractal?
What the coastline? Yeah, that was a big one. Lewis
Fry Richardson was an English mathematician early twenty century, and
he very brilliantly said, you know what, if you take
a yardstick and you measured the coastline of England, you're
(11:04):
gonna get a number. If you take a one ft
ruler and measure the coastline, you're gonna get a different number.
If you take a one inch ruler and measure the coastline,
you're gonna get a different number. And it's basically infinite
in that the smaller you go with your your unit
of measure or your tool is the larger number you're
(11:26):
gonna get. Because the coastline is so infinitely varied in
its little nooks and crannies, right exactly It's a very
cool way of thinking about it. There's a second part
of that to Chuck, is that so depending on the you,
what you're using, the measure, the tool you're using, the measure,
the number, the perimeter of that coastline could go on infinitely,
(11:47):
but it still contains the same finite amount of space
within its paradox. That is a big time paradox because
things aren't supposed to be infinite and finite at the
same time, right right, Um and uh Lewis Fry Richardson
he basically established in that coming up with that paradox,
this kind of revolution and thought that fractal geometry is
(12:09):
based on that. You can have the infinite mixed with
the finite. You can get it from pretty simple formulas
that create very increasingly complex systems, right Um. And Fry
wasn't the He wasn't He was the first guy to
really kind of put forth this idea of thought, but
he wasn't the first one to notice this paradox. Yeah,
(12:30):
and before people even knew they were fractals, there were
there were artists like da Vinci that saw this pattern
and tree branches that was um I know in the
Nova documentary and the article, they point out the uh
Katsu Chica Hokusai Japanese artists created the Great Wave off Kanagawa,
(12:52):
and uh those are fractals. It's a it's ocean waves
breaking and at the top of the crest of the
waves are a little self similar or waves breaking off
into smaller and smaller self similar versions. And that's a
natural fractal, or in this case, it's a depiction of one.
So they were you know, early African and Nabajo artists
were doing this and they didn't realize that they were
(13:12):
fractals and that there were fractals all around us. No,
they just saw crystals in a snowflake or another good one, yeah, exactly. Um,
they were just they saw that there was what they
were looking at was a repeating pattern that was self
similar and recursive. Right, yeah, that's it. That's a fractal, right. Yeah.
And and Ben Wha Mandel brought was the first one
(13:33):
to say, you know what, we can we can use
math equations to actually apply to this. And he was
a big star for a while, and then they sort
of turned on him and said, you know what, this
is all cool and trippy looking, but it's useless. Right,
and he said, oh yeah, screw you guys, watch this
and he wrote another book which started to uh give
(13:56):
some practical applications which are pretty exciting. UM. So the
whole thing, the whole principle that is based on UM
is that you can take a formula and plug in
a very simple UM, well, a relatively simple formula like
mantle Brod's formula. Will take that one. For example, his
(14:17):
is um ZED goes to ZED squared plus c. Right,
that's what it's called. If you're in England, zed, we
say z Z. Well, anyway, Zed goes to which is
and the goes to is the key right here. This
(14:37):
is what makes it fractal goes to means that um,
it's an error. It's an equal sign. It looks like
an equal sign with a part of an arrow pointing
towards ZED, the other point pointing towards the rest of
the formula, which means that the the there's that feedback
loop where it's like, okay, once you have the number
that this punches out, you have, you feed it back
(15:00):
can and you'll get another number and knows, just keep
going and going and going, and 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 iteration of that very simple formula.
(15:23):
UM and Mandel brought set Uh. This is the one
that's like it's probably the most famous one. That's the
one that the Deadheads like because it's like this crazy
juxtaposition between like black and like different colors and everything.
And with his formula, two things happen with the number
that you put in. It either goes towards zero or
(15:46):
it shoots off to the infinite. And what they did
for this for the the Mandel brought set fractals was
they assigned a color to a number based on how
quickly it goes off to towards infinity. Right, so let's
say that you have like four, If you plug four
into this and in ten generations, it'll it'll become an
(16:07):
infinite number. UM. Then say that that would be grouped
into a blue color like ten generations blue, eight generations
is red, ninety generations is orange. See what I'm saying. UM.
And then the other direction, like say if you put
in four point two or something like that, it'll go
towards zero and any number that eventually will go towards
(16:29):
zero is represented as black. So what you have then,
is this really intricate depending on where you're zooming in
or out on the fractal, this intricate change of colors,
and what you're really just seeing our numbers that are
plots on a plane, and that's your fractal, and then
the black parts are numbers that will eventually be be zero. Right,
(16:51):
And most of the mental mental brought set is black. Yeah,
but if you zoom in, like that's the whole point.
You zoom in on one of those little uh what
do we even call those little spikes? Uh? I guess
you could call it a plot. A plot, and it's
gonna look like what you just saw. And the Nova
documentary is very cool when they zoom in on these,
(17:13):
it's sort of mind blowing. Yeah, it is very I
strongly recommend watching that because they explain it way better
than us. Well, it helps to see it for sure,
Oh yeah, big time. So um or draw it as
I have done. It's a pretty nice little fract Yeah.
(17:53):
So we've talked about fractals, We talked about the Mandel
brought set, we talked about where they started to come
from um and the the idea. Remember Lewis fried Richardson,
he was talking about measuring the coastline and going off
into the infinite, but still containing a finite amount um.
A guy came after him named Helga von Coke. He
(18:15):
came up with a Coke snowflake, which is pretty cool.
If you take a straight line, or you take a triangle,
and then on each side of the triangle in the
middle you bust out the middle into another triangular hump.
You do that over and over and over again. It
goes off into infinity. Although it contains a finite amount
of space. The perimeter goes off to the infinite. A
(18:36):
guy named Georg Cantor came up with the cancer set,
which is you just take a straight line and you
take the middle out of it, and then for each
of those two lines that produces, you do the same
thing and it just keeps going on and on and
rather than going to nothingness like you're like, well, if
you take a six inch line, eventually you're gonna bust
it down and nothingness again. That doesn't happen. They found
(18:56):
that it goes off to the infinite. So they realized
Ben Wall mantel Brought was plugging all these into computers,
because that's what it took people realize this, Like George
Cantor um Man I hope that's how you say his
first name. He was he was working in the eighteen eighties,
Um Gaston Julio came up with the Julia sets for
producing a repeating pattern using feedback loop. All these guys
(19:19):
were like nineteenth century early twentieth century mathematicians and it
was strictly theoretical until the late seventies when guys like
Mantel Brought who worked at IBM, started feeding these things
into these new fangled computers and seeing the results like
this fractals like the mantel Brought set that he saw right,
(19:39):
So Um, almost immediately there was a practical use for
fractals that came in the form of c g I. Yeah.
They interviewed that one guy in the documentary um who
worked on the first c g I shot in motion
picture history, which was Star Trek to the Wrath of
(20:01):
con and Uh. He was tasked with making a c
g I uh land surface like mountain range and pretty
mind blowing with it. Yeah, and he did. I mean,
now you look back and it kind of looks silly,
but at the time it was completely revolutionary. And once
he learned about fractals in the geometry and the math
of fractals, it was pretty easy for him, and he
(20:23):
made it seem like he was like, oh, well, this
is the key, this is how you do it right.
So well, and it is kind of easy, especially if
you know what you're doing with computer programming and math,
because what you're basically doing to create a fractal generator
is teaching your computer to to do something within a
certain formula. That's your fractal formula, right, And so what
(20:44):
Lauren Carpenter, the guy who created the the Star Trek
to landscape for the first c G all c g
I shot ever, what he basically did was created a
computer program that said, hey, computer, I'm gonna give you
a bunch of triangles. Because I think that was the
earliest stuff he was working with. Um, I'm gonna give
you a bunch of triangles, and I want you to
(21:04):
take those triangles and generate a new fractal set from it, right,
And then I want you to do it again and
again and again, and then every third time I want
you to start turning them forty degrees, so it's going
to change the pattern slightly, and then all of a
sudden you have these infinite variations. The reason why when
(21:24):
you go back and look at that shot that it
still looks kind of you know today, is because the
computer he was working at didn't have the computing power
to do that many times. Now we have higher computer
computing power, and so what we're doing is telling our
computers to keep going and going and going, swapping out
that initiator, that one single black triangle everywhere it can
(21:47):
find it in this pattern, this pattern of triangles in
the fractal with a brand new fractal. So it's just
creating more and more and more and more fractals, which
creates a finer and finer and finer resolution, which makes
something look all the more real. Yeah, like the part
in the doc about the Star Wars, I was making
the lava splashing. It's amazing, Yes, it was because they
(22:08):
showed the first one they did it looks kind of plain,
and then once you fed it through this infinite feedback loop,
it just like shattered and and and uh, fractured, not fractaled,
although I want to say fractaled off and just look
more detailed, more detailed, more detailed, until it looked like
lava splashing. Right, it's pretty amazing. Well, that's where the
(22:28):
word fractal comes from. Is um Mandel brought coined in
to say, to indicate how the things fracture off and
they form irregular patterns. Um, you can create a fractal
that that is regularly repeating, but it doesn't look as natural.
And with like say, if you're creating lava, you've got
(22:52):
to have that one rule that like every third generation
kicks forty degrees or whatever the rule is. That just
kind of throws a little bit of dissimilarity and too
because if something is too self similar, it's not going
to look right. It's not gonna look natural, it's not
gonna look real, which kind of leads you to think, chuck.
Then that there is a an application for studying natural
(23:13):
phenomenon using fractals, right, while there are I guess all kinds, Um,
well this isn't so much natural. But the documentary interviewed
Nathan Cohen who was a ham radio operator and his
landlord said, dude, you can't have that huge antenna hanging
out of your apartment so he started bending wires a
(23:35):
straight wire into essentially a fractal and found that on
the very first go it got better reception, um, merely
by the fact that it was bent in that way
and it was self similar. So he eventually used that
two I hope make a lot of money. I got
the impressing that he did, okay, um by applying that
(23:57):
technology to cell phones. Um, and the way they describe
it as all the different things a cellphone can do,
if you were to have a different antenna for each
one of those functions, it would be like carrying around
a little porcupine. So what cell phones now are based
on is a fractal design called Manger sponge. Minger sponge, Yeah,
I think, man, and uh it's basically a box fractal.
(24:20):
And if you crack up in your little cell phone,
you're gonna see it wired that way. 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 recursive, self similar pattern. And you, friend, are
looking at a fractal. It's all around us. Yeah, Um,
it's also all around us in nature. There's uh in
(24:42):
that same uh documentary that NOVA program. There was a
team from I think University of Arizona. There's a team
of academics. Yeah, that was pretty cool. Who um, we're
trying to figure out if you predict the amount of
carbon capturing capacity an entire rainforest has just by measuring
UM and figuring out the self similar system that a
(25:05):
single tree in that rainforest UM has. That makes sense? Well,
it does, but it's kind of a leap. It's like, okay,
so as 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 UH system
found in that tree is similar to the the growth
(25:30):
of the trees in the rainforest as a whole. Pretty cool. Yes, UM.
(26:01):
Tumors in the human body. UH. One of the keys
to getting rid of of cancer is or any kind
of tumors. Spotting these tumors early on. But with our
ultrasound technology you can only get so small and so
detailed that you can't see some of these natural fractals
that you know, your blood vessels are fractals essentially, just
(26:21):
like the branches of a tree are UM. So they
are now using geometry too. Now if I'm not sure
if I got this right, but I think it shows up.
It shows the flow of the blood because ultrasound can
pick that up through these fractals when they can't even
pick up the vessels themselves. Is that right, early earlier
(26:43):
tumor spotting, which right, well, for all intents of purposes,
they're looking at the vessels by finding the blood because
they see where it's flowing. But yeah, depending on the
pattern that it follows. If it follows like a like
a tree branching shape, it's healthy, right, yeah. And then
the tumors, all the veins are all bent and crooking,
going in all crazy directions. The read out of a heartbeat, yeah,
(27:04):
it's not consistent. It's a fractical yeah. So they use
fractal analysis now to study your heart rate and use
that to better understand how arrhythmia happens through math. So
there's the especially with natural systems. That's kind of like
the biggest contribution that UM Fractal geometry is produced so far,
(27:27):
I think, aside from c G I is what medical
uh well, just the that whole understanding that was first
really kind of um voiced by Lewis Fry Richardson with
the coastline that there's, um, there are natural systems out
there that we can't really that we're not quite paying
attention to, we don't really know how to deal with that.
(27:50):
We're trying to apply something like Euclidean geometry to something
that you can't really use that for um. That that's
what fractal geometry is really contributed so far as basically say, hey,
there's a lot of natural systems out here that are
self similar and recursive, and now that we kind of
see in the fractal world, we see them everywhere and
(28:11):
we have a better understanding of them. And one of
the best examples of that, I thought was figuring out
how larger animals use less energy than smaller animals. They
use energy more efficiently, and um, this is a kind
of a biological paradox for a really long time, and
these guys figured it out using I guess kind of
(28:31):
the um same kind of insight that fractal geometry has.
That if you take genes and genes are the mathematical
formula or the equivalent of a mathematical formula, and you
uh feed in uh, these genetic processes, what it's going
to put out. Is this self similar recursive pattern to
(28:56):
where the bigger the organism is, the more this thing
goes and goes and goes, the less energy it's going
to use because there's more of it and it doesn't
require very much energy to produce past a certain point.
So if you have a very small animal, it's 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 your genetic code, right UM,
(29:22):
to carry out a very complex, seemingly complex UM system,
which is your organs or you as an organism. So
in the end, an elephant uses less energy than a mouse, yes,
because they're both using the same formula, the same input.
And then eventually you reach a point where it just
gets easier and easier and easier to to use something
(29:44):
simple to create a complex system. I love it. I
do too. Uh. I got one more thing. You heard
this guy, Jason Paget, Huh, this is pretty crazy. UM.
This guy like nine years ago, I think UM was
mugged and to come Washington got hit in the back
of the head really hard, knocked him out, and he
(30:05):
acquired UM a form of synesthesia in which he sees
fractals from being hit in the head. And um, basically
it's an acquired savant savantism, which is pretty rare to
acquire this later on. Um, and this guy hated math,
and his family used to make fun of him, he said,
(30:26):
because he was the worst at pictionary. Uh, I couldn't
draw a thing, couldn't draw a lick. Now, this guy
can draw reportedly mathematically correct fractals by hand, and he's
the only person on earth that can do this. And
you should see these things. They're like, you know, a
huge you know, two by two fractal that looks like
(30:50):
it was plotted by like a supercomputer. And this guy
does these by hand now out of nowhere because he
got hit on the head. That's pretty amazing. Yeah, it's crazy.
He got him in the fractal center. Huh he did.
That's strange that we would have like that ability latent
in us, you know. Yeah. Well, they studied his brain,
of course, UM, and they found that the two areas
that lit up in the left hemisphere were the areas
(31:13):
that control exact math and mental imagery. So they have
it well, and he's you know, he's fine with it,
although he says that he's a bit obsessive about it
because he's it's one of those deals where everywhere he
looks now he sees fractals. Oh yeah, Well, I got
the impression that people who are who are fractal geometers
have the same thing. Yeah, you know, they're like, click
(31:34):
at that cloud. I I can figure out how to
describe it completely. Yeah with math. Yeah, it's crazy, um.
And then it's everywhere canopies of the trees. Like. I
got that impression as well that once you start seeing
fractals in natural systems, like then everything becomes um fractals
and a lot simpler to understand. I realized today that
I have always doodled in fractals. Oh yeah, yeah, because
(31:56):
I can't really draw, so whenever I doodle, it's like
it's all aways been um little fractal shapes. Like I
would draw some kind of geometric shape, then split off
from that and make it smaller, and in the end
they're sort of like fractals. Oh your fractal tree that
you showed me, it's pretty awesome. So you got anything else?
Uh No, I would strongly urge you to read this
(32:20):
article a few more times. And then maybe go off
and read some more about fractals, because we definitely have
not covered all of it. I watched that Nova documentary. Yeah,
that's good stuff. What is it? Chasing the hidden dimentioned?
Is that what it's called? And you call it chasing
the dragon? Well, there's the dragon curve fractal. It's pretty boss,
That's right, it is boss. Um. So you want to
(32:40):
type fractals in the search bar how stuff works dot
com to start, and that will bring up this very
very good article. And I said search bar, which means
it's time for a listener mail. Josh, I'm gonna call this, uh,
don't eat your peanuts around me, jerk. Yeah. Remember when
the Air Traffic Control remark that never heard the announcement that, uh,
(33:03):
no one can eat peanuts on the plane. I've flown
a lot in my life and I've never heard that before.
So Ian Hammer writes in on the Air Traffic Control episode,
you were talking about peanuts being completely absent on some flights,
And as a person that is really allergic to peanuts,
I can shed some light. My allergy is bad enough
to wear the smell of peanuts, which is really just
(33:24):
the presence of peanut molecules in the air will cause
me to get itchy and swollen. Uh. In the case
that I am in contact with a peanut have the
superpower of becoming a balloon, and I'll swell up to
the point where I will be dead in a matter
of minutes. I can delay the anaphylactic shock for ten minutes,
give or take with an injection of epinephrin, and this
will only work twice twice in his life. I think, so, um,
(33:48):
if I do have a reaction, I have twenty minutes
plus the fifteen minutes I have before normal anaphylactic shock
would kill me. There really is in a way to
save me in that instance, unless I can be administered
the proper treatment that you can get only at a hospital.
Because you can imagine when a plane is at thirty
feet there's not much can be done to get me
to a hospital within that thirty five minute time frame.
(34:10):
So flying can be a pretty scary thing when someone
near you. Besides that they really want a peanut buttercup.
People do this sometimes and it's a real pain to
have to deal with. I just wanted to give you
guys an overview of peanut allergy sufferers when it comes
to flying. Keep up the incredible work. Look forward to
seeing a TV pilot Ian Hammer. So incredible, is right?
If we were insensitive to that, then all apologies. He
(34:34):
didn't indicate that, but I know we weren't. I just
remember being surprised. Yeah, I was surprised, but I knew
allergies could get bad. But man, that I think on
the plane, I was like, what I've known about this
since I saw an episode of Freaks and Geeks wherein
one of the characters almost died because like some bully
at school like gave him some peanuts. Oh yeah, was
that it was the Martin Star character, the analog to
(34:58):
Paul from Wonder Years, Okay, which was, Um, I can't
remember his name. I book for some weeks. Yeah, it's good,
good show. Um, well, let's see allergies. How about a
practice story if you know something about fractals that we don't,
or can correct us or explain it better than we did,
(35:18):
which I'm not sure that that's much of a long shot. Um,
we want to hear about it. You can tweet to
us at s Y s K Podcast. You can visit
us on Facebook at facebook dot com. Slash Stuff you
Should Know, or you can send us an email to
Stuff podcast at how stuff works dot com. Stuff you
(35:38):
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