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4 Ways Fractals Changed Tech Forever - Video học tiếng Anh
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4 Ways Fractals Changed Tech Forever
4 Ways Fractals Changed Tech Forever
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0:00
Before they were called “fractals”, infinitely intricate shapes like the
0:04
Koch snowflake and the Sierpiński gasket were known as “monsters”.
0:08
At least to mathematicians who kept seeing their buddies
0:11
invent ever more complicated versions of the things.
0:13
But until the 1980s, fractals were bound to
0:16
the realm of so-called “pure” mathematics.
0:19
No one thought they existed in nature,
0:21
and there were no real-world applications.
0:23
This is, of course, not true.
0:25
Fractals are everywhere, from the edges of clouds,
0:28
to snowflakes, coastlines, even broccoli.
0:32
And what can you do with fractals? It turns out, quite a lot.
0:36
Over the last few decades, engineers have been busy
0:38
using fractals to solve all kinds of hard-hitting problems…
0:42
from boosting your 5G signal, to generating worlds in Minecraft.
0:47
[♪INTRO]
0:49
Before we get into any actual applications,
0:52
let’s take a quick trip back to the 80s,
0:53
when Benoit Mandelbrot was working at IBM.
0:56
By the way, Benoit used to joke that his middle initial was B,
1:00
and that the B in Benoit B. Mandelbrot
1:03
stood for Benoit B. Mandelbrot.
1:07
He made a fractal out of his own name.
1:10
Using some of the most powerful computers available at the time,
1:13
he started playing around with some mathematical functions
1:16
that would, under the right circumstances, act really weird.
1:20
Basically, all he had to do was take the output of a function
1:23
and then plug it back in to get a new output,
1:27
then plug that back in, over and over and over.
1:30
When he used a computer to print what one set of functions
1:33
actually looked like on a graph, out popped one of
1:36
the most iconic shapes in all of math: the Mandelbrot set.
1:40
By studying shapes like these, Mandelbrot discovered
1:43
what made them special: you can pick one spot on the edge
1:46
and no matter how long you zoomed in, that bit of edge
1:49
would never smooth out into a boring straight line.
1:52
You’d just see intricate shape after intricate shape.
1:55
Mandelbrot then noticed the same characteristic appears
1:58
in real-world shapes that don’t perfectly repeat themselves,
2:01
like coastlines or eddies in swirling water.
2:04
It was he who named these kinds of shapes fractals, and kicked off
2:09
a revolution in finding, understanding, and even creating new ones.
2:13
There are, in fact, infinitely many
2:15
fractals to keep mathematicians busy.
2:18
But we don’t have an infinite amount of time,
2:20
so let’s jump into our first application.
2:23
Many electronic devices use antennas to send and receive signals.
2:27
Whether they stick out like rabbit ears on top of a vintage television,
2:31
or get buried inside your smartphone, they’re usually a piece of metal
2:34
whose electrons wiggle in response to being hit by a radio wave.
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Those moving electrons create an electric current that
2:41
your device can convert into text, images, and sounds.
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And your device can, in turn, drive a current through
2:47
the antenna to send radio waves somewhere else.
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It turns out, if you shape an antenna like a fractal, it can act like
2:54
multiple different antennas in one awesome looking design.
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Those classic antennas that were basically just a straight line…
3:00
or maybe a handful of straight lines sticking out of one another…
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worked just fine for picking up a limited
3:06
set of specific radio wave frequencies.
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Think one metal stick for each frequency.
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But in the 21st century, we often want our devices
3:14
to keep track of a bunch of different frequencies.
3:17
Like if you want to pair your phone with your wireless earbuds,
3:20
call your mom, and book her tickets
3:22
for a BTS show in Vegas all at the same time.
3:25
Without fractals, you’d need a whole bunch of
3:27
different antennas on the same device.
3:29
And on devices we want to keep light…
3:32
say, microchip ID tags or drones…
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all that extra weight would be a problem.
3:37
But some fractals, like the Hilbert curve, snake around
3:40
with a whole bunch of length in a fairly tiny space.
3:43
This makes them really efficient at
3:44
packing an antenna into a small space,
3:47
a property mathematicians call a space filling curve.
3:51
In fact, even without creating a perfect fractal,
3:54
engineers are currently using patterns like those in the Hilbert curve
3:58
to squeeze more antenna length into smaller electronic spaces.
4:02
But the real magic comes from a fractal’s repeating patterns.
4:05
Thanks to a physics phenomenon called resonance,
4:08
different parts of the antenna with the same pattern,
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just larger or smaller, can wiggle in sync to create a clearer signal.
4:15
You couldn’t get that by just scrunching up
4:17
an antenna randomly into a small space!
4:19
Plus, when you’ve got the same
4:21
patterns repeating on different scales,
4:23
your antenna can resonate with different radio wave frequencies.
4:26
For example, in one paper from 2022, a research team describes
4:30
an antenna they made that’s just a few centimeters wide.
4:32
One side features a kind of Sierpinski gasket,
4:35
and the other a Hilbert Curve.
4:37
The team found their antenna did a good job receiving
4:40
signals over three different bands of frequencies
4:43
without any unwanted interference, which they say
4:46
makes it great for handling some kinds of 5G signal.
4:49
In the future, this might be used to improve
4:51
reception on our phones even more.
4:53
Which, honestly, there could use here in the mountains of Montana.
4:57
Fractals don’t just help us communicate, of course.
5:00
Engineers have also applied their weird
5:02
patterns to help keep tiny devices cool.
5:04
Stuff like fuel cells, or microchips that are used
5:07
to mix tiny amounts of chemicals in laboratory settings.
5:10
One traditional way of keeping technology from overheating,
5:14
be it a nuclear reactor or a refrigerator,
5:17
is to add plumbing that pushes a cooler-than-everything-else
5:20
liquid into a place it can absorb unwanted heat,
5:23
and then carries that heat away.
5:25
But this plumbing trick gets, well, tricky when we shrink things down.
5:30
The viscosity of liquids, or how easily they flow,
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starts to matter a whole lot more.
5:35
The further the liquid flows down those tiny tubes,
5:38
the more and more pressure you need to make it move,
5:41
and the harder it is to carry away heat properly.
5:44
Unless, of course, you make the whole thing a fractal!
5:47
Engineers have created heat exchangers with
5:49
a whole bunch of branches that splinter off into tinier parts,
5:53
sort of like the branches on a tree, or even a spider’s web.
5:56
At each branching-off point, the liquid that’s getting pushed through
5:59
the tubes experiences what scientists call pressure recovery.
6:03
It encounters a greater surface area and a smooth taper that
6:07
decreases the amount of pressure
6:08
needed to push it through each branch.
6:10
Plus at every one of those branches,
6:12
all the stuff flowing in the tubes gets mixed up.
6:16
This helps bring the hotter liquid traveling along the center of the
6:19
tubes out towards the walls, where it can lose its heat more easily.
6:23
It’s a lot like how stirring some piping hot tea helps it cool down.
6:27
Research suggests that with a fractal layout,
6:29
these kinds of heat exchangers can be
6:31
as much as 25% more efficient.
6:34
Which might not sound like a lot, but in tiny devices that tend
6:38
to malfunction when they get too hot, every bit helps.
6:41
Up next, a quick ad, brought to you by the antenna
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6:47
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7:31
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7:37
How did those researchers get the idea
7:39
to cool stuff down using fractal plumbing?
7:42
By noticing the fractal plumbing inside of you.
7:45
Many biological circulatory systems are fractal-like in nature,
7:49
from blood vessels, to sweat ducts, to the veins in a leaf.
7:53
And biomedical researchers have used this to develop diagnostic tech
7:57
that can tell you if you have a greater risk of developing a disease.
8:01
But to explain how this technology works,
8:03
we have to talk about a weird concept called fractal dimension.
8:06
Remember, the key feature of fractals are their
8:09
intricate patterns on lots of different scales.
8:12
Mathematicians want to find a way to capture that intricacy
8:15
and represent it with a single value, a single “dimension”,
8:19
which they can then use to compare fractals against one another.
8:22
One such way is called the box-counting dimension.
8:25
It starts with something straightforward: drawing boxes.
8:28
Imagine taking a sheet of paper and
8:30
drawing a square grid over the entire thing…
8:32
unless you’ve still got some graph
8:34
paper from math class lying around.
8:36
Draw a 2D shape. A circle, a hexagon, whatever.
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Then, count up how many of the grid’s
8:41
boxes overlap with your shape’s boundary.
8:44
For any overachievers out there,
8:46
you can also imagine doing the 3D version of this,
8:48
with a 3D grid and drawing a sphere or the ever nerdy d20.
8:53
Now, you may have realized that for the exact same shape,
8:56
you’ll get a different number of overlapping
8:58
boxes based on how small the boxes are.
9:01
But whatever the size of grid you’re using,
9:03
for simple shapes like lines, hexagons, and d20s,
9:07
the total number of overlaps will always scale
9:10
with the dimension each shape is in: 1, 2 or 3.
9:14
That doesn’t happen with fractals.
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A Sierpinski gasket, for example, comes out as 1.585.
9:22
Like it’s halfway between being a one-dimensional
9:24
shape and a two-dimensional shape.
9:26
The coastlines of various countries, for another example,
9:29
have a fractal dimension of about 1.1 to 1.3.
9:33
Researchers in the real world don’t have
9:35
to draw their own grids and shapes, of course.
9:37
They can program computers to do it for them, count up
9:40
the digital boxes and calculate a fractal’s dimension.
9:43
Which brings us back to blood vessels.
9:45
In a 2009 study, published in the journal Diabetes Care,
9:49
over 700 young people with Type 1 diabetes had
9:52
photographs taken of their retinas,
9:54
and the network of arteries and veins in the back of their eyes.
9:58
After cross referencing each participant’s unique fractal dimension
10:01
with their own health data, the team found that every 0.01 increase in
10:06
dimension carried a 40% increase in risk of developing retinopathy,
10:11
a condition that causes blurry vision,
10:13
or even blindness if left untreated.
10:16
Then, in a 2022 study from Frontiers of Digital Health,
10:19
a different group of researchers used the same idea
10:22
with more than 6,000 patients with Type 2 diabetes.
10:26
The results showed a higher fractal dimension
10:28
in retinal arteries came with an increased risk of dementia,
10:32
but a higher dimension for veins decreased risk of Alzheimer's.
10:36
Time will tell how this research may turn into
10:39
yet another test you take at the optometrist.
10:41
But in the meantime, I’m gonna ask my doctor to print out
10:44
my retina on some graph paper. I want to try something…
10:48
For our final entry, let’s cover something a bit more fun.
10:51
Or agonizing, if the hiss of a Creeper gives you a rush of anxiety.
10:55
Fractals are how games like Minecraft can present players
10:58
with endless systems of mountains and caves to explore,
11:02
without also being like 50 billion terabytes in size.
11:06
It all comes back to those funky math functions
11:08
Mandelbrot was studying in the 80s.
11:10
The ones that repeatedly act on their own output.
11:13
With just a tiny set of rules programmed into a computer,
11:16
you can create amazing looking fractals.
11:19
Like with a mere four equations,
11:21
you can generate a shape known as the Barnsley fern.
11:24
Programmers can use tricks like this to easily
11:27
generate all kinds of shapes with super fine details.
11:30
For example, to create its cave systems,
11:32
Minecraft uses a technique called Perlin noise.
11:35
By adding tiny, random changes to the numbers
11:37
that are plugged back into the functions at each step,
11:40
Perlin noise can make detailed structures on finer and finer scales.
11:44
And what’s extra nice is you don’t need a bunch of
11:46
complex structures stored in computer memory,
11:49
waiting for a player to stumble across them.
11:52
You can generate landscapes on the fly
11:54
when a player gets close enough!
11:55
If the player is far away, you use just a few iterations
11:58
to get something vaguely mountain-looking,
12:01
then apply more iterations to add further
12:03
detail as the player approaches.
12:05
Which is way kinder to your computer processor.
12:08
The same idea is used to give computer
12:10
generated objects more realistic textures, too.
12:13
That is, admittedly, less of a thing you
12:16
have to worry about in Minecraft.
12:17
But it’s also not exclusive to infinitely sprawling
12:20
video game worlds, or video game worlds at all.
12:23
Which I mention because of the people
12:25
who are currently shouting at the screen,
12:27
“Why didn’t you talk about CGI?!”
12:30
Like I said, the number of fractals is infinite,
12:32
but our time here today isn’t.
12:38
[♪OUTRO]
