Before they were called “fractals”,  infinitely intricate shapes like the Koch snowflake and the Sierpiński  gasket were known as “monsters”.

At least to mathematicians  who kept seeing their buddies invent ever more complicated  versions of the things. But until the 1980s, fractals were bound to the realm of so-called “pure” mathematics.

No one thought they existed in nature, and there were no real-world applications. This is, of course, not true. Fractals are everywhere, from the edges of clouds, to snowflakes, coastlines, even broccoli.

And what can you do with fractals?  It turns out, quite a lot. Over the last few decades,  engineers have been busy using fractals to solve all  kinds of hard-hitting problems… from boosting your 5G signal, to  generating worlds in Minecraft. [♪INTRO] Before we get into any actual applications, let’s take a quick trip back to the 80s, when Benoit Mandelbrot was working at IBM. By the way, Benoit used to joke  that his middle initial was B, and that the B in Benoit B.

Mandelbrot stood for Benoit B. Mandelbrot. He made a fractal out of his own name.

Using some of the most powerful  computers available at the time, he started playing around with  some mathematical functions that would, under the right  circumstances, act really weird. Basically, all he had to do was  take the output of a function and then plug it back in to get a new output, then plug that back in, over and over and over. When he used a computer to  print what one set of functions actually looked like on a graph, out popped one of the most iconic shapes in all  of math: the Mandelbrot set.

By studying shapes like  these, Mandelbrot discovered what made them special: you  can pick one spot on the edge and no matter how long you  zoomed in, that bit of edge would never smooth out into  a boring straight line. You’d just see intricate  shape after intricate shape. Mandelbrot then noticed the  same characteristic appears in real-world shapes that don’t  perfectly repeat themselves, like coastlines or eddies in swirling water.

It was he who named these kinds  of shapes fractals, and kicked off a revolution in finding, understanding,  and even creating new ones. There are, in fact, infinitely many fractals to keep mathematicians busy. But we don’t have an infinite amount of time, so let’s jump into our first application.

Many electronic devices use antennas  to send and receive signals. Whether they stick out like rabbit  ears on top of a vintage television, or get buried inside your smartphone,  they’re usually a piece of metal whose electrons wiggle in response  to being hit by a radio wave. Those moving electrons create  an electric current that your device can convert into  text, images, and sounds.

And your device can, in  turn, drive a current through the antenna to send radio waves somewhere else. It turns out, if you shape an antenna  like a fractal, it can act like multiple different antennas  in one awesome looking design. Those classic antennas that were  basically just a straight line… or maybe a handful of straight  lines sticking out of one another… worked just fine for picking up a limited set of specific radio wave frequencies.

Think one metal stick for each frequency. But in the 21st century, we often want our devices to keep track of a bunch of different frequencies. Like if you want to pair your  phone with your wireless earbuds, call your mom, and book her tickets for a BTS show in Vegas all at the same time.

Without fractals, you’d need a whole bunch of different antennas on the same device. And on devices we want to keep light… say, microchip ID tags or drones… all that extra weight would be a problem. But some fractals, like the  Hilbert curve, snake around with a whole bunch of length  in a fairly tiny space.

This makes them really efficient at packing an antenna into a small space, a property mathematicians  call a space filling curve. In fact, even without creating a perfect fractal, engineers are currently using patterns  like those in the Hilbert curve to squeeze more antenna length  into smaller electronic spaces. But the real magic comes from  a fractal’s repeating patterns.

Thanks to a physics phenomenon called resonance, different parts of the  antenna with the same pattern, just larger or smaller, can wiggle  in sync to create a clearer signal. You couldn’t get that by just scrunching up an antenna randomly into a small space! Plus, when you’ve got the same patterns repeating on different scales, your antenna can resonate with  different radio wave frequencies.

For example, in one paper from  2022, a research team describes an antenna they made that’s  just a few centimeters wide. One side features a kind of Sierpinski gasket, and the other a Hilbert Curve. The team found their antenna  did a good job receiving signals over three different bands of frequencies without any unwanted interference, which they say makes it great for handling  some kinds of 5G signal.

In the future, this might be used to improve reception on our phones even more. Which, honestly, there could use  here in the mountains of Montana. Fractals don’t just help  us communicate, of course.

Engineers have also applied their weird patterns to help keep tiny devices cool. Stuff like fuel cells, or microchips that are used to mix tiny amounts of chemicals  in laboratory settings. One traditional way of keeping  technology from overheating, be it a nuclear reactor or a refrigerator, is to add plumbing that pushes  a cooler-than-everything-else liquid into a place it can absorb unwanted heat, and then carries that heat away.

But this plumbing trick gets, well,  tricky when we shrink things down. The viscosity of liquids, or how easily they flow, starts to matter a whole lot more. The further the liquid  flows down those tiny tubes, the more and more pressure  you need to make it move, and the harder it is to carry away heat properly.

Unless, of course, you make  the whole thing a fractal! Engineers have created heat exchangers with a whole bunch of branches that  splinter off into tinier parts, sort of like the branches on a  tree, or even a spider’s web. At each branching-off point, the  liquid that’s getting pushed through the tubes experiences what  scientists call pressure recovery.

It encounters a greater surface  area and a smooth taper that decreases the amount of pressure needed to push it through each branch. Plus at every one of those branches, all the stuff flowing in the tubes gets mixed up. This helps bring the hotter liquid  traveling along the center of the tubes out towards the walls, where  it can lose its heat more easily.

It’s a lot like how stirring some  piping hot tea helps it cool down. Research suggests that with a fractal layout, these kinds of heat exchangers can be as much as 25% more efficient. Which might not sound like a lot,  but in tiny devices that tend to malfunction when they get  too hot, every bit helps.

Up next, a quick ad, brought to you by the antenna in your device that may or may not be a fractal. This SciShow video is supported by

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By noticing the fractal plumbing inside of you. Many biological circulatory  systems are fractal-like in nature, from blood vessels, to sweat  ducts, to the veins in a leaf. And biomedical researchers have  used this to develop diagnostic tech that can tell you if you have a  greater risk of developing a disease.

But to explain how this technology works, we have to talk about a weird  concept called fractal dimension. Remember, the key feature of fractals are their intricate patterns on lots of different scales. Mathematicians want to find a  way to capture that intricacy and represent it with a single  value, a single “dimension”, which they can then use to compare  fractals against one another.

One such way is called the box-counting dimension. It starts with something  straightforward: drawing boxes. Imagine taking a sheet of paper and drawing a square grid over the entire thing… unless you’ve still got some graph paper from math class lying around.

Draw a 2D shape. A circle, a hexagon, whatever. Then, count up how many of the grid’s boxes overlap with your shape’s boundary.

For any overachievers out there, you can also imagine doing the 3D version of this, with a 3D grid and drawing a  sphere or the ever nerdy d20. Now, you may have realized  that for the exact same shape, you’ll get a different number of overlapping boxes based on how small the boxes are. But whatever the size of grid you’re using, for simple shapes like lines, hexagons, and d20s, the total number of overlaps will always scale with the dimension each shape is in: 1, 2 or 3.

That doesn’t happen with fractals. A Sierpinski gasket, for  example, comes out as 1.585. Like it’s halfway between being a one-dimensional shape and a two-dimensional shape.

The coastlines of various  countries, for another example, have a fractal dimension of about 1.1 to 1.3. Researchers in the real world don’t have to draw their own grids and shapes, of course. They can program computers  to do it for them, count up the digital boxes and calculate  a fractal’s dimension.

Which brings us back to blood vessels. In a 2009 study, published  in the journal Diabetes Care, over 700 young people with Type 1 diabetes had photographs taken of their retinas, and the network of arteries and  veins in the back of their eyes. After cross referencing each  participant’s unique fractal dimension with their own health data, the team  found that every 0.01 increase in dimension carried a 40% increase  in risk of developing retinopathy, a condition that causes blurry vision, or even blindness if left untreated.

Then, in a 2022 study from  Frontiers of Digital Health, a different group of  researchers used the same idea with more than 6,000 patients  with Type 2 diabetes. The results showed a higher fractal dimension in retinal arteries came with  an increased risk of dementia, but a higher dimension for veins  decreased risk of Alzheimer's. Time will tell how this research may turn into yet another test you take at the optometrist.

But in the meantime, I’m gonna  ask my doctor to print out my retina on some graph paper.  I want to try something… For our final entry, let’s  cover something a bit more fun. Or agonizing, if the hiss of a  Creeper gives you a rush of anxiety. Fractals are how games like  Minecraft can present players with endless systems of  mountains and caves to explore, without also being like 50  billion terabytes in size.

It all comes back to those funky math functions Mandelbrot was studying in the 80s. The ones that repeatedly act on their own output. With just a tiny set of rules  programmed into a computer, you can create amazing looking fractals.

Like with a mere four equations, you can generate a shape  known as the Barnsley fern. Programmers can use tricks like this to easily generate all kinds of shapes  with super fine details. For example, to create its cave systems, Minecraft uses a technique called Perlin noise.

By adding tiny, random changes to the numbers that are plugged back into  the functions at each step, Perlin noise can make detailed  structures on finer and finer scales. And what’s extra nice is you don’t need a bunch of complex structures stored in computer memory, waiting for a player to stumble across them. You can generate landscapes on the fly when a player gets close enough!

If the player is far away,  you use just a few iterations to get something vaguely mountain-looking, then apply more iterations to add further detail as the player approaches. Which is way kinder to your computer processor. The same idea is used to give computer generated objects more realistic textures, too.

That is, admittedly, less of a thing you have to worry about in Minecraft. But it’s also not exclusive  to infinitely sprawling video game worlds, or video game worlds at all. Which I mention because of the people who are currently shouting at the screen, “Why didn’t you talk about CGI?!” Like I said, the number of fractals is infinite, but our time here today isn’t. [♪OUTRO]