Transcription
Did you know that math can be used to perfectly draw anything? Like anything. Your favorite meme, your signature, a detailed portrait. All of it can be drawn using a single massive equation.
To understand how this is possible, we have to go back to the early 1800s to a French mathematician named Joseph Fourier. He was studying how heat flows through a metal plate and he stumbled upon an idea that would change the world forever. Because he realized that any complex wave, no matter how messy or jagged or random it looks, can be broken down into a series of perfectly smooth, simple sine waves.
Think about the sound of my voice. Not how annoying it is. If you look at the audio waveform, it looks like pure chaos. A messy, jagged line jumping up and down. But Fourier's math proved that this messy line was actually just hundreds of perfect musical notes all playing at the exact same time, just at different volumes.
This discovery is called the Fourier transform and is the reason why your phone can compress photos and why MRI machines work and how noise canceling headphones work. A sine wave, when you look at it the right way, is actually just a circle spinning over time. So, what happens if we take all those simple waves and turn them back into circles?
If you take one big circle and attach a second, smaller circle to its edge and you let them both spin, you can start to draw shapes. The first big circle gives you the rough outline. The second circle, spinning a little faster, adds the curves. Then you attach a third circle and a fourth. This is called a Fourier series of epi cycles. And by perfectly tweaking the size and speed of every single circle, you can control exactly where the very last point ends.
If you only use three or four circles, you might get a rough squiggle. But if you chain enough of them together, you can mathematically calculate the exact path needed to draw any 2D shape in existence. Watch what happens when we unleash 500 spinning circles all running on a single massive mathematical formula. Every single loop is perfectly synchronized. They don't know what they're drawing, they just blindly follow the math racing at hyper speed to find their exact coordinate. This is pure mathematics stacking circles, and the craziest part is that this same math is constantly running in the background of your life holding together the modern digital world.