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Today we will learn about the infinite beauty behind fractals. Draw a line, now draw a curved
line off of that line, and keep drawing straight lines and curved lines off of those lines.
And, again, you can repeat this process forever. Literally: you can keep going forever. Anyway,
let's try something else. Let's draw an equilateral triangle, split it into three, split those equilateral
triangles into three and keep doing this, and again, this is an infinite process that
goes on forever. And that's what we call in mathematics and infinite process, because
it goes on forever. Literally. Let's try something else: let's do something called the Koch curve.
If you draw one line, then draw a triangle on that line, and then you just keep drawing
triangles on the line. And again, this is also an infinite process: it goes on forever
and forever and forever and forever. Now, if you keep zooming in, you will see this
pattern repeated again and again and again and again. You can zoom into infinity, and
you still get this. That's why we can say - if it's actually an English word - that
this is infinitely zoomable, because you can zoom into it an infinite amount of times,
and it will still repeat itself. Now, normally we didn't know what these things would look
like. In fact, those are only really basic forms of fractals. You can get things like
the Mandelbrot curve, which also helps in computer generated imagery. Nowadays, we are
able to zoom into those more complex fractals with amazing detail, because of our modern
technologies. So, that's what fractals are: the infinitely small shapes: because you can
zoom into them an infinite amount, and they will still look the same, or have repeated
patterns. SUBSCRIBE! I don't know if anyone was wondering this, but this is how I film
these videos. I have two stools: one of them wooden, and one of them metal and plastic
- both from IKEA. I have two books, on top of which I have my iPad stand. So, just to
put it into perspective, this is the paper that I was using for this video. So you've
got all of the stuff there. If I put this on here. And then it would move around something
like that. That is how I make my videos.