Fractals are typically not self-similar
What fractal dimension is, and how this is the core concept defining what fractals themselves are. Patreon page: https://www.patreon.com/3blue1brown Special ...
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[Intro] Who doesn't like fractals? They're a beautiful blend of simplicity and complexity often including these infinitely repeating patterns. Programmers in particular tend to be especially fond of them, because it often takes a shockingly small amount of code to produce images that are way more intricate than any human hand ever could hope to draw. But a lot of people don't actually know the definition of a fractal; at least not the one that Benoit Mandelbrot, the father fractal geometry, had in mind. A common misconception is the fractals are shapes that are perfectly self-similar. For example this snowflake looking shape right here called the Von Koch snowflake, consists of three different segments, and each one of these is perfectly self-similar, in that whe...
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[Intro] Who doesn't like fractals? They're a beautiful blend of simplicity and complexity often including these infinitely repeating patterns. Programmers in particular tend to be especially fond of them, because it often takes a shockingly small amount of code to produce images that are way more intricate than any human hand ever could hope to draw. But a lot of people don't actually know the definition of a fractal; at least not the one that Benoit Mandelbrot, the father fractal geometry, had in mind. A common misconception is the fractals are shapes that are perfectly self-similar. For example this snowflake looking shape right here called the Von Koch snowflake, consists of three different segments, and each one of these is perfectly self-similar, in that whe...
