Scale-free patterns are fractal

Imagine the pattern of a flock of starlings. The essential dynamics of the flock is identical whether the flock is made of fifty birds, five hundred, or five thousand. That’s because the system dynamics are “such that the numbers can be scaled up or down without changing the character of the whole.”^[1]

The technical term for this property is “scale free,” meaning that the thing is basically the same no matter what size it is. This gives you the magic of what I call “scale-free scalability,” meaning you can scale up or down following the same principles independently of where you are scale–wise, which is exactly what you want in order to build something huge with ease. The mathematician Benoit Mandelbrot, who first laid out the science of scale-free scalability, called this attribute “fractal”—like one of those popular Internet memes in which you see a pattern, then zoom into a detail within the pattern and discover that it looks the same as the pattern as a whole, and you keep zooming in and keep discovering the same pattern.^[2]

#systems #mathematics #networks