The word "fractal" seems to be used to invoke two subtly different ideas which I think it's worth distinguishing.

  • 1) Fractal represents the idea that a system is "structured" at different scalar-levels. In other words, if I look at it at scale "n" I see various types of clusters or repeated things. And if I look at scale "m" I see other types of clusters and repetitions.
  • 2) The idea that the system is structured at different scalar levels and the actual structures at different levels look the same.

It's this second effect we get in things like the Mandelbrot set etc. And in ScaleFree networks.

But I think it's the first if we think of a city. Yes, there's structure at the level of boroughs and at the level of buildings. But there's no claim that the structures or patterns at each level are somehow the same.

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