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[arturis]

I've heard two people recently refer to something as a "fractal phenomenon" because it shows the same trend at all timescales. For the record, that is a crappy metaphor. Fractals are not remarkable for being the same at all levels of magnification, in fact the opposite is true.

Y'know what is known for showing the same trend at all levels of

Comments

[anadamous]

*snap* *snap* *snap*

[tarq]

Fractals are not remarkable for being the same at all levels of magnification, in fact the opposite is true.

Isn't the defining feature of a fractal that it is "A geometric figure that repeats itself under several levels of magnification"? It doesn't look the same at all scales, but it exhibits the same trends, it's those trends that themselves define the shape of the fractal.

What I think is going on here is that while a fractal isn't visually the same at all scales, it is a direct result of repetition across those scales.

I don't know what the "fractal phenomenon" is referring to, but if it is something that has similarities or resemblance on different scales, I think it fits. I would argue that a Sierpiński Triangle looks very similar at all scales. Not every fractal is as varied as a Mandelbrot.

I did dig up a nice YouTube video zoom of a Mandelbrot, however.

http://www.youtube.com/watch?v=G_GBwuYuOOs

[arturis]

Well, the problem is that that isn't what makes fractals unique. Lots of shapes do that, like for instance an infinite number of nested squares. Or a spiral. Or as I already said, a straight line. Fractals are remarkable for much more specific esoteric mathematical reasons. And then of course there are things like the Mandelbrot set that are notably patterned at every level, but not by the same pattern.

[tarq]

Man they're cool.

[radiks]

But if one were choosing to show/compare a trend or metaphor. How do we know that it didn't involve a Mandelbrot set? ...I don't think we have enough to go on without the original two examples...