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Is that really fractal in the sense of fractional dimension? Or is it just self-similar? I watched a video on this for 3b1b and it undid 30 years of thinking I
by FatActor 4y ago
Is that really fractal in the sense of fractional dimension? Or is it just self-similar? I watched a video on this for 3b1b and it undid 30 years of thinking I knew what "fractal" meant and now I know nothing.
- sfpotter 4y agoIf you really want something to be fractal, there needs to be a limiting process. You can't refine something infinitely in physical space, because of fundamental physical limits. So, you could say it is "only" self-similar. But this is kind of missing the point. The engineering benefits of something "being" fractal are realized in this case even though the limiting process terminates below a certain point.
- prvc 4y agoNo material object can be "fractal"--- it is just being used as a buzzword here.
- yarg 4y agoFractaloid would be a more accurate description. True fractals are self-similar regardless of scale.
- FatActor 4y ago> True fractals are self-similar regardless of scale. That's not true: the coastline of England is a well-known fractal and it has zero self-similarity. Self-similarity can be a property of some fractals, but it is not a requirement to be a fractal.