Until infinity?
As you keep zooming in, you think: it's a point! No, it's a line! No, it's a rectangle! No, it's a bunch of points! No... It's a subset of the plane invented by Simon Willerton, which shows that your estimate of the dimension can keep changing as you zoom in more and more.pic.twitter.com/Qn8LhnToNK
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Yes. Or until you stop watching.
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What would this mean for fractals?
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This is a nice example of a space that doesn't have a well-defined fractal dimension. It requires these ideas: Simon Willerton, A scale-dependent notion of dimension for metric spaces (part 1), The n-Category Café, March 11, 2015. https://golem.ph.utexas.edu/category/2015/03/a_scaledependent_notion_of_dim.html …
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I think
@3blue1brown once had the example of a cylinder, that turns out to be a helix (e.g. curved line), that turns out to be a curved thin cylinder, etc.Hvala. Twitter će to iskoristiti za poboljšanje vaše vremenske crte. PoništiPoništi
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Hvala. Twitter će to iskoristiti za poboljšanje vaše vremenske crte. PoništiPoništi
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This is why the box-counting dimension does not work for all spaces.
Hvala. Twitter će to iskoristiti za poboljšanje vaše vremenske crte. PoništiPoništi
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This just looks like a non-overlapping IFS with a * b generators each using a scale factor of S where S is how far you zoom between identical, unique frames. So dimension should just be log(a*b)/log(S), like any other simple IFS. Right?
Hvala. Twitter će to iskoristiti za poboljšanje vaše vremenske crte. PoništiPoništi
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Topologically, looks like a Cantor set (or Cantor set x Z).
Hvala. Twitter će to iskoristiti za poboljšanje vaše vremenske crte. PoništiPoništi
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Same as we two dimensional moon. And stars as a point.
Hvala. Twitter će to iskoristiti za poboljšanje vaše vremenske crte. PoništiPoništi
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Čini se da učitavanje traje već neko vrijeme.
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