It certainly has a different density of intersections with a diagonal line relative to a line along the principal axes. Brent On 8/22/2016 4:24 PM, James Propp wrote:

What sorts of anisotropy does the Peano curve exhibit, from which its origins as a limit of paths on ever-finer square grids could be deduced?

I mention the Peano curve for definiteness, but I intend my question to be taken in a more general context.

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