Take the graph of a square-filling parametrized path from [0,1] onto [0,1]x[0,1], as an object in [0,1]^3; does it in any meaningful sense have a Fourier transform? If so, perhaps the anisotropy of the graph would show up in the transform in some more localized fashion. Jim Propp On Tue, Aug 23, 2016 at 1:43 PM, Joerg Arndt <arndt@jjj.de> wrote:
* Bill Gosper <billgosper@gmail.com> [Aug 23. 2016 19:35]:
[...] Technically, these functions _are_ curves, being continuous images of one- dimensional sets. But people confuse curves with their graphs, and their graphs are blobs. [...]
Isn't that a non-problem resolved by differentiating between the "finite approximations" (certainly curves!) and the limits? Note how I dance around that by saying "shapes" (limits) and "iterates" (curves) in my arXiv paper.
Best regards, jj
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