I know it’s not obvious from the title, but I’m pretty sure this idea could be used to create topologically-correct rectangular cartograms for arbitrary geographies and values. https://arxiv.org/pdf/1505.05785.pdf …
The tiles in the rectangular cartogram correspond to edges of a resistor network, right? Is there an easy way to see how to go from an arbitrary "geography" to the resistor network?
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Hmm. Yeah. Maybe it’s harder than I naively thought. There’s a distinction between horizontal and vertical adjacency, and maybe you can only guarantee to preserve one or the other, not both.
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Actually I don’t think that’s a problem, because the horizontal and vertical adjacencies are related by planar duality. You would have to decide, for each border, whether you wanted it to be horizontal or vertical on the cartogram.
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