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Hilbert's Curve: Is infinite math useful?

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Further reading 1

What becomes visible when you change representation? →An average, a spectrum and a geometric diagram each foreground a different structure. Before asking which view is intuitive, ask which comparison you need it to support.This video helps answer · Is touching every pixel the same as filling the plane?

Caption notes

A finite approximation can visit every pixel without hitting every point within it. The square-filling object is the limit of a sequence of curves, not one particularly high-resolution rendering.

Creator’s caption track ↗
Original passages · 2
The output of the Hilbert curve function evaluated on this input is just defined to be the limit of those points.
Hilbert's Curve: Is infinite math useful? · ▶ 13:51–13:59
Instead it's the limit of all of them.
Hilbert's Curve: Is infinite math useful? · ▶ 9:40–9:42

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