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HilbertCurve

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Line through all cells of the 2^n x 2^n grid in Hilbert order (integer grid; DataRange maps to reals)

HilbertCurve[n]
HilbertCurve[n, d]
Graphics[HilbertCurve[2]] → -Graphics-Table[RegionMeasure[HilbertCurve[n]], {n, 5}]//Rationalize → {3, 15, 63, 255, 1023}Graphics[{Thickness[Large], HilbertCurve[4] /. Line -> BSplineCurve}] → -Graphics-
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