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Hilbert’s space filling curves and geodesic laminations. (English) Zbl 1047.28006
Summary: We present a modified version of the classical Hilbert’s space filling curve and we associate to this curve a geodesic lamination on the disk together with a transversal measure. The lamination helps us to understand how the points of the interval are mapped to the square. We generalize this construction to space filling curves from the interval to the regular \(n\)-gon.

MSC:
28A80 Fractals
26A27 Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives
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