For example, the image of the Peano curve completely fills the square.
2.
This process follows the Space Filling Peano Curve.
3.
The designs are either generalized Peano curves, or based on a new space-filling construction technique.
4.
The related random Peano curve outlining the uniform spanning tree was shown to converge to SLE with ? = 8.
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His thesis, " Peano curves and smoothness of functions ", was written under Adriano M . Garsia.
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The DNA Hilbert Peano curve is a 2D color image of a genomic sequence that can highlight all structures of interest in a sequence at once.
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For example, the image of a curve can cover a positive Lebesgue measure ( the last example can be obtained by small variation of the Peano curve construction ).
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Another bit of perspective might be gained by studying more pathological examples, like the Koch curve, Peano curve, and Weierstrass function . talk ) 20 : 09, 3 February 2008 ( UTC)
9.
Mandelbrot shows how to calculate the Hausdorff dimension of each of these curves, each of which has a dimension " D " between 1 and 2 ( he also mentions but does not give a construction for the space-filling Peano curve, which has a dimension exactly 2 ).
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