Peano curves Do you know what Peano curve is? Peano curve is the first example of space-filling curve or any continuous mapping of numerical interval onto flat square. The first such curve was constructed by Italian mathematician Giuseppe Peano in 1890 (Algorithm of construction for this curve can be found here en.wikipedia.org/wiki/Peano_curve). A year later, David Gilbert proposed his space-filling curve, which became more famous because of its symmetry and simplicity of construction. Now all such curves are called Peano curves. Like all fractals, Peano curves are widely used in various fields of modern science (for example, in computational mathematics for numerical integration of functions of several variables). By the way, scientists from Harvard University in the United States came to the conclusion that DNA fills every cell so that its spatial design approaches the design of a Peano curve. Also these curves are applied in Graph Theory, image processing. John Bartholdi in his article described application of a Peano curve to the traveling salesman problem. He proposed to impose the Peano curve on the city scheme and visit points in the same sequence as they are visited by Peano curve. Construction of the Hilbert curve sciencemag.org/content/326/5950/289 crd.lbl.gov/assets/pubs_presos/LBNL-63126.pdf
Posted on: Tue, 12 Aug 2014 08:30:00 +0000
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