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National Repository of Grey Literature 1 records found  Search took 0.00 seconds. 
Space filling curves
 Štěpánek, Adam ; Hencl, Stanislav (advisor) ; Pyrih, Pavel (referee)
Peano curves are continuous mappings from the unit interval [0, 1] onto the n- dimensional square [0, 1]n , n ∈ N. There are many such curves and therefore we focuses especially on the Hilbert curve. We informally outline its geometrical interpretation and then we describe the construction in R2 by writing a number in a quaternary form. For such defined mapping we prove that it is a Peano curve and that it is 1/2 - Hölder con- tinuous. In conclusion, using the Haussdorf dimension, we show that there is no Peano curve in Rn that is also α - Hölder continuous for α > 1/n. 1
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