International Journal of Information Technology and Computer Science(IJITCS)

ISSN: 2074-9007 (Print), ISSN: 2074-9015 (Online)

Published By: MECS Press

IJITCS Vol.7, No.12, Nov. 2015

An Iterated Function System based Method to Generate Hilbert-type Space-filling Curves

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Ruisong Ye, Li Liu

Index Terms

Hilbert-type space-filling curve;iterated function system;fractal


Iterated function system has been found to be an important method to generate fractal sets. Hilbert space-filling curve is one kind of fractal sets which has been applied widely in digital image processing, such as image encoding, image clustering, image encryption, image storing/retrieving, and pattern recognition. In this paper, we will explore the generation of Hilbert-type space-filling curves via iterated function system based approach systematically. Cooperating a recursive calling of the common Hilbert's original space-filling curve at resolution n-1 and an IFS consisting of four affine transformations, one can generate the vertices for Hilbert-type space-filling curves at any resolution n. The merit is that the recursive algorithm is easy to implement and can be generalized to produce any other Hilbert-type space-filling curves and their variation versions.

Cite This Paper

Ruisong Ye, Li Liu,"An Iterated Function System based Method to Generate Hilbert-type Space-filling Curves", International Journal of Information Technology and Computer Science(IJITCS), vol.7, no.12, pp.12-22, 2015. DOI: 10.5815/ijitcs.2015.12.02


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