Self-similarity of space filling curves Report as inadecuate

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Luis E. Múnera ;Ingeniería y Competitividad 2016, 18 2

Author: Luis F. Cardona



Ingeniería y Competitividad ISSN: 0123-3033 Universidad del Valle Colombia Cardona, Luis F.; Múnera, Luis E. Self-Similarity of Space Filling Curves Ingeniería y Competitividad, vol.
18, núm.
2, 2016, pp.
113-124 Universidad del Valle Cali, Colombia Available in: How to cite Complete issue More information about this article Journals homepage in Scientific Information System Network of Scientific Journals from Latin America, the Caribbean, Spain and Portugal Non-profit academic project, developed under the open access initiative Ingeniería y Competitividad, Volumen 18, No.
2, p.
113 - 124 (2016) COMPUTATIONAL SCIENCE AND ENGINEERING Self-Similarity of Space Filling Curves INGENIERÍA DE SISTEMAS Y COMPUTACIÓN Auto-similaridad de las Space Filling Curves Luis F.
Cardona*, Luis E.
Múnera** *Industrial Engineering, University of Louisville.
KY, USA. ** ICT Department, School of Engineering, Department of Information and Telecommunication Technologies, Faculty of Engineering, Universidad Icesi.
Cali, Colombia.*,** (Recibido: Noviembre 04 de 2015 – Aceptado: Abril 05 de 2016) Abstract We define exact self-similarity of Space Filling Curves on the plane.
For that purpose, we adapt the general definition of exact self-similarity on sets, a typical property of fractals, to the specific characteristics of discrete approximations of Space Filling Curves.
We also develop an algorithm to test exact selfsimilarity of discrete approximations of Space Filling Curves on the plane.
In addition, we use our algorithm to determine exact self-similarity of discrete approximations of four of the most representative Space Filling Curves.
We found that SFCs like Moore’s based on recursive structure are actually not selfsimilar, highlighting the need to establish a formal definition of the concept for SFCs. Keywords: Fractals, self-s...

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