An intelligent approach for curve filling

Issue title: Special Section: Iteration, Dynamics and Nonlinearity

Guest editors: Manuel Fernández-Martínez and Juan L.G. Guirao

Article type: Research Article

Authors: Fernández-Martínez, Manuel^{a; *; 1} | Guirao, Juan L.G.^{b; 1}

Affiliations: [a] University Centre of Defence at the Spanish Air Force Academy, MDE-UPCT, Santiago de la Ribera, Murcia, Spain | [b] Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Hospital de Marina, Cartagena, Murcia, Spain

Correspondence: [*] Corresponding author. Manuel Fernández-Martínez, University Centre of Defence at the Spanish Air Force Academy, MDE-UPCT, 30720 Santiago de la Ribera, Murcia, Spain. E-mail: fmm124@gmail.com.

Note: [1] Both authors have been partially supported by Grants No. 19219/PI/14 from Fundación Séneca of Región de Murcia and No. MTM2015-64373-P from Spanish Ministry of Economy and Competitiveness.

Abstract: In this paper, we highlight an intelligent system to properly construct a function between a pair of generalized-fractal spaces: the d-cube [0, 1] d endowed with its natural fractal structure, and the closed unit interval endowed with a natural-like fractal structure. Such a function allows the definition of space-filling curves by levels as well as the calculation of the box dimension of higher dimensional subsets through the box dimension of subsets on the real line.

Keywords: Fractal, fractal dimension, box-counting dimension, fractal structure, space-filling curve, Hilbert curve, Sierpinśki gasket

DOI: 10.3233/JIFS-169716

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 4, pp. 3931-3936, 2018