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[Licence| Download | New Version Template] aeeg_v3_0.tar.gz(12250 Kbytes)
Manuscript Title: Hyper-Fractal Analysis: Visual tool for estimating the fractal dimension of 4D objects
Authors: I.V. Grossu, I. Grossu, D. Felea, C. Besliu, Al. Jipa, T. Esanu, C.C. Bordeianu, E. Stan
Program title: Hyper-Fractal Analysis (Frcatal Analysis v03)
Catalogue identifier: AEEG_v3_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 184(2013)1344
Programming language: MS Visual Basic 6.0.
Computer: PC.
Operating system: MS Windows 98 or later.
RAM: 100M
Supplementary material: The Figure 1 mentioned below can be viewed here.
Keywords: Hyper fractal analysis, 4D box-counting algorithm.
Classification: 14.

Does the new version supersede the previous version?: Yes

Nature of problem:
Estimating the fractal dimension of 4D images.

Solution method:
Optimized implementation of the 4D box-counting algorithm.

Reasons for new version:
Inspired by existing applications of 3D fractals in biomedicine [3], we extended the optimized version of the box-counting algorithm [1,2] to the four-dimensional case. This might be of interest in analyzing the evolution in time of 3D images.

Summary of revisions:
  1. Extend the box-counting algorithm in order to support 4D objects, stored in comma separated values files
  2. A new form was added for generating 2D, 3D, and 4D test data

Additional comments:
  1. The application was tested on 4D objects with known dimension, e.g. Sierpinski Hypertetrahedron Gasket, Df = ln(5)/ln(2) (Fig.1.)
  2. The algorithm could be extended, with minimum effort, to higher number of dimensions.
  3. Easy integration with other applications by using the very simple comma separated values file format for storing multi-dimensional images
  4. Implementation of X2 test as a criteria for deciding if an object is fractal or not.
  5. User friendly graphical interface.

Running time:
In a first approximation, the algorithm is linear [2].

References:
[1] I.V. Grossu, D. Felea, C. Besliu, Al. Jipa, C.C. Bordeianu, E. Stan, T. Esanu, Computer Physics Communications, 181 (2010) 831-832
[2] I.V. Grossu, C. Besliu, M.V. Rusu, Al. Jipa, C. C. Bordeianu, D. Felea, Computer Physics Communications, 180 (2009) 1999-2001
[3] J. Ruiz de Miras, J. Navas, P. Villoslada, F.J. Esteban, Computer Methods and Programs in Biomedicine, 104 Issue 3 (2011) 452-460