Share This Article:

Mathematical and Physical Fractals

Abstract Full-Text HTML Download Download as PDF (Size:4623KB) PP. 1791-1800
DOI: 10.4236/am.2014.512172    2,902 Downloads   3,848 Views  

ABSTRACT

A review of the concepts developed about mathematical and physical fractals is presented followed by experimental results of the latter, considered to be a fourth state of matter which pervades the universe from galaxies to submicroscopic systems. A model of multiple fractal aggregation via a computer code is shown to closely simulate physical fractals experiments carried out in simulated and in real low gravity.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Slobodrian, R. (2014) Mathematical and Physical Fractals. Applied Mathematics, 5, 1791-1800. doi: 10.4236/am.2014.512172.

References

[1] Mandelbrot, B. (1982) The Fractal Geometry of Nature. Freeman, San Francisco.
[2] Mandelbrot, B. (1989) Les Objets Fractals, Forme, Hasard, Dimension. 3rd Edition, Flammarion, Paris.
[3] Cantor, G. (1883) über unendliche, lineare Punktmannigfaltigkeiten V. Mathematische Annalen, 21, 545-591.
http://dx.doi.org/10.1007/BF01446819
[4] Kolmogorov, A.N. and Tihomirov, V.M. (1993) Classics on Fractals. Addison-Wesley Pub. Co., Boston.
[5] Rioux, C., Potvin, L. and Slobodrian, R.J. (1995) Particle-Particle Aggregation with 1/r2 Forces in Reduced Gravity Environments. Physical Review, E52, 2099.
http://dx.doi.org/10.1103/PhysRevE.52.2099
[6] Blum, J., et al. (2000) Growth and Form of Planetary Seedlings: Results from a Microgravity Aggregation Experiment. Physical Review Letters, 85, 2426.
[7] Slobodrian, R.J. (2013) Metallic Fractal Aggregates and Monomers. LAP LAMBERT, Saabrücken.
[8] Brack, M. and Bhaduri, R.K. (1997) Semiclassical Physics. Addison Wesley, Boston.
[9] Bohr, N. (1923) über die Anwendung der Quantentheorie auf den Atombau. Zeitschrift für Physik, 13, 117-165.
http://dx.doi.org/10.1007/BF01328209
[10] Pietronero, L. (Ed.) (1989) Fractals’ Physical Origin an Properties. Plenum Press, New York.
http://dx.doi.org/10.1007/978-1-4899-3499-4
[11] Grassberger, P. (1990) Information and Complexity Measures in Dynamical Systems. Plenum Press, New York.
[12] Task Group on Fundamental Physics and Chemistry (1988) Space Science in the Twenty First Century: Imperatives for the Decades 1995 to 2015. National Academy Press, Washington D.C.

  
comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.