AM  Vol.5 No.12 , June 2014
Mathematical and Physical Fractals
Author(s) R. J. Slobodrian

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.

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

[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.

[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.

[10]   Pietronero, L. (Ed.) (1989) Fractals’ Physical Origin an Properties. Plenum Press, New York.

[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.