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.

Highlights

  • Fractal geometry and structures pervade our universe, living matter included

  • The word fractal was coined by Benoît Mandelbrot [1], who introduced the concepts of fractal geometry and fractal dimension

  • Mandelbrot retracted the definition given above because it would exclude many physical fractals and replace it introducing the concept of self-similarity: A fractal is a shape made by parts similar to the whole in some way [2]

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Summary

Introduction

Fractal geometry and structures pervade our universe, living matter included. The field of fractals has developed after the advent of fast digital computers which provides easy means for their study. Mandelbrot gave in 1982 a tentative definition of a fractal: A set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension. The latter are axiomatically 0 (zero) for a “point”, 1 (one) for a line, 2 (two) for a surface, etc. Mandelbrot retracted the definition given above because it would exclude many physical fractals and replace it introducing the concept of self-similarity: A fractal is a shape made by parts similar to the whole in some way [2] This definition entails scale invariance of the appearance of parts of a whole. Algorithms (or a set of definite rules) and may exhibit an infinite range of scale invariance

A Mathematical Fractal
Example of a Two Dimensional Fractal
Physical Fractal Aggregates
Nomenclature of Fractals
Computer Simulation of Aggregation
Low Gravity Powder Aggregates
Evaporation—Condensation Aggregation
Multiple Fractal Aggregations and Simulations
Concluding Remarks
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