Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2004-01-14
Nonlinear Sciences
Adaptation and Self-Organizing Systems
8 pages, 4 figures, submitted to "Chaos, Solitons & Fractals"
Scientific paper
To seek for a possible origin of fractal pattern in nature, we perform a molecular dynamics simulation for a fragmentation of an infinite fcc lattice. The fragmentation is induced by the initial condition of the model that the lattice particles have the Hubble-type radial expansion velocities. As time proceeds, the average density decreases and density fluctuation develops. By using the box counting method, it is found that the frequency-size plot of the density follows instantaneously a universal power-law for each Hubble constant up to the size of a cross-over. This cross-over size corresponds to the maximum size of fluctuation and is found to obey a dynamical scaling law as a function of time. This instantaneous generation of a nascent fractal is purely of dynamical origin and it shows us a new formation mechanism of a fractal patterns different from the traditional criticality concept.
Chikazumi Shinpei
Iwamoto Akira
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