An Observation of a nascent fractal pattern in MD simulation for a fragmentation of an fcc lattice

Chikazumi, Shimpei*; Iwamoto, Akira

Chaos, Solitons and Fractals, 23(1), p.73 - 78, 2005/01

https://doi.org/10.1016/j.chaos.2004.03.002

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 patters different from the traditional criticality concept.