Abstract
The author simulates a new type of aggregation process: particles follow deterministic trajectories. The trajectories have a fractal dimension, dw, of two. dw is defined as S(r) approximately rdw, where S(r) is the total number of sites a particle visits while travelling a distance r. When the growth process is started with a single stationary particle on a square lattice, a large aggregate looks like diffusion-limited aggregation (DLA). The fractal dimension, df, of the aggregate is nearly equal to 1.7; that of DLA is 1.67+or-0.05. Moreover, the aggregate has axial anisotropy, although it includes less than one thousand particles. Therefore the aggregation belongs to the same universality class of DLA and is supposed to be the highly noise-reduced model for DLA. Because the Laplace equation has no relationship to the aggregation process, the Laplace equation does not seem to be a necessary condition for producing aggregates like DLA.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.