In this notebook I am simulating diffusion limited aggregation, and calculate the objects fractal dimension, and multifractal spectrum and plot some interactive plots about the growing cluster and the attachment of particles to the cluster.
Steps:
- start with an aggregate made of one point.
- release particles randomly on a circle outside the bounding box of the aggregate.
- simluate Brownian motion until the particle reaches the aggregate, or it goes outside a larger circle.
I decided to implement the aggregate as a dictionary. The keys are the coordinates, and the values show the indices of the particles (temporal order). I find it more intuitive and flexibe than storing a grid.
I calculate the objects fractal dimension using the Correlation dimension. The expected result is
Simply using the definition, and multiple pivot points. The distances are running from 20 to 50. Vicsek et al uses 100x cutting at the edges, I don't have that large aggregate.
References
- Vicsek, T., F. Family, and P. Meakin. "Multifractal geometry of diffusion-limited aggregates." EPL (Europhysics Letters) 12.3 (1990): 217.
Author: Dezso Ribli