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Related Experiment Video

Updated: May 30, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Off-lattice Eden-C cluster growth model.

C Y Wang¹, P L Liu, J B Bassingthwaighte

¹Departments of Mathematics and Physiology, Michigan State University, MI, USA.

Journal of Physics A: Mathematical and General

|September 28, 2011

Summary

This summary is machine-generated.

A novel cluster growth model, similar to the lattice-free Eden-C model, was developed. Computer simulations reveal a constant interior density and a fractal boundary with thickness scaling with the mean radius.

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Area of Science:

Physics
Materials Science
Computational Modeling

Background:

Cluster growth models are crucial for understanding pattern formation in various physical systems.
The Eden model and its variants are widely studied for their fractal properties.

Purpose of the Study:

To introduce and analyze a new non-trivial cluster growth model.
To investigate the scaling properties of the model's density and boundary.

Main Methods:

A lattice-free growth model was constructed by randomly adding contiguous, non-overlapping circles.
Large-scale computer simulations were employed to observe cluster evolution.

Main Results:

The interior density of the growing clusters was found to be constant at approximately 0.650.
The boundary of the clusters exhibited fractal characteristics.
The boundary thickness was observed to scale with the mean radius, following a power law with an exponent of 0.396.

Conclusions:

The proposed model offers a new perspective on cluster growth phenomena.
The findings highlight the interplay between constant density and fractal boundaries in this growth model.
The scaling exponent provides quantitative insight into the boundary's structure.