Fractal Dimension of Backbone of Eden Trees

TL;DR

This paper explores the fractal and spectral dimensions of Eden trees' backbones and introduces a novel numerical method to estimate the dynamical exponent z in three dimensions, providing precise measurements.

Contribution

It establishes a relationship between fractal/spectral dimensions and the dynamical exponent z, offering new insights and a numerical approach for three-dimensional Eden trees.

Findings

Fractal dimension of backbone in 2D is 4/3.

Spectral dimension of Eden trees in 2D is 5/4.

Estimated dynamical exponent z in 3D is 1.617 ± 0.004.

Abstract

We relate the fractal dimension of the backbone, and the spectral dimension of Eden trees to the dynamical exponent z. In two dimensions, it gives fractal dimension of backbone equal to 4/3 and spectral dimension of trees equal to 5/4. In three dimensions, it provides us a new way to estimate z numerically. We get z=1.617 +/- 0.004.