Fractal Dimension of Backbone of Eden Trees

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.

6 pages, Latex, and 4 postscript figures, uuencoded. Minor typographical errors, and problems with postscript files fixed

References in corpus (4)

• Continuum Model for River Networks
• A quasi-random spanning tree model for the early river network
• Diffusion and spectral dimension on Eden tree
• Scaling Exponents for Driven Two-Dimensional Growth

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