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Multifractals in ecology using R

tags: real-examples math equations


Description/Summary

Disclaimer This post is from the link posted by GitHub user lsaravia in this comment. All credit for this post goes to the original author. Multifractals Many natural systems cannot be characterized by a single number such as the fractal dimension. Instead an infinite spectrum of dimensions must be introduced. Multifractal definition Consider a given object \(\Omega\), its multifractal nature is practically determined by covering the system with a set of boxes \(\{B_i( r)\}\) with \((i=1,…, N( r))\) of side length \(r\) These boxes are nonoverlaping and such that


Content

Disclaimer
This post is from the link posted by GitHub user lsaravia in this comment. All credit for this post goes to the original author.

Multifractals

Multifractal definition

Box counting

The generalized dimensions

Generalized dimensions 1

Exercise

Two important dimensions

Application

Mass exponent and Hurst exponent

Paper

  1. Kellner JR, Asner GP (2009) Convergent structural responses of tropical forests to diverse disturbance regimes. Ecology Letters 12: 887–897. <10.1111/j.1461-0248.2009.01345.x>.

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