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Physics in Computer
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Rubio, John Kenneth V. AP 1562012 – 46175 09/08/15
There are different methods of solving fractal dimension aside from the box counting method that was discussed. These methods are:
1. Fractal SignatureThis signature of an image is the change in a measured area with a changing scale. For a pure fractal gray image, the area A at a scale e is given by
A (ε )=F ε 2−D,
where ε is the resolution of the gray levels in the image, D is fractal dimension and F is a constant [1].
2. Information DimensionThe information function I is defined to be
I ≡−∑i=1
N
P i (δ ) ln [ Pi (δ )]
where Pi (δ ) is the probability that element i is populated, normalized such that
∑i=1
N
Pi (δ )=1
Thus, the information dimension is given by [2]d inf ≡− lim
δ→
0+¿ Iln (δ )
¿
¿
¿ limδ
→0+¿∑
i=1
N Pi (δ ) ln [Pi (δ )]ln ( δ )
¿
¿
Reference[1] Annadson, A. (2012). Methods of Fractal Dimension Computation. IRACST - International Journal of Computer Science and Information Technology & Security (IJCSITS), ISSN: 2249-9555, Vol. 2, No. 1[2] http://mathworld.wolfram.com/InformationDimension.html