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