Tag Archives: Fractal

Fractal Dimension and Box Counting

In this post I will present a technique for generating a one dimensional (quasi) fractal data set using a modified Matérn point process, perform a simple box-couting procedure, and then calculate the lacunarity and fractal dimension using linear regression. Lacunarity is actually a pretty large topic, and we will only cover one accepted interpretation here. This material was motivated by an interesting paper on the fractal modelling of fractures in tight gas reservoirs. Tight gas reservoirs refer to reservoirs with very low permeability. To provide a sense of perspective, oil reservoirs typically have a permebility of ten to a hundred millidarcies, whereas shale gas reservoirs are usually less than 0.1 microdarcies, which is about the same permeability as a granite countertop.

Continue reading