FractalParameterEstimation (version 1.1.2)

GSC: Simulation of Random Sierpinski-Carpets

Description

This function simulates random Sierpinski-Carpets using a constant probability for the computation of the Bernoulli random variables placed in the matrix. An additional parameter determines the number of ramifications in this procedure.

Usage

GSC(p,N,sierp=TRUE)

Arguments

p

A numeric value between 0 and 1 indicating the probability of success (0 or 1) for the Bernoulli random variables of the matrix.

N

An integer value indicating the number of ramifications used for simulating the Sierpinski-Carpet.

sierp

An optional logical parameter: if TRUE then the center of the matrix is automatically set to 0 as for the general Sierpinski-Carpet, else also a Bernoulli random variable is simulated.

Value

This function creates a matrix of size 3^N x 3^N containing simulated zeros and ones from Bernoulli distribution under given probability p.

References

Hermann, P., Mrkvicka, T., Mattfeldt, T., Minarova, M., Helisova, K., Nicolis, O., Wartner, F., and Stehlik, M. (2015). Fractal and stochastic Geometry Inference for Breast Cancer: a Case Study with Random Fractal Models and Quermass-Interaction Process. Statistics in Medicine, 34(18), 2636-2661. doi: 10.1002/sim.6497.

Examples

# NOT RUN {
GSC(p = 0.2, N = 4, sierp = TRUE)
GSC(p = 0.8, N = 2, sierp = FALSE)
# }