GSC: Simulation of Random Sierpinski-Carpets In FractalParameterEstimation: Simulation and Parameter Estimation of Randomized Sierpinski Carpets using the p-p-p-q-Model

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

 `1` ```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`.

Author(s)

Philipp Hermann; Jozef Kiselak; Milan Stehlik\ philipp.hermann@jku.at; jozef.kiselak@upjs.sk; mlnstehlik@gmail.com

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

 ```1 2``` ```GSC(p = 0.2, N = 4, sierp = TRUE) GSC(p = 0.8, N = 2, sierp = FALSE) ```

FractalParameterEstimation documentation built on July 10, 2019, 5:05 p.m.