Estimating the parameters p and q of the random fractal [p-p-p-q]-model. Random fractal models can be also simulated.
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FractalParameterEstimation is an R package for estimating parameters p and q of a random Sierpinski-Carpet model named [p-p-p-q] from Hermann et. al (2015). Furthermore, we also provide functions which simulate random Sierpinski-Carpets under constant and variable probabilities with different ramifications. A PDF-manual of the package is uploaded and a PDF-version of the paper containing detailed descriptions is available from here.

Author (Requests)

Please contact me in case of questions, comments, bug reports, etc...

Author: Philipp Hermann

Dependencies & System Requirements

This package requires an installation of R (>= 2.2) and uses functions which are directly installed.


The most recent version of FractalParameterEstimation is contained in Sources. The ZIP-File of the package can be downloaded via "Clone or download". The installation is performed as usually in R via a the command:

install.packages("/PathToFPE/FractalParameterEstimation_<version>.tar.gz", repos=NULL, type="source")


The R-package contains several example data sets for estimating the parameters p and q of the [p-p-p-q]-model. These estimations can be performed with the following commands:

## Example 1: Original p-Value: 0.2; Original q-value: 0.1
estimationFunction(Data0201, decs = 2)
## Example 2: Original p-value: 0.3; Original q-value: 0.25
estimationFunction(Data03025) # testData2
## Example 3: Original p-value: 0.5; Original q-value: 0.1
## Example 4: Original p-value: 0.6; Original q-value: 0.3

The most recent version also contains functions to simulate Sierpinski-Carpets under user defined ramifications. Therefore, both, constant as well as variable probabilities can be used with the following commands:

  • Constant Case:
GSC(p = 0.2, N = 4, sierp = TRUE)
GSC(p = 0.8, N = 2, sierp = FALSE)
  • Variable Case:
GSC_seq(p = c(0.1,0.2,0.1,0.4), sierp = TRUE)
GSC_seq(p = c(rep(0.1,3),0.05), sierp = FALSE)

Note that the last case reflects a simulation of a Sierpinski-Carpet using four ramifications under the [p-p-p-q]-model. The output could be used to directly estimate the according parameters p and q.

Detailed descriptions of the main functions and all adjacent functions can be found as general in R via e.g.