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# # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# Function:
# preRIFS() - a sample of fractal points in R^n
# generated with a random iterated function system.
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# Arguments:
# n - a sample size;
# Z - a matrix of protofractal points coordinates;
# P - a probability distribution of protofractal points;
# M - a partition coefficients distribution of protofractal points.
# Variables:
# z - a random sample of indexes for protofractal points;
# X - a random sample of fractal points (prefractal points).
# Value:
# list(pre, proto, distr, index)
# $pre - a sample of fractal points;
# $proto - a set of protofractal points;
# $distr - a distribution of probabilities & coefficients;
# $index - a sample of protofractal indexes.
# # # # # # # # # # # # # # # # # # # # #
preRIFS <- function(n=10000, Z=R2ngon(),
P=rep(1/nrow(Z), times=nrow(Z)),
M=rep(1, times=nrow(Z))) {
z <- sample.int(nrow(Z), size=n, prob=P, replace=TRUE)
X <- array(0, dim=c(n, ncol(Z)))
X[1,] <- colMeans(Z)
for (i in 2: n)
X[i,] <- (X[i-1,] + M[z[i]]*Z[z[i],])/(1 + M[z[i]])
return(list(pre=X, proto=Z,
distr=cbind(p=P, mu=M),
index=z))
}
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