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A fractal Christmas tree plot in R
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# http://www.r-bloggers.com/merry-christmas-5/?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+RBloggers+%28R+bloggers%29 | |
# Each row is a 2x2 linear transformation | |
# Christmas tree | |
L <- matrix( | |
c(0.03, 0, 0 , 0.1, | |
0.85, 0.00, 0.00, 0.85, | |
0.8, 0.00, 0.00, 0.8, | |
0.2, -0.08, 0.15, 0.22, | |
-0.2, 0.08, 0.15, 0.22, | |
0.25, -0.1, 0.12, 0.25, | |
-0.2, 0.1, 0.12, 0.2), | |
nrow=4) | |
# ... and each row is a translation vector | |
B <- matrix( | |
c(0, 0, | |
0, 1.5, | |
0, 1.5, | |
0, 0.85, | |
0, 0.85, | |
0, 0.3, | |
0, 0.4), | |
nrow=2) | |
prob = c(0.02, 0.6,.08, 0.07, 0.07, 0.07, 0.07) | |
# Iterate the discrete stochastic map | |
N = 1e5 #5 # number of iterations | |
x = matrix(NA,nrow=2,ncol=N) | |
x[,1] = c(0,2) # initial point | |
k <- sample(1:7,N,prob,replace=TRUE) # values 1-7 | |
for (i in 2:N) | |
x[,i] = crossprod(matrix(L[,k[i]],nrow=2),x[,i-1]) + B[,k[i]] # iterate | |
# Plot the iteration history | |
par(bg='darkblue',mar=rep(0,4)) | |
plot(x=x[1,],y=x[2,], | |
col=grep('green',colors(),value=TRUE), | |
axes=FALSE, | |
cex=.1, | |
xlab='', | |
ylab='' )#,pch='.') | |
bals <- sample(N,20) | |
points(x=x[1,bals],y=x[2,bals]-.1, | |
col=c('red','blue','yellow','orange'), | |
cex=2, | |
pch=19 | |
) | |
text(x=-.7,y=8, | |
labels='Merry', | |
adj=c(.5,.5), | |
srt=45, | |
vfont=c('script','plain'), | |
cex=3, | |
col='gold' | |
) | |
text(x=0.7,y=8, | |
labels='Christmas', | |
adj=c(.5,.5), | |
srt=-45, | |
vfont=c('script','plain'), | |
cex=3, | |
col='gold' | |
) | |
text(x=-0.6,y=0, | |
cex=0.8, | |
labels="To Chengdu R Users Group members", | |
col="white" | |
) |
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