Merry Christmas

December 21, 2014
By

(This article was first published on Wiekvoet, and kindly contributed to R-bloggers)

Based on The DO loop, since I wanted a fractal Christmas tree and there is no point in inventing what has been made already. Besides, this is not the first time this year that I used R to do what has been done in SAS.

Code

# http://blogs.sas.com/content/iml/2012/12/14/a-fractal-christmas-tree/
# Each row is a 2×2 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 
png(‘card.png’)
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’
)

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