**Ripples**, and kindly contributed to R-bloggers)

If you can walk you can dance. If you can talk you can sing (Zimbabwe Proverb)

There are two things in this picture I would like to emphasise. First one is that everything is made using points and lines. The moon is an enormous point, stars are three small nested points and the tree is a set of straight lines. Points and lines over a simple *cartesian* graph, no more. Second one is that the tree is a *jittered* fractal. In particular, is a *jittered* L-system fractal, a formalism invented in 1968 by a biologist (Aristid Lindemayer) that yields a mathematical description of plan growth. Why *jittered*? Because I add some positive noise to the angle in which branches are divided by two iteratively. It gives to the tree the sense to be rocked by the wind. This is the picture:

I generated 120 images and gathered in this video to *make the wind happen*. The stunning song is called *Kothbiro* performed by Ayub Ogada.

Here you have the code:

depth <- 9 angle<-30 #Between branches division L <- 0.90 #Decreasing rate of branches by depth nstars <- 300 #Number of stars to draw mstars <- matrix(runif(2*nstars), ncol=2) branches <- rbind(c(1,0,0,abs(jitter(0)),1,jitter(5, amount = 5)), data.frame()) colnames(branches) <- c("depth", "x1", "y1", "x2", "y2", "inertia") for(i in 1:depth) { df <- branches[branches$depth==i,] for(j in 1:nrow(df)) { branches <- rbind(branches, c(df[j,1]+1, df[j,4], df[j,5], df[j,4]+L^(2*i+1)*sin(pi*(df[j,6]+angle)/180), df[j,5]+L^(2*i+1)*cos(pi*(df[j,6]+angle)/180), df[j,6]+angle+jitter(10, amount = 8))) branches <- rbind(branches, c(df[j,1]+1, df[j,4], df[j,5], df[j,4]+L^(2*i+1)*sin(pi*(df[j,6]-angle)/180), df[j,5]+L^(2*i+1)*cos(pi*(df[j,6]-angle)/180), df[j,6]-angle+jitter(10, amount = 8))) } } nodes <- rbind(as.matrix(branches[,2:3]), as.matrix(branches[,4:5])) png("image.png", width = 1200, height = 600) plot.new() par(mai = rep(0, 4), bg = "gray12") plot(nodes, type="n", xlim=c(-7, 3), ylim=c(0, 5)) for (i in 1:nrow(mstars)) { points(x=10*mstars[i,1]-7, y=5*mstars[i,2], col = "blue4", cex=.7, pch=16) points(x=10*mstars[i,1]-7, y=5*mstars[i,2], col = "blue", cex=.3, pch=16) points(x=10*mstars[i,1]-7, y=5*mstars[i,2], col = "white", cex=.1, pch=16) } # The moon points(x=-5, y=3.5, cex=40, pch=16, col="lightyellow") # The tree for (i in 1:nrow(branches)) {lines(x=branches[i,c(2,4)], y=branches[i,c(3,5)], col = paste("gray", as.character(sample(seq(from=50, to=round(50+5*branches[i,1]), by=1), 1)), sep = ""), lwd=(65/(1+3*branches[i,1])))} rm(branches) dev.off()

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**Ripples**.

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