Mixing Waves

Fill a cocktail shaker with ice; add vodka, triple sec, cranberry, and lime, and shake well; strain into a chilled cocktail glass and garnish with orange twist (Cosmopolitan Cocktail Recipe)

This is a tribute to Blaise Pascal and Joseph Fourier, two of the greatest mathematicians in history. As Pascal did in his famous triangle, I generate a set of random curves (sines or cosines with random amplitudes between 1 and 50) and I arrange them over the lateral edges of the triangle. Each inner curve in the triangle is the sum of the two directly curves above it.  This is the result for a 6 rows triangle:

Adding Waves

Two comments:

  1. Inner curves are noisy. The greater is the distance from the edge, the higher the entropy. When I was a child, I used to play a game called the broken telephone; I can see some kind of connection between this graphic and the game.
  2. I have read that using eval+parse in sympton of being a bad programmer. Does anyone have an idea to do this in some other way without filling the screen of code?

This is the code:

library(ggplot2)
library(gridExtra)
nrows=6
for (i in 1:nrows){
  eval(parse(text=paste("f",i,1,"=function(x) ", sample(c("sin(","cos("),1), runif(min=1, max=50,1) ,"*x)",sep="")))
  eval(parse(text=paste("f",i,i,"=function(x) ", sample(c("sin(","cos("),1), runif(min=1, max=50,1) ,"*x)",sep="")))}
for (i in 3:nrows) {
  for (j in 2:(i-1)) eval(parse(text=paste("f",i, j, "=function(x) f",(i-1),(j-1), "(x) + f",(i-1),j,"(x)",sep="")))}
vplayout=function(x, y) viewport(layout.pos.row = x, layout.pos.col = y)
opts=theme(legend.position="none",
           panel.background = element_rect(fill="gray95"),
           plot.background = element_rect(fill="gray95", colour="gray95"),
           panel.grid = element_blank(),
           axis.ticks=element_blank(),
           axis.title=element_blank(),
           axis.text =element_blank())
setwd("YOUR WORKING DIRECTORY HERE")
grid.newpage()
jpeg(file="Adding Waves.jpeg", width=1800,height=1000, bg = "gray95", quality = 100)
pushViewport(viewport(layout = grid.layout(nrows, 2*nrows-1)))
for (i in 1:nrows) {
  for (j in 1:i) {
    print(ggplot(data.frame(x = c(0, 20)), aes(x)) + stat_function(fun = eval(parse(text=paste("f",i,j,sep=""))), colour = "black", alpha=.75)+opts, vp = vplayout(i, nrows+(2*j-(i+1))))
  }
}
dev.off()
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3 thoughts on “Mixing Waves

  1. So:

    f<-function()
    {
    a<-sample(c(sin,cos),1)[[1]]
    b<-sample(1:50,1)

    function(x)
    a(b*x)
    }

    replicate(11,f())

    Pascal<-lapply(
    2:6,
    function(i)
    c(f(),rep(NA,i-2),f())
    )

    Pascal<-c(f(),Pascal)

    for(i in 3:6)
    {
    for(j in 2:(i-1))
    {
    k<-function()
    {
    f1<-Pascal[[i-1]][[j-1]]
    f2<-Pascal[[i-1]][[j]]

    function(x)
    f1(x)+f2(x)
    }
    Pascal[[i]][[j]]<-k()
    }
    }

    Pascal

    Now you have a list of lists (rows and columns) of functions that you can evaluate with two nested lapply 🙂

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