# Slice bivariate densities, or the Joy Division “waterfall plot”

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This has been on my to-do list for a long old time. Lining up slices through a bivariate density seems a much more intuitive way of depicting it than contour plots or some ghastly rotating 3-D thing (urgh). Of course, there is the danger of features being hidden, but you know I’m a semi-transparency nut, so it’s no surprise I think that’s the answer to this too.

Here’s an R function for you:

# x, y: data # slices: number of horizontal slices through the data # lboost: coefficient to increase the height of the lines # gboost: coefficient to increase the height of the graph (ylim) # xinc: horizontal offset for each succesive slice # (typically something like 1/80) # yinc: vertical offset for each succesive slice # bcol: background color # fcol: fill color for each slice (polygon) # lcol: line color for each slice # lwidth: line width # NB if you want to cycle slice colors through vectors, you # need to change the function code; it sounds like a # pretty bad idea to me, but each to their own. slicedens<-function(x,y,slices=50,lboost=1,gboost=1,xinc=0,yinc=0.01, bcol="black",fcol="black",lcol="white",lwidth=1) { ycut<-min(y)+((0:(slices))*(max(y)-min(y))/slices) height<-gboost*((slices*yinc)+max(density(x)$y)) plot( c(min(x),max(x)+((max(x)-min(x))/4)), c(0,height), xaxt="n",yaxt="n",ylab="",xlab="") rect(par("usr")[1],par("usr")[3],par("usr")[2],par("usr")[4],col=bcol) for(i in slices:1) { miny<-ycut[i] maxy<-ycut[i+1] gx<-(i-1)*(max(x)-min(x))*xinc gy<-(i-1)*(height)*yinc dd<-density(x[y>=miny & y<maxy]) polygon(dd$x+gx,lboost*dd$y+gy,col=fcol) lines(dd$x+gx,lboost*dd$y+gy,col=lcol,lwd=lwidth) } } # Example: y<-runif(5000,min=-1,max=1) x<-runif(5000,min=-1,max=1)+rnorm(5000,mean=1/(y+1.1),sd=0.8-(y*0.5)) slicedens(x,y,lboost=0.2,fcol=rgb(0,0,0,200,maxColorValue=255))

Some places call this a waterfall plot. Anyway, the white-on-black color scheme is clearly inspired by the Joy Division album cover. Enjoy.

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