kingsdream.r

pickover <- function(prev, p){
  c(
    sin(p[1]*prev[2])+p[3]*sin(p[1]*prev[1]),
    sin(p[2]*prev[1])+p[4]*sin(p[2]*prev[2])
  )
}

computeAttractor <- function(params,funs,n=1e4,startX){
  X=matrix(NA, nrow=n, ncol=length(startX))
  X[1,] <- startX
  for(i in 2:n) {
    X[i,] <- funs(prev=X[i-1,], params)
  }
  X
}

pngAttractor <- function(X,filename, 
                         width=2000,
                         height=2000, 
                         h=.6,s=0,v=1, alpha=0.1,
                         bg="white",
                         mar=rep(5,4),
                         type="p"){
  png(filename, width=width, height=height, type="cairo")
  par(bg=bg,mar=mar)
  plot(X[,1], X[,2], axes=F, ann=F,
       pch=".",  col=hsv(h=h,s=s,v=v,alpha=alpha), type=type)
  dev.off()
}

points=1e6
## Set to 1e8 for very high quality, but takes a few minutes to run

paramlist <- list(c(-0.966918, 2.879879, 0.765145, 0.744728))
img1 <- computeAttractor(paramlist[[1]], pickover, startX = c(0.1,0.1),n = points) 
pngAttractor(img1, "king7.png", width=4000, bg="black", height=4000, h=0,s=0,v=1,alpha=0.5, mar=rep(20,4))