Geometric animation

escape.R

# You'll need to install ffmpeg to make this work.
# Creates a lot of pngs and an mp4 in the working directory, 
# and will overwrite anything with the same name
# so be careful.

lt <- 600
mt <- 400
t <- seq(0,mt,l=lt)
a <- 1 # I don't use 'a' in this particular animation.
d <- expand.grid(a=a, t=t)
li <- seq(0,2,l=600)[-1]

for(ai in 1:length(li)){
  d <- within(d, {
  z1 <- (1i*cos(2*t*pi)*(1) +(sin(2*t*pi))*(1) ) ;
  z <- z1*(3+(sin(2*Arg(z1)+li[ai]*3*pi)*
        cos(2*Arg(z1)*cos(1*Arg(z1)-pi*li[ai]*2))))
        })
    l=4
  png(filename=sprintf("escape%05d.png",ai), type="cairo", width=1000,height=1000)
  par(mar=c(0,0,0,0), bg="#fafafa")
  plot(NA, axes=F, xlim=c(-l,l), ylim=c(-l,l))
  by(d, INDICES=list(d$a), FUN=function(d2){
    points(d2$z, col="black", pch=20, lwd=0.5, cex=0.5, type="l")
    })
  dev.off()
  }

shell("ffmpeg -framerate 40 -i escape%05d.png -c:v libx264 -vf \"format=yuv420p\" -loop 0 -y escape.mp4")