z <- (0+1i)^(1/4) * c(1, 1.05, 0.95)

colori = c('blue', 'red', 'green')   # colori 

plot(0+1i, xlim=c(-2,2), ylim=c(-2,2), xlab='Re()', ylab='Im()', asp=1, cex=2)

for (n in 1:3) {
  for( k in 1:16) {
     points(z[n]^k, pch=19, col=colori[n])
     lines(c(0, Re(z[n]^k)), c(0, Im(z[n]^k)), col=colori[n] )
     Sys.sleep(0.2)
  }
}