aRt.r

Archimedian_Spiral = function(seq_start, seq_end, seq_space, bg, color) {
  t = seq(seq_start, seq_end, by = seq_space) # set
  # create points
  x = t * cos(t) # moves the centrepoiunt of the spiral outward from the origin
  y = t * sin(t) # controls the distance between loops
  #bg color
  par(bg = bg)
  # Plot spiral
  plot(
    x,
    y,
    col = color,
    axes = FALSE,
    pch = 8,
    ann = FALSE
  )
  # return x and y as a dateframe
  a = rbind(x, y)
}
Archimedian_Spiral(seq_start = 0,seq_end = 10000, seq_space = 0.75, bg = "royalblue", color = "seashell")

# Vectorized version
mandelbrot_vectorized <- function(xmin=-2, xmax=2, nx=500,
                                  ymin=-1.5, ymax=1.5, ny=500,
                                  n=10000, showplot=TRUE,
                                  cols=colorRampPalette(c("blue","yellow","red","black"))(11))
{

  # variables
  x <- seq(xmin, xmax, length.out=nx)
  y <- seq(ymin, ymax, length.out=ny)
  c <- outer(x,y*1i,FUN="+")
  z <- matrix(0.0, nrow=length(x), ncol=length(y))
  k <- matrix(0.0, nrow=length(x), ncol=length(y))

  for (rep in 1:n) {
    index <- which(Mod(z) < 2)
    z[index] <- z[index]^2 + c[index]
    k[index] <- k[index] + 1
  }

  if (showplot==TRUE) { image(x,y,k,col=cols, xlab="Re(c)", ylab="Im(c)")}

  return(k)

}

mandelbrot_vectorized()