The Mandelbrot set is a set of complex numbers  c for which the function  does not diverge to infinity when iterate from , and therefore remains bounded in absolute value.

For little stretching, we can create a Mandlebrot set and draw it with image function.

MandelBrotImage <- function(){
    
    cols <- colorRampPalette(c("white","black","white","grey","black"))(11)
    n <- 400
    x <- seq(-2, 1, length.out=250)
    y <- seq(-1.5, 1.5, length.out=250)
    c <- outer(x,y*1i,"+")
    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) { 
      for (i in 1:250) { 
        for (j in 1:250) { 
          if(Mod(z[i,j]) < 2 && k[i,j] < n) {
            z[i,j] <- z[i,j]^2 + c[i,j]
            k[i,j] <- k[i,j] + 1
          }
        }
      }
    }
    image(x,y,k, col=cols, axes = FALSE, xlab = "" , ylab = "" )
}


# run function
MandelBrotImage()

As always, code is available on Github in  Useless_R_function repository. The sample file in this repository is here (filename: MandelbrotSet.R) Check the repository for future updates.

Happy R-coding and stay healthy!