R/plot_IFS.R

In lbozyk/IFSbmp: Plotting IFS type fractals

#' Draws a plot for an object of class IFS with adjustable parameters of depth and starting point for IFS iterations.
#'
#' @param x A list of class IFS.
#' @param depth Parameter indicating number of iterations to be executed.
#' @param start Coordinates of the starting point for the IFS method.
#' @param ... Additional parameters of the generic plot function.
#' @return Plotted fractal image.
#' @export
#' @examples
#' lin <- function(a,b,c,d,e,f){function(x,y) {c(a*x+b*y+c,d*x+e*y+f)}}
#' plot(createIFS(lin(.5,-.5,0,.5,.5,0),lin(-.5,-.5,1,.5,-.5,0)),depth=16,type="p",cex=.1,col="orange")
#'
#' f <- lin(1/2,0,0,0,1/2,0); g <- lin(1/2,0,1/2,0,1/2,0); h <- lin(1/2,0,1/4,0,1/2,sqrt(3)/4)
#' plot(createIFS(f,g,h),depth=8,cex=.1)
#'
#' lin3 <- function(a,b) {lin(1/3,0,a/3,0,1/3,b/3)}
#' plot(createIFS(lin3(0,0),lin3(0,1),lin3(0,2),lin3(1,0),lin3(1,2),lin3(2,0),lin3(2,1),lin3(2,2)))
#'
#' plot(createIFS(lin(0,0,0,0,0.16,0),lin(0.85,0.04,0,-0.04,0.85,1.6),lin(0.2,-0.26,0,0.23,0.22,1.6),
#' lin(-0.15,0.28,0,0.26,0.24,0.44)),depth=9,type="p",cex=.5,col="green")
#' @rdname plot_IFS


plot.IFS <- function(x=NULL,start=c(0,0),depth=1,...) {

  functions <- x

  ## Initialize
  ListOfPoints <- list(start)
  NumberOfFunctions <- length(functions)

  ## Generate the set of points to be plotted
  for(d in 1:depth) {

    ## Initialize a list of (lists of) new points
    ListOfNewPoints <- list(list())

    ## Iterate
    for(n in 1:NumberOfFunctions) {

      ## Generate new points for n-th function from the list of points
      NewPoints <- lapply(ListOfPoints,function(x){
        functions[[n]](x[1],x[2])
      })

      ## Add list of new points to the list of lists
      ListOfNewPoints[[n]] <- NewPoints

    }

    ## Merge lists of new points to the new list of points
    ListOfPoints <- unlist(ListOfNewPoints, recursive = FALSE)

  }

  ## Arrange coordinates of points in a matrix
  M <- matrix(unlist(ListOfPoints), ncol=2, byrow=TRUE)

  ## Plot
  plot(M[,1],M[,2],...)

}