R/canvas_mandelbrot.R

In aRtsy: Generative Art with 'ggplot2'

# Copyright (C) 2021-2023 Koen Derks

# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.

# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.

# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.

#' Draw the Mandelbrot Set
#'
#' @description This function draws the Mandelbrot set and other related fractal sets on the canvas.
#'
#' @usage canvas_mandelbrot(
#'   colors,
#'   iterations = 100,
#'   zoom = 1,
#'   set = c("mandelbrot", "multibrot", "julia", "ship"),
#'   left = -2.16,
#'   right = 1.16,
#'   bottom = -1.66,
#'   top = 1.66,
#'   resolution = 500
#' )
#'
#' @param colors      a string or character vector specifying the color(s) used for the artwork.
#' @param iterations  a positive integer specifying the number of iterations of the algorithm.
#' @param zoom        a positive value specifying the amount of zoom to apply.
#' @param set         a character indicating which fractal set to draw. Possible options are \code{mandelbrot} for the Mandelbrot set, \code{multibrot} for variations of the Mandelbrot set (aka the Multibrot sets), \code{julia} for the Julia set and \code{ship} for the Burning ship set.
#' @param left        a value specifying the minimum location on the x-axis.
#' @param right       a value specifying the maximum location on the x-axis.
#' @param bottom      a value specifying the minimum location on the y-axis.
#' @param top         a value specifying the maximum location on the y-axis.
#' @param resolution  resolution of the artwork in pixels per row/column. Increasing the resolution increases the quality of the artwork but also increases the computation time exponentially.
#'
#' @return A \code{ggplot} object containing the artwork.
#'
#' @references \url{https://en.wikipedia.org/wiki/Mandelbrot_set}
#'
#' @author Koen Derks, \email{koen-derks@hotmail.com}
#'
#' @keywords artwork canvas
#'
#' @seealso \code{colorPalette}
#'
#' @examples
#' \donttest{
#' canvas_mandelbrot(colors = colorPalette("tuscany1"), set = "mandelbrot")
#' canvas_mandelbrot(colors = colorPalette("flag"), set = "julia", zoom = 2)
#' }
#'
#' @export

canvas_mandelbrot <- function(colors,
                              iterations = 100,
                              zoom = 1,
                              set = c("mandelbrot", "multibrot", "julia", "ship"),
                              left = -2.16,
                              right = 1.16,
                              bottom = -1.66,
                              top = 1.66,
                              resolution = 500) {
  .checkUserInput(resolution = resolution, iterations = iterations)
  set <- match.arg(set)
  if (zoom > 1) {
    for (i in 1:(zoom - 1)) {
      xmin_tmp <- left
      xmax_tmp <- right
      ymin_tmp <- bottom
      ymax_tmp <- top
      left <- xmin_tmp + abs(xmin_tmp - xmax_tmp) / 4
      right <- xmax_tmp - abs(xmin_tmp - xmax_tmp) / 4
      bottom <- ymin_tmp + abs(ymin_tmp - ymax_tmp) / 4
      top <- ymax_tmp - abs(ymin_tmp - ymax_tmp) / 4
    }
  }
  x <- seq(left, right, length.out = resolution)
  y <- seq(bottom, top, length.out = resolution)
  mk <- sample(3:5, size = 1)
  if (set != "julia") {
    z <- matrix(0, nrow = length(x), ncol = length(y))
    c <- outer(x, y * 1i, FUN = "+")
  } else {
    z <- outer(x, y * 1i, FUN = "+")
    c <- -0.4 + 0.6 * 1i
  }
  canvas <- matrix(0, nrow = length(x), ncol = length(y))
  for (rep in 1:iterations) {
    index <- which(Mod(z) < 2)
    z[index] <- switch(set,
      "mandelbrot" = z[index]^2 + c[index],
      "multibrot" = z[index]^mk + c[index],
      "julia" = z[index]^2 + c,
      "ship" = (abs(Re(z[index])) + abs(Im(z[index])) * 1i)^2 + c[index]
    )
    canvas[index] <- canvas[index] + 1
  }
  full_canvas <- .unraster(canvas, names = c("x", "y", "z"))
  artwork <- ggplot2::ggplot(data = full_canvas, ggplot2::aes(x = x, y = y, fill = z)) +
    ggplot2::geom_raster(interpolate = TRUE, alpha = 0.9) +
    ggplot2::xlim(c(0, resolution + 1)) +
    ggplot2::ylim(c(0, resolution + 1)) +
    ggplot2::scale_fill_gradientn(colours = colors)
  artwork <- theme_canvas(artwork)
  return(artwork)
}