Snowflakes (generative)

Load packages

library(plotrix)
library(gsl)
library(RColorBrewer)
library(data.table)

Set the background of the graphics device to black and generate a vector of colours.

par(bg = "black")
colours <- brewer.pal(10, "Set3")

Make necessary functions

A regular polygon of n sides

By default, this function draws the polygon and returns a data.table with the corresponding x and y coordinates.

draw_regular_polygon <- function(centre.x, centre.y, radius = 0.1, n_sides = 6, rotation = 0, return = TRUE, draw = TRUE, colour = "black", fill = NULL) {
  # https://stackoverflow.com/questions/7198144/how-to-draw-a-n-sided-regular-polygon-in-cartesian-coordinates
  vertices = 1:n_sides
  x = radius * cos(2*pi*vertices/n_sides + rotation) + centre.x
  y = radius * sin(2*pi*vertices/n_sides + rotation) + centre.y
  if (draw) { polygon(x, y, border = colour, col = fill) }
  if (return) { return(data.table(x = x, y = y))}
}

draw_tiny_hexagons <- function(centre.x, centre.y, ...) {
  invisible(lapply(1:length(centre.x), function(z) draw_regular_polygon(centre.x, centre.y, ...)))
}

This function draws the ‘spokes’ of a regular polygon.

make_spokes <- function(centre.x, centre.y, ...) {
  polygon.df <- draw_regular_polygon(centre.x, centre.y, draw = FALSE, ...)
  dt.list <- invisible(lapply(1:nrow(polygon.df), function(x) data.table(x = c(centre.x, polygon.df[x][["x"]]), y = c(centre.y, polygon.df[x][["y"]]))))
  return(dt.list)
}

draw_spokes <- function(centre.x, centre.y, colour = "black", ...) {
  invisible(lapply(make_spokes(centre.x = centre.x, centre.y = centre.y, col = colour, ...), lines, col = colour))
}

This function draws a star.

make_star <- function(centre.x, centre.y, radius = 0.5, depth = 3, rotation = 0, ...) {
  df1 <- draw_regular_polygon(centre.x, centre.y, radius = radius, draw = FALSE, rotation = rotation, ...)
  df2 <- draw_regular_polygon(centre.x, centre.y, radius = radius/depth, draw = FALSE, rotation = rotation + pi/6, ...)
  return(rbind(df1[, c("pt", "id") := .(1:6, c("df1"))], df2[, c("pt", "id") := .(1:6, c("df2"))])[order(pt, id)])
}

draw_star <- function(centre.x, centre.y, colour = "black", ...) {
  polygon(make_star(centre.x = centre.x, centre.y = centre.y, ...), border = colour)
}

These functions draw the ‘spikes’ on the spokes of a regular polygon.

make_spikes <- function(centre.x, centre.y, radius = 0.5, spikiness = 1.25, rotation = pi/12, ...) {
  df1 <- draw_regular_polygon(centre.x, centre.y, radius = radius, draw = FALSE, ...)
  df2 <- draw_regular_polygon(centre.x, centre.y, radius = radius*spikiness, n_sides = 12, draw = FALSE, rotation = rotation, ...)
  df1[, pt := 1:6]
  df2[, pt := rep(1:6, each = 2)]
  dt.list <- invisible(lapply(1:nrow(df1), function(z) {
    rbind(df1[z], df2[pt == z][1], df1[z], df2[pt == z][2])
    }))
  return(dt.list)
}

draw_spikes <- function(centre.x, centre.y, colour = "black", ...) {
  invisible(lapply(make_spikes(centre.x = centre.x, centre.y = centre.y, ...), lines, col = colour))
}

And this function returns the x, y coordinates of the tips of the spikes.

make_spike_tips <- function(centre.x, centre.y, radius = 0.5, spikiness = 1.25, rotation = pi/12, ...) {
  df1 <- draw_regular_polygon(centre.x, centre.y, radius = radius, draw = FALSE, ...)
  df2 <- draw_regular_polygon(centre.x, centre.y, radius = radius*spikiness, n_sides = 12, draw = FALSE, rotation = rotation, ...)
  df1[, pt := 1:6]
  df2[, pt := rep(1:6, each = 2)]
  return(rbind(df1, df2)[, 1:2])
}

Drawing the snowflakes

plot_random <- function(n = 50, limit = 3, set.y, fileno = 0) {
  random.x <- runif(n, 0, limit)
  random.y <- set.y
  random.radius <- runif(n, 0.02, 0.08)
  random.colours <- sample(colours, n, replace = TRUE)
  random.rotation <- sample(c(pi/2, pi/3, pi/4, pi/5, pi/6, pi/7, pi/8, pi/9, pi/10), n, replace = TRUE)
  random.function <- sample(c(draw_star, draw_spokes, draw_spikes), n, replace = TRUE)
  svg(paste0("snowflakes_", fileno, ".svg"), bg = "black", width = 12, height = 12)
  plot.new()
  plot.window(xlim=c(0, limit), ylim = c(0, limit))
  # plot(-20, -20, xlim = c(0, limit), ylim = c(0, limit))
  # mapply(function(x, y, radius) draw_star(x, y, radius = radius), random.x, random.y, random.radius)
  # mapply(function(x, y, radius) draw_spokes(x, y, radius = radius), random.x, random.y, random.radius)
  invisible(mapply(function(random.function, x, y, radius, colour) random.function(x, y, radius = radius, colour = colour), random.function, random.x, random.y, random.radius, random.colours))
  invisible(mapply(function(random.function, x, y, radius, colour) draw_spikes(x, y, radius = radius, colour = colour), random.function, random.x, random.y, random.radius, random.colours))
  random.radius <- runif(n, 0.02, 0.08)
  invisible(mapply(function(random.function, x, y, radius, colour) draw_spikes(x, y, radius = radius, colour = colour), random.function, random.x, random.y, random.radius, random.colours))
  invisible(mapply(function(x, y, radius, colour) draw_spokes(x, y, radius = radius, colour = colour), random.x, random.y, random.radius, random.colours))
  random.function <- sample(c(draw_star, draw_spokes), n, replace = TRUE)
  invisible(mapply(function(random.function, x, y, radius, colour) random.function(x, y, radius = radius, colour = colour), random.function, random.x, random.y, random.radius, random.colours))
  random.function <- sample(c(draw_star, draw_spokes), n, replace = TRUE)
  invisible(mapply(function(random.function, x, y, radius, colour) random.function(x, y, radius = radius, colour = colour), random.function, random.x, random.y, random.radius, random.colours))
  random.function <- sample(c(draw_star, draw_spokes), n, replace = TRUE)
  invisible(mapply(function(random.function, x, y, radius, colour) random.function(x, y, radius = radius, colour = colour), random.function, random.x, random.y, random.radius, random.colours))
  spikes_df <- mapply(function(x, y, radius) make_spike_tips(x, y, radius = radius), random.x, random.y, random.radius)
  # print("spikes_df")
  # print(spikes_df$x)
  x = unlist(as.data.frame(t(spikes_df))$x)
  y = unlist(as.data.frame(t(spikes_df))$y)
  spikes_df <- data.frame(x = x, y = y)
  # print("done")
  random.radius <- runif(n, 0.0075, 0.01)
  invisible(mapply(function(x, y, radius, colour) draw_tiny_hexagons(x, y, radius, colour = colour), spikes_df$x, spikes_df$y, random.radius, random.colours))
  random.radius <- runif(n, 0.06, 0.1)
  new.selection <- sample(1:n, n/2, replace = FALSE)
  random.x <- random.x[new.selection]
  random.y <- random.y[new.selection]
  invisible(mapply(function(x, y, radius, colour) draw_spokes(x, y, radius = radius, colour = colour), random.x, random.y, random.radius, random.colours))
  invisible(mapply(function(x, y, radius, colour) draw_spikes(x, y, radius = radius, colour = colour), random.x, random.y, random.radius, random.colours))
  dev.off()
}

n = 100
limit = 3
y = runif(n, 0, limit)
plot_random(n = n, limit = limit, set.y = y)

## png 
##   2

And here’s the output:

knitr::include_graphics("snowflakes_0.svg")