bansley_fern

# Let's try a different approach with a Barnsley fern
generate_barnsley_fern <- function(n_points = 50000) {
  # Initialize points array
  points <- data.frame(x = numeric(n_points), y = numeric(n_points))

  # Start with (0,0)
  x <- 0
  y <- 0

  # Fill the points
  for(i in 1:n_points) {
    # Store the current point
    points$x[i] <- x
    points$y[i] <- y

    # Choose a random transformation
    r <- runif(1)

    if(r < 0.01) {
      # Transformation 1 (stem)
      x_new <- 0
      y_new <- 0.16 * y
    } else if(r < 0.86) {
      # Transformation 2 (smaller leaflets)
      x_new <- 0.85 * x + 0.04 * y
      y_new <- -0.04 * x + 0.85 * y + 1.6
    } else if(r < 0.93) {
      # Transformation 3 (left leaflet)
      x_new <- 0.20 * x - 0.26 * y
      y_new <- 0.23 * x + 0.22 * y + 1.6
    } else {
      # Transformation 4 (right leaflet)
      x_new <- -0.15 * x + 0.28 * y
      y_new <- 0.26 * x + 0.24 * y + 0.44
    }

    # Update for next iteration
    x <- x_new
    y <- y_new
  }

  # Add a group to color by
  points <- points %>%
    dplyr::mutate(
      group = ceiling(1:n_points / (n_points/7))  # Create 7 groups
    )

  return(points)
}

# Generate the fractal
set.seed(42)
fern <- generate_barnsley_fern(50000)

# Plot the fern
p <- ggplot(fern, aes(x, y, color = factor(group))) +
  geom_point(size = 0.1, alpha = 0.6) +
  scale_color_viridis_d(option = "D") +
  theme_void() +
  theme(
    legend.position = "none",
    panel.background = element_rect(fill = "#0E0E18"),
    plot.background = element_rect(fill = "#0E0E18")
  ) +
  labs(title = "Fractal Dreams") +
  coord_fixed(ratio = 1)

print(p)