fractal flame

ff_b.cpp

#include <Rcpp.h>
using namespace Rcpp;

// turmite function to be called from R
// [[Rcpp::export]]
NumericMatrix flame(int iter, int layers) {
  
  NumericMatrix points(iter, 3); // initially zero
  NumericMatrix coeffs(9, layers);
  
  // set coefficients
  for(int i = 0; i < 9; i++) {
    for(int j = 0; j < layers; j++) {
      coeffs(i,j) = R::runif(-1, 1);
    }
  }
  
  // initial values
  points(0, 0) = R::runif(-1, 1);
  points(0, 1) = R::runif(-1, 1);
  points(0, 2) = R::runif(-1, 1);
  
  // iterate
  int r;
  double x;
  double y;
  double z;
  double s;
  
  for(int t = 1; t < iter; t++) {
    
    r = rand() % layers; // which affine transform to use?
    
    // co-ordinates after random transform
    x = coeffs(0, r) * points(t-1, 0) + coeffs(1, r) * points(t-1, 1) + coeffs(2, r);
    y = coeffs(3, r) * points(t-1, 0) + coeffs(4, r) * points(t-1, 1) + coeffs(5, r);
    z = coeffs(6, r) * points(t-1, 0) + coeffs(7, r) * points(t-1, 1) + coeffs(8, r);
    
    // apply function to the transformed coords
    s = x*x + y*y + z*z;
    x = x/s;
    y = y/s;
    z = z/s;
    
    // store results
    points(t, 0) = x;
    points(t, 1) = y;
    points(t, 2) = (z + points(t-1, 2))/2;
    
  }
  
  return points;
}

fractal_flame_03.R

library(Rcpp)
library(ggplot2)

sourceCpp(here::here("source", "ff_b.cpp"))

# parameters
seed <- 11
iter <- 20000000
layers <- 4
bg <- "ghostwhite"
pl <- "scico::oslo"

set.seed(seed)

df <- flame(iter, layers)
df <- as.data.frame(df)
names(df) <- c("x","y","c")
df <- df[-(1:100),]

p <- ggplot(df, aes(x,y, colour = c)) + 
  geom_point(size = 1.5, alpha = .2, stroke = 0, show.legend = FALSE) + 
  theme_void() + 
  theme(plot.background = element_rect(bg, bg)) + 
  paletteer::scale_color_paletteer_c(pl)

fname <- paste0("ff_03_", seed, ".png")
fpath <- here::here("image", fname)
ggsave(fpath, p, width = 16, height = 16, dpi = 100)

Thank you @coolbutuseless, @mdsumner and @martinmodrak! This is all super helpful!