Clifford Attractor

Inspired by this blog post. The R code below creates the individual video frames (a Clifford attractor where one of the four parameters is stepped along with the frame count), which are then knitted together using FFMPEG.

show the code

library(Rcpp)
library(ggplot2)
library(dplyr)
library(foreach)
library(doParallel)
registerDoParallel(parallel::detectCores())

pic_dir <- "pics"
output_video <- "output.mp4"

opt = theme(legend.position  = "none",
            panel.background = element_rect(fill="black"),
            plot.margin = margin(0, 0, -8, -8, unit = "pt"),
            axis.ticks       = element_blank(),
            panel.grid       = element_blank(),
            axis.title       = element_blank(),
            axis.text        = element_blank())

cppFunction('DataFrame createTrajectory(int n, double x0, double y0, 
            double a, double b, double c, double d) {
            // create the columns
            NumericVector x(n);
            NumericVector y(n);
            x[0]=x0;
            y[0]=y0;
            for(int i = 1; i < n; ++i) {
            x[i] = sin(a*y[i-1])+c*cos(a*x[i-1]);
            y[i] = sin(b*x[i-1])+d*cos(b*y[i-1]);
            }
            // return a new data frame
            return DataFrame::create(_["x"]= x, _["y"]= y);
            }
            ')

# attractor parameters
a=-1.24458046630025
b=-1.25191834103316 
c=-1.81590817030519 
d=-1.90866735205054

# video settings
fps <- 60
duration_secs <- 30
frac_change <- 2 # fractional change in "a" param over course of video

max_a <- a + (a*frac_change/2)
min_a <- a - (a*frac_change/2)

a_vec <- seq(from = min_a, to = max_a, by = (a*frac_change)/((fps-1)*duration_secs)) 

# loop over parameter, write out png
foreach (i = 1:length(a_vec)) %dopar% {
  filename <- file.path(pic_dir, paste0("pic_", i, ".png"))
  df = createTrajectory(10000000, 0, 0, a_vec[i], b, c, d)
  p <- ggplot(df, aes(x, y)) + geom_point(color = "white", shape = 46, alpha = .3) + opt
  
  ggsave(plot = p, filename = filename, width = 10.8, height = 10.8, dpi = 100)
}

#### FFMPEG ####
command <- paste0("ffmpeg -y -r ", fps, " -f image2 -s 1080x1080 -i ", pic_dir,
                  "/pic_%d.png -vcodec libx264 -crf 25 -pix_fmt yuv420p ", output_video)
system(command = command)

# unlink(pic_dir, recursive = TRUE) # tidy up