{"id":385585,"date":"2024-06-30T08:23:48","date_gmt":"2024-06-30T14:23:48","guid":{"rendered":"http:\/\/tomaztsql.wordpress.com\/?p=10010"},"modified":"2024-06-30T08:23:48","modified_gmt":"2024-06-30T14:23:48","slug":"little-useless-useful-r-functions-dragon-curve","status":"publish","type":"post","link":"https:\/\/www.r-bloggers.com\/2024\/06\/little-useless-useful-r-functions-dragon-curve\/","title":{"rendered":"Little useless-useful R functions \u2013 Dragon curve"},"content":{"rendered":"\r\n\r\n
\r\n[This article was first published on R \u2013 TomazTsql<\/a><\/strong>, and kindly contributed to R-bloggers<\/a>]. (You can report issue about the content on this page here<\/a>)\r\n
Want to share your content on R-bloggers? click here<\/a> if you have a blog, or here<\/a> if you don't.\r\n<\/div>\n\n

Let\u2019s play with some dragons. Dragons from the Jurassic park or the board game dungeon and dragons.<\/p>\n\n\n\n

The algorithm is a fractal curve of Hausdorff dimension 2. One starts with one segment. In each iteration the number of segments is doubled by taking each segment as the diagonal of a square and replacing it by half the square (90 degrees). Alternating and doing the left and right function \/ direction to complement in order to get the shape.<\/p>\n\n\n\n

Assume that we start with just a horizontal line (called Dn) as a segment. Since we created two dragons, we will introduce another line (called Cn, which is a derivate of Dn+1). The Dn+1 is obtained from Dn as follows:
1) Translate Dn, moving its end point to the origin.
2) Multiply the translated copy by \u221a1\/2.
3) Rotate the result of previous step by \u221245\u25e6 degrees and call the result Cn.
3) Rotate Cn by \u221290\u25e6 degrees and join this rotated copy to the end of Cn to get Dn+1.<\/p>\n\n\n\n

Translate this to the function, we get the following IFS (iterated function system).<\/p>\n\n\n

\n# Function to generate points using IFS\ngenerate_dragon_curve <- function(iterations) {\n  # Initial point\n  points <- complex(real = 0, imaginary = 0)\n  colors <- c() # Vector to store colors\n\n  # two iterated functions; each for own direction\n  f1 <- function(z) {      (1 + 1i) * z \/ 2 }\n  f2 <- function(z) {  1 - (1 - 1i) * z \/ 2 }\n  \n  # iterate to generate points\n  for (i in 1:iterations) {\n    new_points <- vector("complex", length = length(points) * 2)\n    new_colors <- vector("character", length = length(points) * 2)\n    for (j in 1:length(points)) {\n      new_points[2 * j - 1] <- f1(points[j])\n      new_colors[2 * j - 1] <- ifelse(i %% 2 == 1, "blue", "red") # Alternating colors\n      new_points[2 * j] <- f2(points[j])\n      new_colors[2 * j] <- ifelse(i %% 2 == 1, "red", "blue") # Alternating colors\n    }\n    points <- new_points\n    colors <- c(colors, new_colors)\n  }\n  \n  return(list(points = points, colors = colors))\n}\n<\/pre>\n\n\n
Once we have the points, we need to plot the points with corresponding numbers.<\/p>\n\n\n
\nplot_dragon_curve <- function(iterations) {\n  result <- generate_dragon_curve(iterations)\n  points <- result$points\n  colors <- result$colors\n  plot(Re(points), Im(points), type = "p", pch = ".", col = colors, asp = 1, labels=FALSE, yaxt="n", xaxt="n",\n       xlab = "", ylab = "", main = paste("Heighway Dragon Curve with", iterations, "iterations"))\n}\n<\/pre>\n\n\n
And lastly, execute the function (in this case with 15 iterations):<\/p>\n\n\n
\nplot_dragon_curve(15)\n<\/pre>\n\n\n
This plots the dragon curve.<\/p>\n\n\n
\n
\"\"<\/a><\/figure><\/div>\n\n\n
As always, the complete code is available on GitHub in \u00a0Useless_R_function repository<\/a>. The sample file in this repository is\u00a0here\u00a0(filename:\u00a0Two_dragon_fractal.R<\/a><\/em>). Check the repository for future updates.<\/p>\n\n\n\n
Happy R-coding and stay healthy!<\/p>\n\n\n\n
<\/p>\n\n
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 Let\u2019s play with some dragons. Dragons from the Jurassic park or the board game dungeon and dragons. The algorithm is a fractal curve of Hausdorff dimension 2. One starts with one segment. In each iteration the number of segments is\u2026Read more \u203a<\/div>\n
<\/div>\n
<\/div>\n","protected":false},"author":1281,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[4],"tags":[],"aioseo_notices":[],"jetpack-related-posts":[],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.r-bloggers.com\/wp-json\/wp\/v2\/posts\/385585"}],"collection":[{"href":"https:\/\/www.r-bloggers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.r-bloggers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.r-bloggers.com\/wp-json\/wp\/v2\/users\/1281"}],"replies":[{"embeddable":true,"href":"https:\/\/www.r-bloggers.com\/wp-json\/wp\/v2\/comments?post=385585"}],"version-history":[{"count":4,"href":"https:\/\/www.r-bloggers.com\/wp-json\/wp\/v2\/posts\/385585\/revisions"}],"predecessor-version":[{"id":388508,"href":"https:\/\/www.r-bloggers.com\/wp-json\/wp\/v2\/posts\/385585\/revisions\/388508"}],"wp:attachment":[{"href":"https:\/\/www.r-bloggers.com\/wp-json\/wp\/v2\/media?parent=385585"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.r-bloggers.com\/wp-json\/wp\/v2\/categories?post=385585"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.r-bloggers.com\/wp-json\/wp\/v2\/tags?post=385585"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}