用R来玩分形

A fractal is “a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,”a property called self-similarity. Roots of mathematical interest in fractals can be traced back to the late 19th Century; however, the term “fractal” was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning “broken” or “fractured.” A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion.

(form Wikipedia)

分形几何是几何学中的新分支，其维数可以是任意值。分形图形的一个重要特点是自相似性，据此性质可以人工构造出很多养眼的图片，这里给出四种常见的分形图。更多代码和讨论请移步COS论坛。

1. 树叶

plot.leaf <- function(n=50000, col="green",cex=2){
  x <- c(.5, .5);
  plot(x[1], x[2], xlim=c(-3, 3), ylim =c(0, 10),type="n",xlab="",ylab="")
  p <- c( .85,  .92,  .99,  1.00);
  A <- rbind(c(.85, .04), c(-.04,.85), c(.20,-.26), c(.23,.22),
             c(-.15,.28), c(.26,.24),  c(0, 0), c(0, .16))
  B <- cbind(c(0, 1.6), c(0, 1.6), c(0,.44), c(0,0))

  for (i in 1:n){
     ran  <-  runif(1);
	 ind <- rank(c(p, ran), ties.method="min")[5]
	 x <- A[(2*ind-1):(2*ind),]%*%x + B[,ind]
    points(x[1],x[2], pch=".", cex=cex, col=col)
  }
}
#library(Cairo)
#CairoPNG()
par(mar=c(0,0,0,0)+0.1)
plot.leaf(cex=1.6)
box()
#dev.off()

2. 树

3. 三角

4. 雪花

相关文章

• 2009/12/14 -- 第二届R会议那些事儿(上海) (25)
• 2009/12/08 -- 第二届R会议随想 (47)
• 2011/12/09 -- 中小矩阵的可视化: corrplot 更新至 0.60 (5)
• 2011/10/22 -- 秋雨梧桐叶落时: corrplot包0.40版本出炉 (12)
• 2011/05/03 -- 第四届R会议, R与最优化 (7)
• 2011/04/20 -- EBImage包以及学术模特Lena的八卦 (4)
• 2011/04/13 -- 周总理与小波分析 (小波分析连载系列之零) (12)
• 2010/05/29 -- 相关矩阵中置信区间之涂鸦 (10)
• 2009/08/30 -- corrplot即将提交到CRAN (0)
• 2009/08/23 -- 距离矩阵可视化&用TSP方法重排变量 (0)