mc201415.R

KochSnowflake <- function(colFill = "#E0FFFF", colBorder = "#B0E0E6", colBackground="#FFFFFF"){
  iterate <- function(T,i){
    A = T[ ,1]; B=T[ ,2]; C = T[,3];
    if (i == 0){
      d = A
      e = B
      f = C
    }
    
    if (i == 1){
      d = (A + B)/2
      h = (C-d)
      d = d-(1/3)*h
      e = (2/3)*B + (1/3)*A
      f = (1/3)*B + (2/3)*A
    }
    
    if (i == 2){
      d = B
      e = (2/3)*B + (1/3)*C
      f = (2/3)*B + (1/3)*A
    }
    
    if (i == 3){
      d = (B + C)/2
      h = (A-d)
      d = d-(1/3)*h
      e = (2/3)*C + (1/3)*B
      f = (1/3)*C + (2/3)*B
    }
    
    if (i == 4){
      d = C
      e = (2/3)*C + (1/3)*A
      f = (2/3)*C + (1/3)*B
    }
    
    if (i == 5){
      d = (A + C)/2
      h = (B-d)
      d = d-(1/3)*h
      e = (2/3)*A + (1/3)*C
      f = (1/3)*A + (2/3)*C
    }
    
    if (i == 6){
      d = A
      e = (2/3)*A + (1/3)*C
      f = (2/3)*A + (1/3)*B
    }
    
    Tnew = cbind(d,e,f)
    return(Tnew)
  }
  
  draw <- function(T, colour, border){
    polygon(T[1,],T[2,],col=colour,border=border)
  }
  
  Iterate <- function(T, v, col=colFill, border=colBorder){
    for (i in v) {
      T = iterate(T,i)
    }
    draw(T,col=col,border=border)
  }
  
  A = matrix(c(1, 0), 2, 1)
  B = matrix(c(cos(2 * pi / 3), sin(2 * pi / 3)), 2, 1)
  C = matrix(c(cos(2 * pi / 3), -sin(2 * pi / 3)), 2, 1)
  T0 = cbind(A, B, C);
  
  plot(numeric(0),xlim=c(-1.1,1.1),ylim=c(-1.1,1.1),axes=FALSE,frame=FALSE,ann=FALSE)
  par(mar=c(1.5, 2, 2.5, 2), bg = colBackground)
  par(usr=c(-1.1, 1.1, -1.1, 1.1))
  mtext("Merry Christmas and a Happy New Year 2015", side = 3)
  mtext("~Carles", side = 1)
  
  for (i in 0:6) {
    for (j in 0:6) {
      for (k in 0:6) {
        for (l in 0:6) { 
          Iterate(T0,c(i,j,k,l))
        }
      }
    }
  }
}

KochSnowflake()