Maple Leaf Fractal

Introduction

We are going to conduct a randomized experiment and see how that results in statistical regularity

Setting up initial parameters

n <- 50000
X <- 0
Y <- 0
X_final <- vector(mode = "list", length = n)
Y_final <- vector(mode = "list", length = n)

Running the for loop

for (i in 1:n){
  dice <- sample(1:4, size = 1, replace = TRUE)
  X_old = X
  Y_old = Y
  
  if (dice == 1){
    X = 0.8*X_old + 0.1
    Y = 0.8*Y_old + 0.04
  }
  else if (dice == 2){
    X = 0.5*X_old + 0.25
    Y = 0.5*Y_old + 0.4
  }
  else if (dice == 3){
    X = 0.355*X_old - 0.355*Y_old + 0.266
    Y = 0.355*X_old + 0.355*Y_old + 0.078
  }
  else{
    X = 0.355*X_old + 0.355*Y_old + 0.378
    Y = -0.355*X_old + 0.355*Y_old + 0.434
  }
  
  X_final[[i]] <- X
  Y_final[[i]] <- Y
}

We get the following pattern

pattern <- cbind(unlist(X_final), unlist(Y_final))
plot(pattern, pch = ".")