perlin_noise <- function( 
  n = 5,m = 7,# Size of the grid for the vector field
  N = 100,M = 100   # Dimension of the image
) {
  # For each point on this n*m grid,choose a unit 1 vector
  vector_field <- apply(
    array( rnorm( 2 * n * m ),dim = c(2,n,m) ),2:3,function(u) u / sqrt(sum(u^2))
  )
  f <- function(x,y) {
    # Find the grid cell in which the point (x,y) is
    i <- floor(x)
    j <- floor(y)
    stopifnot( i >= 1 || j >= 1 || i < n || j < m )
    # The 4 vectors,from the vector field,at the vertices of the square
    v1 <- vector_field[,i,j]
    v2 <- vector_field[,i+1,j]
    v3 <- vector_field[,j+1]
    v4 <- vector_field[,j+1]
    # Vectors from the point to the vertices
    u1 <- c(x,y) - c(i,j)
    u2 <- c(x,y) - c(i+1,j)
    u3 <- c(x,j+1)
    u4 <- c(x,j+1)
    # Scalar products
    a1 <- sum( v1 * u1 )
    a2 <- sum( v2 * u2 )
    a3 <- sum( v3 * u3 )
    a4 <- sum( v4 * u4 )
    # Weighted average of the scalar products
    s <- function(p) 3 * p^2 - 2 * p^3
    p <- s( x - i )
    q <- s( y - j )
    b1 <- (1-p)*a1 + p*a2
    b2 <- (1-p)*a3 + p*a4
    (1-q) * b1 + q * b2
  }
  xs <- seq(from = 1,to = n,length = N+1)[-(N+1)]
  ys <- seq(from = 1,to = m,length = M+1)[-(M+1)]
  outer( xs,ys,Vectorize(f) )
}

image( perlin_noise() )

通过添加这些矩阵,您可以拥有更多的分形结构,
具有不同的网格尺寸.

a <- .6
k <- 8
m <- perlin_noise(2,2,2^k,2^k)
for( i in 2:k )
  m <- m + a^i * perlin_noise(2^i,2^i,2^k)
image(m)
m[] <- rank(m) # Histogram equalization
image(m)