Diamond-square algorithm
The diamond-square algorithm is a method for generating heightmaps for computer graphics. It is a slightly better algorithm than the three-dimensional implementation of the midpoint displacement algorithm, which produces two-dimensional landscapes. It is also known as the random midpoint displacement fractal, the cloud fractal or the plasma fractal, because of the plasma effect produced when applied.
The idea was first introduced by Fournier, Fussell and Carpenter at SIGGRAPH in 1982.
The diamond-square algorithm starts with a two-dimensional grid, then randomly generates terrain height from four seed values arranged in a grid of points so that the entire plane is covered in squares.
Python 으로 구름 이미지 생성하기 (Cloud images using the diamond-square algorithm)
종이에 남은 물자국에 가꾸운 느낌의 "구름"을 랜덤으로 생성하는 알고리즘.
The Diamond-square algorithm is a popular method for generating images which resemble terrain, clouds or plasma. Its description on Wikipedia is as good as any and will not be repeated here.
In the code below, the image size is N=2n+1. Since plt.imshow interpolates quite well anyway, n=6
gives acceptable results for the image size it produces. For high-resolution images, increase n accordingly.
This code is also available on my github page.
import numpy as np
import matplotlib.pyplot as plt
# The array must be square with edge length 2**n + 1
n = 6
N = 2**n + 1
# f scales the random numbers at each stage of the algorithm
f = 1.0
# Initialise the array with random numbers at its corners
arr = np.zeros((N, N))
arr[0::N-1,0::N-1] = np.random.uniform(-1, 1, (2,2))
side = N-1
nsquares = 1
while side > 1:
sideo2 = side // 2
# Diamond step
for ix in range(nsquares):
for iy in range(nsquares):
x0, x1, y0, y1 = ix*side, (ix+1)*side, iy*side, (iy+1)*side
xc, yc = x0 + sideo2, y0 + sideo2
# Set this pixel to the mean of its "diamond" neighbours plus
# a random offset.
arr[yc,xc] = (arr[y0,x0] + arr[y0,x1] + arr[y1,x0] + arr[y1,x1])/4
arr[yc,xc] += f * np.random.uniform(-1,1)
# Square step: NB don't do this step until the pixels from the preceding
# diamond step have been set.
for iy in range(2*nsquares+1):
yc = sideo2 * iy
for ix in range(nsquares+1):
xc = side * ix + sideo2 * (1 - iy % 2)
if not (0 <= xc < N and 0 <= yc < N):
continue
tot, ntot = 0., 0
# Set this pixel to the mean of its "square" neighbours plus
# a random offset. At the edges, it has only three neighbours
for (dx, dy) in ((-1,0), (1,0), (0,-1), (0,1)):
xs, ys = xc + dx*sideo2, yc + dy*sideo2
if not (0 <= xs < N and 0 <= ys < N):
continue
else:
tot += arr[ys, xs]
ntot += 1
arr[yc, xc] += tot / ntot + f * np.random.uniform(-1,1)
side = sideo2
nsquares *= 2
f /= 2
plt.imshow(arr, cmap=plt.cm.Blues)
plt.axis('off')
plt.show()