import random

def makeHeightField(level):
	size = 2**level + 1
	h = [[0]*size for _ in range(0,size)]
	displacement = 1.0
	for l in range(level-1, -1, -1):
		print 'level', l
		step = 2**l
		for i in range(0, size, step*2):
			for j in range(step, size, step*2):
				h[i][j] = (h[i][j-step]+h[i][j+step])/2.0 + random.gauss(0,displacement)
		for i in range(step, size, step*2):
			for j in range(0, size, step*2):
				h[i][j] = (h[i-step][j]+h[i+step][j])/2.0 + random.gauss(0,displacement)
		for i in range(step, size, step*2):
			for j in range(step, size, step*2):
				h[i][j] = (h[i-step][j]+h[i+step][j]+h[i][j-step]+h[i][j+step])/4.0 + random.gauss(0,displacement)
		displacement /= 1.8
	return h

hf = makeHeightField(9)

import Image
width = len(hf)
height = len(hf)
img = Image.new('L',(width,height))

maxheight = max([max(l) for l in hf])
minheight = min([min(l) for l in hf])

for i in range(0,width):
	for j in range(0,height):
		v = (hf[i][j]-minheight) * 255 / (maxheight-minheight)
		img.putpixel((i,j),int(v))

img.save('terrain.tif')