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我正在研究一个 Python 脚本，该脚本以与通常顺序相反的顺序生成（环绕）菱形方形分形：它不是从外角开始并细分为更小的正方形，而是从任意点开始并递归地向外工作，仅生成最终值所依赖的点。这是我为确定如何处理每个点而编写的函数：

def stepinfo(x, y):
    y1 = y-(y&(y-1))
    x1 = x-(x&(x-1))
    sum = x1 + y1
    return [((sum&(sum-1)) == 0), min(y1, x1)]

返回的第一个值是一个布尔值，指定该点应该由菱形还是正方形步长生成；第二个值指定步骤的网格大小。它工作得很好，除非 x 或 y 为零——然后返回的步长为零并且脚本循环。但是，如果我将分形平铺成 2x2 网格并通过单击平铺的右下角副本（即远离窗口的零轴）指定点，则整个分形将完美生成。但是我似乎无法通过将瓷砖大小的倍数添加到鼠标坐标或沿着这些线的任何东西来“伪造”这个结果。

有什么建议么？

这是完整的脚本（如果 x 或 y = 0，我通过停止递归来避免无限循环，但它仍然会在缺失点处生成伪影）：

MAPEXPONENT = 8

import pygame
import random

MAPSIZE = 2**int(MAPEXPONENT)
MAP = [[[None] for col in range(MAPSIZE)] for row in range(MAPSIZE)]

def point(x, y):
    return MAP[x%MAPSIZE][y%MAPSIZE]

def displace(value, scale):
    displaced = (value + (random.random()-.5) * scale * 12)
    if displaced > 1 or displaced < 0: displaced = 1-displaced%1
    return displaced

def average(values):
    realvalues = []
    for value in values:
        if value <> None: realvalues.append(value)
    if realvalues: return float(sum(realvalues, 0)) / len(realvalues)
    else: return 0

def color_point(x, y, array):
    pixel = point(x, y)[0]
    green = pixel*255
    red = pixel**.5*255
    blue = 255-green
    array[x%MAPSIZE][y%MAPSIZE] = [min(255, max(0, int(red))),
                                   min(255, max(0, int(green))),
                                   min(255, max(0, int(blue)))]

def stepinfo(x, y):
    y1 = y-(y&(y-1))
    x1 = x-(x&(x-1))
    sum = x1 + y1
    return [((sum&(sum-1)) == 0), min(y1, x1)]

def makepoint(x, y, map_array):
    midpoint = point(x, y)
    if midpoint[0] == None:
        step = stepinfo(x, y)
        size = step[1]
        scale = float(size)/MAPSIZE
        heights = []
        if step[0]: points = [[x-size, y-size], [x+size, y-size],
                              [x-size, y+size], [x+size, y+size]]
        else:       points = [[x, y-size],      [x, y+size],
                              [x-size, y],      [x+size, y]]
        for p in points:
            if point(p[0], p[1])[0] == None and p[0] and p[1]:
                makepoint(p[0], p[1], map_array)
            heights.append(point(p[0], p[1])[0])
        midpoint[0] = displace(average(heights), scale)
        color_point(x, y, map_array)
    return midpoint

pygame.init()
screen = pygame.display.set_mode((2*MAPSIZE, 2*MAPSIZE))
map_surface = pygame.surface.Surface((MAPSIZE, MAPSIZE))
brush = 4+MAPSIZE/32

map_surface_array = pygame.surfarray.pixels3d(map_surface)
MAP[0][0][0] = random.random()
color_point(0, 0, map_surface_array)
del map_surface_array

running = True
while running:
    event = pygame.event.wait()
    if event.type == pygame.MOUSEBUTTONDOWN:
        while event.type <> pygame.MOUSEBUTTONUP:
            event = pygame.event.wait()
            x0, y0 = pygame.mouse.get_pos()
            map_surface_array = pygame.surfarray.pixels3d(map_surface)
            for x in range(x0-brush, x0+brush):
                for y in range(y0-brush, y0+brush):
                    if (x-x0)**2+(y-y0)**2 < brush**2:
                        makepoint(x, y, map_surface_array)
            del map_surface_array
            for x, y in [(0,0), (MAPSIZE,0), (0,MAPSIZE), (MAPSIZE,MAPSIZE)]:
                screen.blit(map_surface, (x, y))
            pygame.display.update()
    elif event.type == pygame.QUIT:
        running = False
pygame.quit()
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1 回答 1

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根据http://gameprogrammer.com/fractal.html#diamond中的描述，我认为问题在于，如果 x==0 或 y==0，您会在正方形与菱形上做出错误的决定。

我认为您可以将正确的决定编码为：

def stepinfo(x, y):
    y1 = y-(y&(y-1))
    x1 = x-(x&(x-1))
    return [x1==y1, min(y1, x1)]

甚至更简单：

def stepinfo(x, y):
    y1 = y&-y
    x1 = x&-x
    return [x1==y1, min(y1, x1)]
于 2012-01-11T20:12:37.050 回答