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# -*- coding: utf-8 -*-"""从一条山脊到一整片大陆.ipynbAutomatically generated by Colab.Original file is located at    https://colab.research.google.com/drive/1Huc6gsj8JWXMhVpzBvpS9RDTmPrmqp5f"""import numpy as npimport matplotlib.pyplot as pltfrom matplotlib.colors import LinearSegmentedColormapfrom mpl_toolkits.mplot3d import Axes3Ddef diamond_square(iterations=8,                   initial_displacement=1.0,                   decay=0.55,                   seed=7):    """    用钻石—正方形算法生成二维山地。    iterations:        迭代次数。最终网格大小为 (2^iterations + 1) × (2^iterations + 1)    initial_displacement:        第一次迭代时的随机偏移幅度    decay:        每轮迭代后，随机偏移缩小的比例    seed:        随机种子。相同种子会生成相同的山脉    """    rng = np.random.default_rng(seed)    size = 2 ** iterations + 1    terrain = np.zeros((size, size))    # 给平面的四个角设置初始高度    terrain[0, 0] = rng.uniform(-0.2, 0.2)    terrain[0, -1] = rng.uniform(-0.2, 0.2)    terrain[-1, 0] = rng.uniform(-0.2, 0.2)    terrain[-1, -1] = rng.uniform(-0.2, 0.2)    step = size - 1    displacement = initial_displacement    while step > 1:        half = step // 2        # -------------------------        # 第一步：正方形步骤        # -------------------------        # 找到每个正方形的中心点，        # 取四个角高度的平均值，再加入随机偏移        for y in range(half, size - 1, step):            for x in range(half, size - 1, step):                top_left = terrain[y - half, x - half]                top_right = terrain[y - half, x + half]                bottom_left = terrain[y + half, x - half]                bottom_right = terrain[y + half, x + half]                average = (                    top_left                    + top_right                    + bottom_left                    + bottom_right                ) / 4                terrain[y, x] = average + rng.uniform(                    -displacement,                    displacement                )        # -------------------------        # 第二步：钻石步骤        # -------------------------        # 找到每个菱形的中心点，        # 取周围已有点的平均值，再加入随机偏移        for y in range(0, size, half):            start_x = half if (y // half) % 2 == 0 else 0            for x in range(start_x, size, step):                neighbors = []                if y - half >= 0:                    neighbors.append(terrain[y - half, x])                if y + half < size:                    neighbors.append(terrain[y + half, x])                if x - half >= 0:                    neighbors.append(terrain[y, x - half])                if x + half < size:                    neighbors.append(terrain[y, x + half])                average = np.mean(neighbors)                terrain[y, x] = average + rng.uniform(                    -displacement,                    displacement                )        # 网格尺度缩小        step //= 2        # 随着尺度变小，随机偏移也逐渐减小        displacement *= decay    # 把高度归一化到 0～1    terrain -= terrain.min()    terrain /= terrain.max()    return terrain# 生成二维山地terrain = diamond_square(    iterations=8,    initial_displacement=1.0,    decay=0.55,    seed=7)# 自定义地形颜色：# 深蓝—浅蓝—绿色—棕色—白色terrain_colors = LinearSegmentedColormap.from_list(    "terrain_colors",    [        (0.00, "#264653"),        (0.18, "#4f8a8b"),        (0.32, "#84a98c"),        (0.55, "#52734d"),        (0.72, "#8b6f47"),        (0.88, "#b8a88a"),        (1.00, "#f5f5f5")    ])# 建立平面坐标size = terrain.shape[0]x = np.linspace(0, 1, size)y = np.linspace(0, 1, size)X, Y = np.meshgrid(x, y)# 为了让山峰更加明显，对高度稍作非线性处理Z = terrain ** 1.35# 绘制三维山脉fig = plt.figure(figsize=(14, 9))ax = fig.add_subplot(111, projection="3d")surface = ax.plot_surface(    X,    Y,    Z,    cmap=terrain_colors,    linewidth=0,    antialiased=True,    rcount=180,    ccount=180)ax.view_init(elev=42, azim=-125)# 调整纵向比例，使山脉更有立体感ax.set_box_aspect((1, 1, 0.38))ax.set_axis_off()ax.set_title(    "Diamond-Square Fractal Mountain",    fontsize=18,    pad=10)plt.tight_layout()plt.show()