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80 lines
2.8 KiB
Markdown
80 lines
2.8 KiB
Markdown
# 阴影和增强标准化渲染
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通过使用与幂归一化色图（gamma = 0.3）相关联的归一化重新计数，可以改善Mandelbrot集渲染。 由于阴影，渲染可以进一步增强。
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maxiter给出了计算的精度。 在大多数现代笔记本电脑上，maxiter = 200应该需要几秒钟。
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```python
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import numpy as np
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def mandelbrot_set(xmin, xmax, ymin, ymax, xn, yn, maxiter, horizon=2.0):
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X = np.linspace(xmin, xmax, xn).astype(np.float32)
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Y = np.linspace(ymin, ymax, yn).astype(np.float32)
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C = X + Y[:, None] * 1j
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N = np.zeros_like(C, dtype=int)
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Z = np.zeros_like(C)
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for n in range(maxiter):
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I = np.less(abs(Z), horizon)
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N[I] = n
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Z[I] = Z[I]**2 + C[I]
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N[N == maxiter-1] = 0
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return Z, N
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if __name__ == '__main__':
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import time
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import matplotlib
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from matplotlib import colors
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import matplotlib.pyplot as plt
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xmin, xmax, xn = -2.25, +0.75, 3000/2
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ymin, ymax, yn = -1.25, +1.25, 2500/2
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maxiter = 200
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horizon = 2.0 ** 40
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log_horizon = np.log(np.log(horizon))/np.log(2)
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Z, N = mandelbrot_set(xmin, xmax, ymin, ymax, xn, yn, maxiter, horizon)
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# Normalized recount as explained in:
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# https://linas.org/art-gallery/escape/smooth.html
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# https://www.ibm.com/developerworks/community/blogs/jfp/entry/My_Christmas_Gift
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# This line will generate warnings for null values but it is faster to
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# process them afterwards using the nan_to_num
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with np.errstate(invalid='ignore'):
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M = np.nan_to_num(N + 1 -
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np.log(np.log(abs(Z)))/np.log(2) +
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log_horizon)
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dpi = 72
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width = 10
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height = 10*yn/xn
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fig = plt.figure(figsize=(width, height), dpi=dpi)
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ax = fig.add_axes([0.0, 0.0, 1.0, 1.0], frameon=False, aspect=1)
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# Shaded rendering
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light = colors.LightSource(azdeg=315, altdeg=10)
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M = light.shade(M, cmap=plt.cm.hot, vert_exag=1.5,
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norm=colors.PowerNorm(0.3), blend_mode='hsv')
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plt.imshow(M, extent=[xmin, xmax, ymin, ymax], interpolation="bicubic")
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ax.set_xticks([])
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ax.set_yticks([])
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# Some advertisement for matplotlib
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year = time.strftime("%Y")
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text = ("The Mandelbrot fractal set\n"
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"Rendered with matplotlib %s, %s - http://matplotlib.org"
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% (matplotlib.__version__, year))
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ax.text(xmin+.025, ymin+.025, text, color="white", fontsize=12, alpha=0.5)
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plt.show()
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```
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Total running time of the script: ( 0 minutes 4.800 seconds)
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## 下载这个示例
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- [下载python源码: mandelbrot.py](https://matplotlib.org/_downloads/mandelbrot.py)
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- [下载Jupyter notebook: mandelbrot.ipynb](https://matplotlib.org/_downloads/mandelbrot.ipynb) |