python代码画一个图形_如何用Python画各种著名数学图案|附图+代码

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用Python绘制著名的数学图片或动画&＃xff0c;展示数学中的算法魅力。

本项⽬目将持续更更新&＃xff0c;数学中有着太多有趣的事物可以⽤用代码去展示。  欢迎提出建议和参与建设&＃xff01;

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Mandelbrot 集

代码&＃xff1a;46 lines (34 sloc)  1.01 KB&＃39;&＃39;&＃39;A fast Mandelbrot set wallpaper rendererreddit discussion: https://www.reddit.com/r/math/comments/2abwyt/smooth_colour_mandelbrot/&＃39;&＃39;&＃39;import numpy as npfrom PIL import Imagefrom numba import jitMAXITERS &＃61; 200RADIUS &＃61; 100&＃64;jitdef color(z, i):v &＃61; np.log2(i &＃43; 1 - np.log2(np.log2(abs(z)))) / 5if v <1.0:return v**4, v**2.5, velse:v &＃61; max(0, 2-v)return v, v**1.5, v**3&＃64;jitdef iterate(c):z &＃61; 0jfor i in range(MAXITERS):if z.real*z.real &＃43; z.imag*z.imag > RADIUS:return color(z, i)z &＃61; z*z &＃43; creturn 0, 0 ,0def main(xmin, xmax, ymin, ymax, width, height):x &＃61; np.linspace(xmin, xmax, width)y &＃61; np.linspace(ymax, ymin, height)z &＃61; x[None, :] &＃43; y[:, None]*1jred, green, blue &＃61; np.asarray(np.frompyfunc(iterate, 1, 3)(z)).astype(np.float)img &＃61; np.dstack((red, green, blue))Image.fromarray(np.uint8(img*255)).save(&＃39;mandelbrot.png&＃39;)if __name__ &＃61;&＃61; &＃39;__main__&＃39;:main(-2.1, 0.8, -1.16, 1.16, 1200, 960)

多米诺洗牌算法

代码链接&＃xff1a;https://github.com/neozhaoliang/pywonderland/tree/master/src/domino

正二十面体万花筒

代码&＃xff1a;53 lines (40 sloc)  1.24 KB&＃39;&＃39;&＃39;A kaleidoscope pattern with icosahedral symmetry.&＃39;&＃39;&＃39;import numpy as npfrom PIL import Imagefrom matplotlib.colors import hsv_to_rgbdef Klein(z):&＃39;&＃39;&＃39;Klein&＃39;s j-function&＃39;&＃39;&＃39;return 1728 * (z * (z**10 &＃43; 11 * z**5 - 1))**5 / \(-(z**20 &＃43; 1) &＃43; 228 * (z**15 - z**5) - 494 * z**10)**3def RiemannSphere(z):&＃39;&＃39;&＃39;    map the complex plane to Riemann&＃39;s sphere via stereographic projection    &＃39;&＃39;&＃39;t &＃61; 1 &＃43; z.real*z.real &＃43; z.imag*z.imagreturn 2*z.real/t, 2*z.imag/t, 2/t-1def Mobius(z):&＃39;&＃39;&＃39;    distort the result image by a mobius transformation    &＃39;&＃39;&＃39;return (z - 20)/(3*z &＃43; 1j)def main(imgsize):x &＃61; np.linspace(-6, 6, imgsize)y &＃61; np.linspace(6, -6, imgsize)z &＃61; x[None, :] &＃43; y[:, None]*1jz &＃61; RiemannSphere(Klein(Mobius(Klein(z))))# define colors in hsv spaceH &＃61; np.sin(z[0]*np.pi)**2S &＃61; np.cos(z[1]*np.pi)**2V &＃61; abs(np.sin(z[2]*np.pi) * np.cos(z[2]*np.pi))**0.2HSV &＃61; np.dstack((H, S, V))# transform to rgb spaceimg &＃61; hsv_to_rgb(HSV)Image.fromarray(np.uint8(img*255)).save(&＃39;kaleidoscope.png&＃39;)if __name__ &＃61;&＃61; &＃39;__main__&＃39;:import timestart &＃61; time.time()main(imgsize&＃61;800)end &＃61; time.time()print(&＃39;runtime: {:3f} seconds&＃39;.format(end - start))

Newton 迭代分形

代码&＃xff1a;46 lines (35 sloc)  1.05 KBimport numpy as npimport matplotlib.pyplot as pltfrom numba import jit# define functions manually, do not use numpy&＃39;s poly1d funciton!&＃64;jit(&＃39;complex64(complex64)&＃39;, nopython&＃61;True)def f(z):# z*z*z is faster than z**3return z*z*z - 1&＃64;jit(&＃39;complex64(complex64)&＃39;, nopython&＃61;True)def df(z):return 3*z*z&＃64;jit(&＃39;float64(complex64)&＃39;, nopython&＃61;True)def iterate(z):num &＃61; 0while abs(f(z)) > 1e-4:w &＃61; z - f(z)/df(z)num &＃43;&＃61; np.exp(-1/abs(w-z))z &＃61; wreturn numdef render(imgsize):x &＃61; np.linspace(-1, 1, imgsize)y &＃61; np.linspace(1, -1, imgsize)z &＃61; x[None, :] &＃43; y[:, None] * 1jimg &＃61; np.frompyfunc(iterate, 1, 1)(z).astype(np.float)fig &＃61; plt.figure(figsize&＃61;(imgsize/100.0, imgsize/100.0), dpi&＃61;100)ax &＃61; fig.add_axes([0, 0, 1, 1], aspect&＃61;1)ax.axis(&＃39;off&＃39;)ax.imshow(img, cmap&＃61;&＃39;hot&＃39;)fig.savefig(&＃39;newton.png&＃39;)if __name__ &＃61;&＃61; &＃39;__main__&＃39;:import timestart &＃61; time.time()render(imgsize&＃61;400)end &＃61; time.time()print(&＃39;runtime: {:03f} seconds&＃39;.format(end - start))

李代数E8 的根系

代码链接&＃xff1a;https://github.com/neozhaoliang/pywonderland/blob/master/src/misc/e8.py