|
用Python繪制著名的數(shù)學圖片或動畫,， 展示數(shù)學中的算法魅力,。 代碼：46 lines (34 sloc) 1.01 KB
| reddit discussion: https://www./r/math/comments/2abwyt/smooth_colour_mandelbrot/ |
| ''' |
| import numpy as np |
| fromPILimport Image |
| v = np.log2(i +1- np.log2(np.log2(abs(z)))) /5 |
| if v 1.0: |
| return v**4, v**2.5, v |
| v =max(0, 2-v) |
| return v, v**1.5, v**3 |
| z =0j |
| if z.real*z.real + z.imag*z.imag RADIUS: |
| return color(z, i) |
| z = z*z + c |
| x = np.linspace(xmin, xmax, width) |
| y = np.linspace(ymax, ymin, height) |
| z = x[None, :] + y[:, None]*1j |
| red, green, blue = np.asarray(np.frompyfunc(iterate, 1, 3)(z)).astype(np.float) |
| img = np.dstack((red, green, blue)) |
| Image.fromarray(np.uint8(img*255)).save('mandelbrot.png') |
 播放GIF 代碼鏈接：https://github.com/neozhaoliang/pywonderland/tree/master/src/domino 代碼：53 lines (40 sloc) 1.24 KB
| ''' |
| A kaleidoscope pattern with icosahedral symmetry. |
| ''' |
| return1728* (z * (z**10+11* z**5-1))**5/ \ |
| ''' |
| map the complex plane to Riemann's sphere via stereographic projection |
| ''' |
| t =1+ z.real*z.real + z.imag*z.imag |
| return2*z.real/t, 2*z.imag/t, 2/t-1 |
| ''' |
| distort the result image by a mobius transformation |
| ''' |
| x = np.linspace(-6, 6, imgsize) |
| y = np.linspace(6, -6, imgsize) |
| # define colors in hsv space |
| H = np.sin(z[0]*np.pi)**2 |
| S = np.cos(z[1]*np.pi)**2 |
| V =abs(np.sin(z[2]*np.pi) * np.cos(z[2]*np.pi))**0.2 |
| HSV= np.dstack((H, S, V)) |
| # transform to rgb space |
| img = hsv_to_rgb(HSV) |
| Image.fromarray(np.uint8(img*255)).save('kaleidoscope.png') |
| import time |
| start = time.time |
| main(imgsize=800) |
| end = time.time |
| print('runtime: {:3f} seconds'.format(end - start)) |
代碼：46 lines (35 sloc) 1.05 KB
| # define functions manually, do not use numpy's poly1d funciton! |
| @jit('complex64(complex64)', nopython=True) |
| # z*z*z is faster than z**3 |
| num =0 |
| whileabs(f(z)) 1e-4: |
| num += np.exp(-1/abs(w-z)) |
| z = w |
| x = np.linspace(-1, 1, imgsize) |
| y = np.linspace(1, -1, imgsize) |
| img = np.frompyfunc(iterate, 1, 1)(z).astype(np.float) |
| fig = plt.figure(figsize=(imgsize/100.0, imgsize/100.0), dpi=100) |
| ax = fig.add_axes([0, 0, 1, 1], aspect=1) |
| ax.axis('off') |
| ax.imshow(img, cmap='hot') |
| fig.savefig('newton.png') |
| import time |
| render(imgsize=400) |
| print('runtime: {:03f} seconds'.format(end - start)) |
代碼鏈接：https://github.com/neozhaoliang/pywonderland/blob/master/src/misc/e8.py 代碼鏈接： 播放GIF 代碼鏈接： 播放GIF 代碼鏈接：https://github.com/neozhaoliang/pywonderland/tree/master/src/wilson 播放GIF 代碼鏈接： 代碼：69 lines (48 sloc) 2.18 KB
| from itertools import combinations, product |
| import numpy as np |
| self.num_lines = num_lines |
| self.shift = shift |
| self.thin_color = thin_color |
| self.fat_color = fat_color |
| self.objs =self.compute_pov_objs(**config) |
| for rhombi, color inself.tile: |
| p1, p2, p3, p4 = rhombi |
| polygon = Polygon(5, p1, p2, p3, p4, p1, |
| Texture(Pigment('color', color), config['default'])) |
| objects_pool.append(polygon) |
| cylinder = Cylinder(p, q, config['edge_thickness'], config['edge_texture']) |
| objects_pool.append(cylinder) |
| x, y = point |
| sphere = Sphere((x, y, 0), config['vertex_size'], config['vertex_texture']) |
| objects_pool.append(sphere) |
| color =self.thin_color |
| else: |
| point = (Penrose.GRIDS[r] * (ks -self.shift[s]) |
| - Penrose.GRIDS[s] * (kr -self.shift[r])) *1j/ Penrose.GRIDS[s-r].imag |
| index = [np.ceil((point/grid).real + shift) |
| for grid, shift inzip(Penrose.GRIDS, self.shift)] |
| for index[r], index[s] in [(kr, ks), (kr+1, ks), (kr+1, ks+1), (kr, ks+1)]: |
| vertices.append(np.dot(index, Penrose.GRIDS)) |
| vertices_real = [(z.real, z.imag) for z in vertices] |
| for r, s in combinations(range(5), 2): |
| for kr, ks in product(range(-self.num_lines, self.num_lines+1), repeat=2): |
| yieldself.rhombus(r, s, kr, ks) |
| return Object(self.objs, *args) |
本文經(jīng)授權(quán)轉(zhuǎn)載自大數(shù)據(jù)文摘 編輯：yangfz 近期熱門文章Top10 ↓ 點擊標題即可查看 ↓ 點此查看以往全部熱門文章
|
