如何用Python画各种著名数学图案 | 附图 代码

用Python绘制著名的数学图片或动画，

展示数学中的算法魅力。

代码：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')

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代码链接：https://github.com/neozhaoliang/pywonderland/tree/master/src/domino

正二十面体万花筒

代码：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))

Newton 迭代分形

代码：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))

李代数E8 的根系

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

模群的基本域

代码链接：

彭罗斯铺砌

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代码链接：

Wilson 算法

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代码链接：https://github.com/neozhaoliang/pywonderland/tree/master/src/wilson

反应扩散方程模拟

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代码链接：

120 胞腔

代码：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)

本文经授权转载自大数据文摘

编辑：yangfz

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