Python编程利用科赫曲线实现三维飘雪效果示例过程

import numpy as np
import matplotlib.pyplot as plt
from numpy.random import rand,randint
M,N = 10,100
x = rand(N)*100
y = rand(N)*100
plt.scatter(x,y,marker='.')
for i in range(N):
 M = randint(5,15)
 r = rand()*3
 for j in range(M):
  theta = np.pi*2/M*j
  plt.plot([x[i],x[i]+r*np.cos(theta)],
  [y[i],y[i]+r*np.sin(theta)])
plt.axis('off')
plt.show()

import numpy as np
import matplotlib.pyplot as plt
from numpy.random import rand,randint
# n>=1，生成科赫雪花的方法
def Koch(L,n=1):
 if n<1 : return
 newL = [] #(x,y)的列表
 for i in range(len(L)-1):
 delta = (L[i+1]-L[i])/3
 x = (L[i][0]+L[i+1][0])/2-np.sqrt(3)/2*delta[1]
 y = (L[i][1]+L[i+1][1])/2+np.sqrt(3)/2*delta[0]
 newL += [L[i],L[i]+delta,np.array([x,y]),L[i]+delta*2]
 newL.append(L[-1])
  return newL if n==1 else Koch(newL,n-1)
L0 = [
 np.array([0,0]),
 np.array([0.5,np.sqrt(3)/2]),
 np.array([1,0]),
 np.array([0,0])
]
def plot_Koch(L):
 for i in range(len(L)-1):
  p = np.array(L[i:i+2]).T
  plt.plot(p[0],p[1],color='lightblue',lw = 1)
 plt.xlim(-0.25,1.25)
 plt.ylim(-0.5,1.25)
 plt.show()
if __name__ == "__main__":
 plot_Koch(Koch(L0,3))

#n为雪花数量，low,high为最低和最高koch雪花阶数
def RandKoch(n,low,high):
 randKochs = []
 rMax = np.sqrt(1/n)
 for _ in range(n):
  cx,cy,t0 = rand(3)
  r = rand()*rMax
  L0 = [np.array([np.cos(t),np.sin(t)])*r+[cx,cy]
for t in (t0-np.arange(4)*np.pi*2/3)]
  randKochs.append(Koch(L0,randint(low,high)))
 return randKochs
def plot_Kochs(Ls):
 for L in Ls:
  for i in range(len(L)-1):
p = np.array(L[i:i+2]).T
plt.plot(p[0],p[1],color='lightblue',lw = 1)
 plt.xlim(-0.2,1.2)
 plt.ylim(-0.2,1.2)
 plt.show()

def plot_Kochs(Ls):
 for L in Ls:
  x,y = np.array(L).T
  plt.fill(x, y, color = 'lightblue')
 plt.xlim(-0.2,1.2)
 plt.ylim(-0.2,1.2)
 plt.show()

#导入PolyCollection绘制实心的3D图形
from mpl_toolkits.mplot3d.art3d import PolyCollection
def plot_Kochs_fill3d(Ls):
 fig = plt.figure()
 ax = fig.gca(projection='3d')
 p3d = PolyCollection(Ls,facecolors=np.repeat('lightblue',len(Ls)),alpha=0.7)
 ax.add_collection3d(p3d,zs=rand(len(Ls)),zdir='y')
 ax.set_xlim3d(0,1)
 ax.set_ylim3d(0,1)
 ax.set_zlim3d(0,1)
 plt.show()