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()