python绘制超炫酷动态Julia集示例

# 这些代码会在后面的程序中反复调用，不再说明
import numpy as np
import time
import matplotlib.pyplot as plt
import cupy as cp

#生成z坐标 x0,y0 为起始点， nx,ny为点数， delta为点距
def genZ(x0, y0, nx, ny, delta):
    real, img = cp.indices([nx,ny])*delta
    real += x0
    img += y0
    return real.T+img.T*1j

#获取Julia集，n为迭代次数，m为判定发散点，大于1即可
def getJulia(z,c,n,m=2):
    t = time.time()
    z,out = z*1, cp.abs(z)
    c = cp.zeros_like(z)+c
    for i in range(n):
        absz = cp.abs(z)
        z[absz>m]=0		#对开始发散的点置零
        c[absz>m]=0		
        out[absz>m]=i	#记录发散点的发散速度
        z = z*z + c
    print("time:",time.time()-t)
    return out

z1 = genZ(-2,-1.5,1000,1000,0.003)
mBrot = getJulia(z1,z1,50)
plt.imshow(mBrot.get(), cmap=plt.cm.jet)
plt.show()

from matplotlib import animation

fig = plt.figure()
fig.subplots_adjust(top=1, bottom=0, left=0, right=1)
ax = plt.subplot()

def getJulias(z,c,n,m=2):
    z,out = z*1, cp.abs(z)
    c = cp.zeros_like(z)+c
    J = []
    for i in range(n):
        z = z*z + c
        absz = cp.abs(z)
        z[absz>m]=0		#对开始发散的点置零
        c[absz>m]=0		
        out[absz>m]=i	#记录发散点的发散速度
        im = ax.imshow(out.get(),cmap=plt.cm.jet, animated=True)
        ax.set_axis_off()
        J.append([im])
    return J

N = 75     #迭代次数
z1 = genZ(-2,-1.5,1000,1000,0.003)
J = getJulias(z1,z1,N)

ani = animation.ArtistAnimation(fig, J, interval=50, blit=True,repeat_delay=1000)
plt.show()
ani.save('julias.gif',writer='imagemagick')

from matplotlib import animation

# 生成z坐标 xy=np.array([xc,yc]) 为起始点，
# nxy=np.array([nx,ny])为点数， delta为点距
def genZbyCenter(xy,nxy,delta):
    x0, y0 = xy-np.array(nxy)*delta/2
    return genZ(x0,y0,*nxy,delta)

mBrots = []
xy = [-0.75,-0.2]
nxy = [1000,1000]
delta0 = 0.003  #初始宽度

fig = plt.figure()
fig.subplots_adjust(top=1, bottom=0, left=0, right=1)
ax = plt.subplot()

for n in range(50):
    z1 = genZbyCenter(xy,nxy,1.1**(-n)*delta0)
    out = getJulia(z1,z1,40)
    im = ax.imshow(out.get(),cmap=plt.cm.jet, animated=True)
    ax.set_axis_off()
    mBrots.append([im])

ani = animation.ArtistAnimation(fig, mBrots, interval=50, blit=True)
plt.show()
ani.save('zoom.gif',writer='imagemagick')

z1 = genZ(-2,-1.5,1000,1000,0.003)

fig = plt.figure()
fig.subplots_adjust(top=1, bottom=0, left=0, right=1)
ax = plt.subplot()

mBrots = []
for x in np.arange(0.5,1,0.01):
    c = x + x*1j
    out = getJulia(z1,c,40)
    im = ax.imshow(out.get(),cmap=plt.cm.jet, animated=True)
    ax.set_axis_off()
    mBrots.append([im])

ani = animation.ArtistAnimation(fig, mBrots, interval=50)
plt.show()
ani.save('julia.gif',writer='imagemagick')