使用Python的matplotlib绘制lozi混沌映射吸引子

# -*- coding: utf-8 -*-
#需要安装matplotlib、numpy等库才能运行
import numpy as np
import pylab as pl
import time
from matplotlib import cm

def iter_point2(x,y):
    #初始化公式的参数，需要改的话，可以改参数
    a = 1
    b = 1.75
    iter = 0 #初始化迭代次数
    for i in range(1, 10):
        iter = i
        dist = (x*x + y*y)  #计算摸长，看是否超过最大限度
        dist *= dist
        #print "dist:" + str(dist)
        if  dist > 200:  #如果超出了最大长度，就跳出循环，返回这个迭代次数
            break
        #临时保存一下x和y
        tempx = x
        tempy = y
        #这里是公式 X = a-b|x| + y ; Y = 0.3x;
        x = a - b*abs(tempx) + tempy
        y = 0.3*tempx
    return iter

#绘制图形时，以cx，xy为中心，距离为d
def draw_lozi(cx, cy, d):
    size = 400
    x0, x1, y0, y1 = cx-d, cx+d, cy-d, cy+d 
    y, x = np.ogrid[y1:y0:size*1j, x0:x1:size*1j] #使用范围生成数组，后面用这个进行迭代
    c = x + y*1j
    x.shape = -1 #转化成线性数组
    y.shape = -1

    start = time.clock()
    lozi = np.ones(c.shape)
    #遍历每一个点，计算迭代次数，赋值给数组lozi
    for j in range(0,size):
        for i in range(0,size):
            lozi[j][i] = iter_point2(x[i],y[j])
            pass

    print ("time="),time.clock() - start
    #使用数组lozi，绘图， 使用蓝色调色板，显示到图上的坐标范围是x0,x1,y0,y1
    pl.imshow(lozi, cmap=cm.Blues_r, extent=[x0,x1,y0,y1])
    #不显示横纵坐标
    pl.gca().set_axis_off()
    #刷新画布
    pl.show()

#鼠标点击触发执行的函数
def on_press(event):
    global g_size
    print (event)
    print (dir(event))
    newx = event.xdata
    newy = event.ydata
    print (newx)
    print (newy)

    #不合理的鼠标点击，直接返回，不绘制
    if newx == None or newy == None  or event.dblclick == True:
        return None
    #不合理的鼠标点击，直接返回，不绘制
    if event.button == 1:  #button ==1 代表鼠标左键按下， 是放大图像
        g_size /= 2
    elif event.button == 3: #button == 3 代表鼠标右键按下， 是缩小图像
        g_size *= 2
    else:
        return None
    print (g_size)

    draw_lozi(newx,newy,g_size)
fig, ax = pl.subplots(1)

g_size = 4.5

#注册鼠标事件
fig.canvas.mpl_connect('button_press_event', on_press)

#初始绘制一个图
draw_lozi(0,0,g_size)

import matplotlib.pyplot as plt
listx=[]
listy=[]
def Henon(x,y,n):
    for i in range(n):
        x1 = 1 - 1.4 * x ** 2 + y
        y1 = 0.3 * x
        x = x1
        y = y1
        listx.append(x)
        listy.append(y)

if __name__ == '__main__':
    Henon(0.13245678,0.13246789,1000)
    plt.plot(listx, listy)
    plt.show()

# -*- coding: utf-8 -*-
"Lorenz's strange attractor"
import matplotlib as plt
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt
xs, ys, zs = [], [], []
def mkPoints():
    a, b, c = 10.0, 28.0, 8.0 / 3.0
    h = 0.01
    x0, y0, z0 = 0.1, 0, 0
    for i in range(10000):
        x1 = x0 + h * a * (y0 - x0)
        y1 = y0 + h * (x0 * (b - z0) - y0)
        z1 = z0 + h * (x0 * y0 - c * z0)
        x0, y0, z0 = x1, y1, z1
        xs.append(x0)
        ys.append(y0)
        zs.append(z0)

if __name__ == "__main__":
    # 画3D的
    fig = plt.figure()
    ax = Axes3D(fig)
    mkPoints()
    ax.plot(xs, ys, zs, label="Lorenz's strange attractor")
    ax.legend()
    plt.show()


    # 画2D的
    # mkPoints()
    # plt.plot(zs, ys)
    # plt.show()