python编程matplotlib交互绘制Julia集示例解析_Python

Julia集

python编程matplotlib交互绘制Julia集示例解析

特别地，当 c = z的初始值时，符合收敛条件的 z 的便构成大名鼎鼎的Mandelbrot集

python编程matplotlib交互绘制Julia集示例解析

在上图中，颜色表示该点的发散速度，可以理解为开始发散时迭代的次数。其生成代码也非常简单：

#mbrot.py
import numpy as np
import time
import pyplotlib.pyplot as plt
#生成z坐标，axis为起始位置，nx，ny为x向和y向的格点个数
def genZ(axis,nx,ny):
    x0,x1,y0,y1 = axis
    x = np.linspace(x0,x1,nx)
    y = np.linspace(y0,y1,ny)
    real, img = np.meshgrid(x,y)
    z = real + img*1j
    return z
#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()
    c = np.zeros_like(z)+c
    out = abs(z)
    for i in range(n):
        absz = 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
if __name__ == "__main__":
    axis = np.array([-2,1,-1.5,1.5])
    z0 = genZ(axis,500,500)
    mBrot = getJulia(z0,z0,50)
    plt.imshow(mBrot, cmap=cm.jet, extent=axis)
    plt.gca().set_axis_off()
    plt.show()

matplotlib绑定事件

下面希望实现点击Mandelbrot集中的一点，生成相应的Julia集。
在mpl中，事件绑定函数mpl_connect被封装在cavnas类中，调用格式为

canvas.mpl_connect("str", func)

其中func事件函数，字符串为被传入事件函数的事件标识，如下所列，望文生义即可

"button_press_event"
"button_release_event"
"draw_event"
"key_press_event"
"key_release_event"
"motion_notify_event"
"pick_event"
"resize_event"
"scroll_event"
"figure_enter_event"
"figure_leave_event"
"axes_enter_event"
"axes_leave_event"
"close_event"

简单起见，可以先检测一下鼠标点击事件"button_press_event"，对此我们需要定义一个事件函数，并将上面的入口函数稍加修改：

def test(evt):
    print(evt.xdata)	#xdata即x方向的坐标
if __name__ == "__main__":
    axis = np.array([-2,1,-1.5,1.5])
    z0 = genZ(axis,500,500)
    mBrot = getJulia(z0,z0,50)
    fig, ax = plt.subplots()
    fig.canvas.mpl_connect("button_press_event", test)#调用事件函数
    plt.imshow(mBrot, cmap=cm.jet, extent=axis)
    plt.gca().set_axis_off()
    plt.show()

于是点击imshow()出来的图片，即可返回相应的x坐标。

python mbrot.py
time: 0.47572827339172363
-0.8652597402597402
-0.7840909090909087
-0.18344155844155807
0.23051948051948123
0.8149350649350655

缩放

那么生成Julia集只需要重新调用一次getJulia这个函数即可。
Mandelbrot集的分形特征意味着我们所生成的图片可以无限放大，但是mpl自带的放大工具并不会重新生成数据，所以是虚假的放大。因此需要重新绑定放大操作，其思路是，当右键点击(‘button_press_event")时，记录此时的坐标，当右键释(‘button_release_event")放时重新绘制图片，为了防止与左键冲突，所以在点击所对应的事件函数中加入左右键判断。

其结果如图

python编程matplotlib交互绘制Julia集示例解析

此外，还可以绑定鼠标滚轮，实现Mandelbrot集在该点的真实缩放，代码如下

import matplotlib.pyplot as plt
import numpy as np
from matplotlib import cm
import matplotlib.backend_bases as mbb
import time
class MandelBrot():
    def __init__(self,x0,x1,y0,y1,n):
        self.oriAxis = np.array([x0,x1,y0,y1])        	#初始坐标
        self.axis = self.oriAxis
        self.nx,self.ny,self.nMax = n,n,n               #x,y方向的网格划分个数
        self.nIter = 100                                #迭代次数
        self.n0 = 0                                     #预迭代次数
        self.z = genZ(self.oriAxis,self.nx,self.ny)
        self.DrawMandelbrot()
    def DrawMandelbrot(self):
        mBrot = getJulia(self.z,self.z,self.nIter)       
        self.fig, ax = plt.subplots()
        plt.imshow(mBrot, cmap=cm.jet, extent=self.axis)
        plt.gca().set_axis_off()        
        self.fig.canvas.mpl_disconnect(self.fig.canvas.manager.key_press_handler_id)
        self.fig.canvas.mpl_connect("button_press_event", self.OnMouse)
        self.fig.canvas.mpl_connect("button_release_event", self.OnRelease)
        self.fig.canvas.mpl_connect("scroll_event", self.OnScroll)       
        plt.show()
    def DrawJulia(self,c0):
        z = genZ([-2,2,-2,2],800,800)
        julia = getJulia(z,c0,self.nIter)        
        jFig,jAx = plt.subplots()
        plt.cla()
        plt.imshow(julia, cmap=cm.jet, extent=self.axis)
        plt.gca().set_axis_off()
        plt.show()
        jFig.canvas.draw_idle()	
	#滚轮缩放
    def OnScroll(self,evt):
        x0,y0 = evt.xdata,evt.ydata
        if evt.button == "up":
            self.axis = (self.axis+[x0,x0,y0,y0])/2
        elif evt.button == "down":
            self.axis = 2*self.axis-[x0,x0,y0,y0]
        z = genZ(self.axis,self.nx,self.ny)
        mBrot = getJulia(z,z,self.nIter)
        plt.cla()
        plt.imshow(mBrot, cmap=cm.jet, extent=self.axis)
        plt.gca().set_axis_off()        
        mBrot[mBrot<1]==self.n0+self.nIter
        self.n0 = int(np.min(mBrot))
        self.fig.canvas.draw_idle()
        pass
    def OnMouse(self, evt):
        self.xStart = evt.xdata
        self.yStart = evt.ydata
        self.fig.canvas.draw_idle()    
    def OnRelease(self,evt):
        x0,y0,x1,y1 = self.xStart,self.yStart,evt.xdata,evt.ydata
        if evt.button == mbb.MouseButton.LEFT:
            self.DrawJulia(x1+y1*1j)		#如果释放的是左键，那么就绘制Julia集并返回
            return
        #右键拖动，可以对Mandelbrot集进行真实的放大
        self.axis = np.array([min(x0,x1),max(x0,x1),
                             min(y0,y1),max(y0,y1)])        
        nxny = self.axis[[1,3]]-self.axis[[0,2]]
        self.nx,self.ny = (nxny/max(nxny)*self.nMax).astype(int)
        z = genZ(self.axis,self.nx,self.ny)
        n = 100     #n为迭代次数
        mBrot = getJulia(z,z,n)
        plt.cla()
        plt.imshow(mBrot, cmap=cm.jet, extent=self.axis)
        plt.gca().set_axis_off()        
        mBrot[mBrot<1]==self.n0+n
        self.n0 = int(np.min(mBrot))
        self.fig.canvas.draw_idle()
def genZ(axis,nx,ny):
    x0,x1,y0,y1 = axis
    x = np.linspace(x0,x1,nx)
    y = np.linspace(y0,y1,ny)
    real, img = np.meshgrid(x,y)
    z = real + img*1j
    return z
def getJulia(z,c,n,n0=0,m=2):
    t = time.time()
    c = np.zeros_like(z)+c
    out = abs(z)
    for _ in range(n0):
        z = z*z + c
    for i in range(n0,n0+n):
        absz = abs(z)
        z[absz>m]=0
        c[absz>m]=0
        out[absz>m]=i
        z = z*z + c
    print("time:",time.time()-t)
    return out
if __name__ == "__main__":
    x,y = 0,0
    brot = MandelBrot(-2,1,-1.5,1.5,1000)

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原文链接：https://blog.csdn.net/m0_37816922/article/details/102530064