In [10]:

    

# Math libraries
import numpy as np
from math import sqrt

# Matplotlib plotting libraries
import matplotlib.pyplot as plt
%matplotlib inline

# Bokeh plotting libraries
import bokeh.plotting as blt
blt.output_notebook()


    

    





    
        
        
        
    

        
        BokehJS successfully loaded.
    

In [17]:

    

class JuliaSet(object):
    
    def __init__(self,c,n=100):
        self.c = c
        self.n = n
        self._d = 0.001
        self._complexplane = np.array([])
        self.set = np.array([])

      
    def juliamap(self,z):
        return z**2 + self.c
    
    def iterate(self,z):
        m=0
        while True:
            z=self.juliamap(z)
            m+=1
            if abs(z)>2:
                return m
            if m>=self.n:
                return 0
            
    def makeplane(self):
        r=np.arange(-2,2,self._d)
        self._complexplane=[complex(p,q) for p in r for q in r]
        
    def set_spacing(self,d):
        self._d=d
        self.makeplane()
        
    def generate(self):
        self.set=[self.iterate(a) for a in self._complexplane]
        return self.set


    

In [18]:

    

class JuliaSetPlot(JuliaSet):
    """Extend JuliaSet to add plotting functionality"""
    
    def __init__(self, *args, **kwargs):
        # Invoke constructor for JuliaSet first, unaltered
        JuliaSet.__init__(self, *args, **kwargs)
        # Add another attribute: a rendered image array
        self.img = np.array([])
    
    def get_dim(self):
        """Return linear number of points in axis"""
        return int(sqrt(self.img.size))
    
    def render(self):
        """Render image as square array of ints"""
        if not self.set: self.generate()
        # Convert inefficient list to efficient numpy array
        self.img = np.array(self.set)
        # Reshape array into a 2d complex plane
        dim = int(sqrt(len(self.img)))
        self.img = np.reshape(self.img, (dim,dim)).T
        
    def show(self):
        """Use matplotlib to plot image as an efficient mesh"""
        if not self.img.size: self.render()
        plt.figure(1, figsize=(12,9))
        xy = np.linspace(-2,2,self.get_dim())
        plt.pcolormesh(xy, xy, self.img, cmap=plt.cm.hot)
        plt.colorbar()
        plt.show()
        
    def interact(self):
        """Use bokeh to plot an interactive image"""
        from matplotlib.colors import rgb2hex
        if not self.img.size: self.render()
        # Mimic matplotlib "hot" color palette
        colormap = plt.cm.get_cmap("hot")
        bokehpalette = [rgb2hex(m) for m in colormap(np.arange(colormap.N))]
        # Create bokeh figure
        f = blt.figure(x_range=(-2,2), y_range=(-2,2), plot_width=600, plot_height=600)
        f.image(image=[self.img], x=[-2], y=[-2], dw=[4], dh=[4], palette=bokehpalette, dilate=True)
        blt.show(f)


    

In [19]:

    

j = JuliaSetPlot(-1.037 + 0.17j)
%time j.set_spacing(0.006)
%time j.generate()
%time j.show()


    

    




CPU times: user 356 ms, sys: 4 ms, total: 360 ms
Wall time: 482 ms
CPU times: user 3.24 s, sys: 8 ms, total: 3.24 s
Wall time: 5.09 s






    













    




CPU times: user 1.54 s, sys: 912 ms, total: 2.45 s
Wall time: 3.2 s