In [16]:

    

import numpy as np

class JuliaSet(object):

    def __init__(self, c, n=100):
        self.c = c
        self.n = n
        self._d = 0.001
        self._complexplane=[]
        self.set=[]

    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
            elif m>=self.n:
                return 0
    
    def drange(self, start, stop, step):
        r = start
        while r <= stop:
            yield r
            r += step
    
    # Generate evenly spaced values over x and y planes
    def get_complexplane(self):
        self._complexplane = []
        _range=self.drange(-2, 2, self._d)
        for x in self.drange(-2, 2, self._d):
            for y in self.drange(-2, 2, self._d):
                np.append(_complexplane, complex(x,y))
    
    def set_spacing(self, d):
        self._d = d
        self.get_complexplane()
        
    def generate(self):
        for x in self._complexplane:
            np.append(self.iterate(x), self.iterate(x))
        return self.set


    

In [17]:

    

from juliaset import JuliaSet
# 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()

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(4.0 / self._d)
    
    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)


    

    





    
        
        
        
    

        
        BokehJS successfully loaded.
    

In [ ]:

    

j = JuliaSetPlot( -0.835 - 0.2321j)
%time j.set_spacing(0.006)
%time j.generate()
%time j.interact()


    

    




CPU times: user 388 ms, sys: 16 ms, total: 404 ms
Wall time: 1.06 s
CPU times: user 2 s, sys: 36 ms, total: 2.04 s
Wall time: 6.63 s






    















    




CPU times: user 372 ms, sys: 28 ms, total: 400 ms
Wall time: 2.07 s

In [ ]:

    

j = JuliaSetPlot(0)
%time j.set_spacing(0.006)
%time j.generate()
%time j.interact()


    

In [ ]: