In [1]:

    

# 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()


    

In [5]:

    

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 makeplane(self):

        i=np.arange(-2,2,self._d)

        self._complexplane=[complex(x,y) for x in i for y in i]

                

    def juliamap(self, z):

        return (z**2) + self.c

    

    def iterate(self, z):

        m = 0

        while True:

            z=self.juliamap(z)

            m = m + 1

            if  abs(z) > 2:

                return m

            if m >=self.n:

                return 0



    def set_spacing(self, d):

        self._d = d

        self.makeplane()



    def generate(self):

        self.set = [self.iterate(z) for z in self._complexplane]

        return self.set


    

In [6]:

    

class JuliaSetPlot(JuliaSet):
    """Extend JuliaSet to add plotting functionality"""
    
    def __init__(self, *args, **kwargs):
        # Invoke constructor for JuliaSet first, unaltered
        super(JuliaSetPlot, self).__init__(*args, **kwargs)
        # Add one more attribute: a rendered image array
        self.img = np.array([])
    
    def get_dim(self):
        # get what should be an attribute
        return int(sqrt(self.img.size)) #int(4.0 / self._d)
    
    def render(self):
        if not self.set: self.generate()
        # Convert inefficient list to efficient numpy array
        self.img = np.array(self.set)
        dim = self.get_dim()
        # Reshape array into a 2d complex plane
        self.img = np.reshape(self.img, (dim,dim)).T
        
    def show(self):
        if not self.img.size: self.render()
        # Specify complex plane axes efficiently
        xy = np.linspace(-2,2,self.get_dim())
        # Use matplotlib to plot image as an efficient mesh
        plt.figure(1, figsize=(12,9))
        plt.pcolormesh(xy,xy,self.img, cmap=plt.cm.hot)
        plt.colorbar()
        plt.show()
        
    def interact(self):
        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))]
        # Use bokeh to plot an interactive image
        f = blt.figure(x_range=[-2,2], y_range=[-2,2], plot_width=600, plot_height=600)
        f.image(image=[j.img], x=[-2,2], y=[-2,2], dw=[4], dh=[4], palette=bokehpalette)
        blt.show(f)


    

In [7]:

    

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


    

In [8]:

    

j = JuliaSetPlot(-0.624 + 0.435j)
%time j.set_spacing(0.006)
%time j.interact()


    

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