Julia Set Plotting Extension

Load module for a JuliaSet that conforms to the specified interface.

It is wise to run the test suite in test_juliaset.py with nosetests prior to attempting to plot here.

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from juliaset import JuliaSet

Load additional libraries needed for plotting and profiling.

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# 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

Extend JuliaSet class with additional functionality.

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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)
    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)

Visualize a Julia set using matplotlib.

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

Visualize a different Julia set using Bokeh as an interactive Javascript plot.

In [ ]:
j = JuliaSetPlot(-0.624 + 0.435j)
%time j.set_spacing(0.006)
%time j.generate()
%time j.interact()

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%prun j.generate()

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%load_ext line_profiler
%lprun -f j.generate j.generate()

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