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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
blt.output_notebook()
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
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(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)
Visualize a Julia set using matplotlib.
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j = JuliaSetPlot(-1.037 + 0.17j)
%time j.set_spacing(0.006)
%time j.show()
Visualize a different Julia set using Bokeh as an interactive Javascript plot.
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j = JuliaSetPlot(-0.624 + 0.435j)
%time j.set_spacing(0.006)
%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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