In [1]:
# Math libraries
import numpy as np
import math
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 [2]:
class JuliaSet(object):
def __init__(self, c, n = 100):
self.c = c
self.n = n
self._d = .001
self.set = np.array([])
def juliamap(self, z):
return z ** 2 + self.c
def iterate(self, z):
for m in np.arange(1, self.n+1):
z = self.juliamap(z)
if abs(z) > 2:
return m
return 0
def setcomplexplane(self, _d, r=-2, r1=2):
plane = np.arange(r,r1,self._d)
plane = np.append(plane, 2)
x, y = np.meshgrid(plane, plane)
z = x + y*1j
self._complexplane = z
def set_spacing(self, d, r=-2, r1=2):
self._d = d
self.setcomplexplane(d, r=-2, r1=2)
def generate(self):
i = np.vectorize(self.iterate)
self.set = i(self._complexplane)
return self.set
To improve the speed of JuliaSet I used meshgrid to evaluate the complexplane without any loops so the complexplane would be generated faster. I also changed the generate function to vectorize the iterate function and apply it to the complexplane instead of using loops
In [3]:
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(math.sqrt(self.img.size))
def render(self):
if not self.set: self.generate()
# Convert inefficient list to efficient numpy array
dim = int(math.sqrt(self.set.size))
# Reshape array into a 2d complex plane
self.img = np.reshape(self.set, (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 [4]:
j = JuliaSetPlot(-1.037 + 0.17j)
%time j.set_spacing(0.006)
%time j.show()
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