In [9]:
# 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 [10]:
import math
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 = np.array([])
self.set = np.array([])
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
if m >= self.n:
return 0
def makeplane(self):
plane = [i * self._d for i in range(int(-2 / self._d), int(2 / self._d), 1)]
self._complexplane=[complex(x,y) for x in plane for y in plane]
def set_spacing(self, d):
self._d = d
self.makeplane()
def generate(self):
self.set = [self.iterate(i) for i in self._complexplane]
return self.set
In [11]:
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)
In [12]:
j = JuliaSetPlot(-1.037 + 0.17j)
%time j.set_spacing(0.006)
%time j.show()
In [13]:
j = JuliaSetPlot(-0.624 + 0.435j)
%time j.set_spacing(0.006)
%time j.interact()
In [14]:
%prun j.generate()
In [15]:
%load_ext line_profiler
%lprun -f j.generate j.generate()