import numpy as np
from scipy.integrate import odeint

from bokeh.plotting import figure, show, output_file

sigma = 10
rho = 28
beta = 8.0/3
theta = 3 * np.pi / 4

def lorenz(xyz, t):
    x, y, z = xyz
    x_dot = sigma * (y - x)
    y_dot = x * rho - x * z - y
    z_dot = x * y - beta* z
    return [x_dot, y_dot, z_dot]

initial = (-10, -7, 35)
t = np.arange(0, 100, 0.006)

solution = odeint(lorenz, initial, t)

x = solution[:, 0]
y = solution[:, 1]
z = solution[:, 2]
xprime = np.cos(theta) * x - np.sin(theta) * y

colors = ["#C6DBEF", "#9ECAE1", "#6BAED6", "#4292C6", "#2171B5", "#08519C", "#08306B",]

p = figure(title="lorenz example")

p.multi_line(np.array_split(xprime, 7), np.array_split(z, 7),
             line_color=colors, line_alpha=0.8, line_width=1.5)

output_file("lorenz.html", title="lorenz.py example")

show(p)  # open a browser
