%run talktools
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt

np.random.seed(0)
x, y = np.random.normal(size=(2, 100))
s, c = np.random.random(size=(2, 100))
    
def draw_scatter(size=100, cmap='jet', alpha=1.0):
    fig, ax = plt.subplots(figsize=(8, 6))
    points = ax.scatter(x, y, s=size*s, c=c, alpha=alpha, cmap=cmap)
    fig.colorbar(points, ax=ax)
    return fig

draw_scatter(size=100, cmap='jet', alpha=1.0);

from IPython.html.widgets import interact

colormaps = sorted(m for m in plt.cm.datad if not m.endswith("_r"))
interact(draw_scatter, size=[0, 2000], alpha=[0.0, 1.0], cmap=colormaps);

import networkx as nx

def random_lobster(n, m, k, p):
    return nx.random_lobster(n, p, p / m)

def powerlaw_cluster(n, m, k, p):
    return nx.powerlaw_cluster_graph(n, m, p)

def erdos_renyi(n, m, k, p):
    return nx.erdos_renyi_graph(n, p)

def newman_watts_strogatz(n, m, k, p):
    return nx.newman_watts_strogatz_graph(n, k, p)

def plot_random_graph(n, m, k, p, generator):
    g = generator(n, m, k, p)
    nx.draw(g)
    plt.show()

interact(plot_random_graph, n=(2,30), m=(1,10), k=(1,10), p=(0.0, 1.0, 0.001),
        generator={'lobster': random_lobster,
                   'power law': powerlaw_cluster,
                   'Newman-Watts-Strogatz': newman_watts_strogatz,
                   u'Erdős-Rényi': erdos_renyi,
                   });

import numpy as np
from scipy import integrate

from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.colors import cnames
from matplotlib import animation

def solve_lorenz(N=10, angle=0.0, max_time=4.0, sigma=10.0, beta=8./3, rho=28.0):
    
    def lorenz_deriv((x, y, z), t0, sigma=sigma, beta=beta, rho=rho):
        """Compute the time-derivative of a Lorentz system."""
        return [sigma * (y - x), x * (rho - z) - y, x * y - beta * z]

    # Choose random starting points, uniformly distributed from -15 to 15
    np.random.seed(1)
    x0 = -15 + 30 * np.random.random((N, 3))

    # Solve for the trajectories
    t = np.linspace(0, max_time, int(250*max_time))
    x_t = np.asarray([integrate.odeint(lorenz_deriv, x0i, t)
                      for x0i in x0])
    
    # choose a different color for each trajectory
    colors = plt.cm.jet(np.linspace(0, 1, N))

    # plot the results
    fig = plt.figure()
    ax = fig.add_axes([0, 0, 1, 1], projection='3d')
    ax.axis('off')

    # prepare the axes limits
    ax.set_xlim((-25, 25))
    ax.set_ylim((-35, 35))
    ax.set_zlim((5, 55))

    for i in range(N):
        x, y, z = x_t[i,:,:].T
        lines = ax.plot(x, y, z, '-', c=colors[i])
        plt.setp(lines, linewidth=2)

    ax.view_init(30, angle)
    plt.show()

    return t, x_t

t, x_t = solve_lorenz()

from IPython.html.widgets import interactive

w = interactive(solve_lorenz, angle=(0.,360.), N=(0,50), sigma=(0.0,50.0), rho=(0.0,50.0))
display(w)

w.result