betatim/convert.sh

## convert.sh
# Convert your notebook to an interactive webpage
#
#  Attached a notebook (really-interactive-posts.ipynb) and the generated
# output (really-interactive-posts.html). The thebe.tpl template file is
# at the very end of the gist.

$ jupyter nbconvert --template thebe.tpl --to html <notebook.ipynb>


# You can open the generated webpage locally file://... howerver some
# resources will not load properly. Best to open it from a webserver:

$ python3 -m http.server

# or if you'd rather have a local https server (credit to: https://gist.github.com/dergachev/7028596)
# generate certificate with the following command:

$ openssl req -new -x509 -keyout server.pem -out server.pem -days 365 -nodes
$ echo "import BaseHTTPServer, SimpleHTTPServer
import ssl

httpd = BaseHTTPServer.HTTPServer(('localhost', 4443), SimpleHTTPServer.SimpleHTTPRequestHandler)
httpd.socket = ssl.wrap_socket (httpd.socket, certfile='./server.pem', server_side=True)
httpd.serve_forever()" > simple-https-server.py

# run with:

$ python simple-https-server.py

# In your browser, visit:
#    https://localhost:4443

## really-interactive-posts.html

<head>
  <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/codemirror/5.10.0/codemirror.min.css">

  <script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/1.11.0/jquery.min.js" type="text/javascript"></script>
  <script type="text/javascript" src="https://cdn.rawgit.com/oreillymedia/thebe/17fe0971303cac24d7e806c8f1bc8ba3c0c40b23/static/main-built.js"></script>
  <script>
    $(function(){
      new Thebe({url:"https://tmpnb.org/",
                 kernel_name: "python3"});
    });
  </script>
</head>

<div class="cellOOO border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h1 id="Really-Interactive-Blog-Posts">Really Interactive Blog Posts<a class="anchor-link" href="#Really-Interactive-Blog-Posts">&#182;</a></h1><p><em>This notebook first appeared as a <a href="//betatim.github.io/posts/really-interactive-blog-posts">blog post</a> on <a href="//betatim.github.io">Tim Head</a>'s blog.</em></p>
<p><em>License: <a href="http://opensource.org/licenses/MIT">MIT</a></em></p>
<p><em>(C) 2016, Tim Head.</em>
<em>Feel free to use, distribute, and modify with the above attribution.</em></p>

</div>
</div>
</div>
<div class="cellOOO border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>A few days ago I started making my <a href="/posts/interactive-posts/">blog posts interactive</a>.
It was cool, but required you to surf to a different page for the interactive
experience, while the original post was still non-interactive.</p>
<p><a href="//alexpearce.me">Alex</a> pointed out that really you wanted it all in one
page. Basically he was:</p>
<p><img src="/images/meh.gif" width="480" height="270" /></p>
<p>My blog setup follows <a href="https://jakevdp.github.io/blog/2013/05/07/migrating-from-octopress-to-pelican/">Jake Vanderplas'</a> pretty closely. So I created a new <a href="https://github.com/getpelican/pelican-plugins/tree/master/liquid_tags"><code>liquid_tags</code></a> plugin
that has its own template for <code>nbconvert</code> which generates HTML that <a href="https://github.com/oreillymedia/thebe">thebe</a> understands.</p>
<p>No downloading, no installing, no browsing to a separate page! Just interactive blog
posts! (Scroll down to see it in action if you do not care how it was done.)</p>
<h2 id="Do-it-yourself">Do it yourself<a class="anchor-link" href="#Do-it-yourself">&#182;</a></h2><p>I am preparing a write up of how to modify your own <a href="http://blog.getpelican.com/">pelican</a> site have an interactive section. For the keen and eager people, the most important part is using the following template with <code>nbconvert</code>:</p>

<pre><code>{%- extends 'basic.tpl' -%}

{% block codecell %}
&lt;pre data-executable&gt;
{{ cell.source }}
&lt;/pre&gt;
{% endblock codecell %}

{% block markdowncell scoped %}
&lt;div class="cellOOO border-box-sizing text_cell rendered"&gt;
{{ self.empty_in_prompt() }}
&lt;div class="inner_cell"&gt;
&lt;div class="text_cell_render border-box-sizing rendered_html"&gt;
{{ cell.source  | markdown2html | strip_files_prefix }}
&lt;/div&gt;
&lt;/div&gt;
&lt;/div&gt;
{%- endblock markdowncell %}</code></pre>
<p>It embeds code cells in simple <code>&lt;pre&gt;</code> tags and modifies non-code cells so that they do not
match the selectors used inside the notebook machinery. That is it. Then stick a bit of CSS and JS in the <code>&lt;head&gt;</code> of your web page and you are good to go (use the source of this one for inspiration).</p>
<h3 id="Credits">Credits<a class="anchor-link" href="#Credits">&#182;</a></h3><p>Compared to my previous post this setup now only relies on <a href="https://github.com/oreillymedia/thebe">thebe</a>, <a href="https://tmpnb.org">tmpnb</a>, and the kind people at <a href="https://developer.rackspace.com/">rackspace</a> who sponsor the computing power for <code>tmpnb</code>.</p>
<p>Below, the work of the jupyter development team, licensed under the 3 clause BSD license.</p>
<p>Get in touch on twitter @<a href="//twitter.com/betatim">betatim</a>.</p>

</div>
</div>
</div>
<div class="cellOOO border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h1 id="Exploring-the-Lorenz-System-of-Differential-Equations">Exploring the Lorenz System of Differential Equations<a class="anchor-link" href="#Exploring-the-Lorenz-System-of-Differential-Equations">&#182;</a></h1>
</div>
</div>
</div>
<div class="cellOOO border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>In this Notebook we explore the Lorenz system of differential equations:</p>
$$
\begin{aligned}
\dot{x} & = \sigma(y-x) \\
\dot{y} & = \rho x - y - xz \\
\dot{z} & = -\beta z + xy
\end{aligned}
$$<p>This is one of the classic systems in non-linear differential equations. It exhibits a range of different behaviors as the parameters ($\sigma$, $\beta$, $\rho$) are varied.</p>

</div>
</div>
</div>
<div class="cellOOO border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h2 id="Imports">Imports<a class="anchor-link" href="#Imports">&#182;</a></h2>
</div>
</div>
</div>
<div class="cellOOO border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>First, we import the needed things from IPython, NumPy, Matplotlib and SciPy.</p>

</div>
</div>
</div>
<pre data-executable>
%matplotlib inline
</pre>

<pre data-executable>
from ipywidgets import interact, interactive
from IPython.display import clear_output, display, HTML
</pre>

<pre data-executable>
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
</pre>

<div class="cellOOO border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h2 id="Computing-the-trajectories-and-plotting-the-result">Computing the trajectories and plotting the result<a class="anchor-link" href="#Computing-the-trajectories-and-plotting-the-result">&#182;</a></h2>
</div>
</div>
</div>
<div class="cellOOO border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>We define a function that can integrate the differential equations numerically and then plot the solutions. This function has arguments that control the parameters of the differential equation ($\sigma$, $\beta$, $\rho$), the numerical integration (<code>N</code>, <code>max_time</code>) and the visualization (<code>angle</code>).</p>

</div>
</div>
</div>
<pre data-executable>
def solve_lorenz(N=10, angle=0.0, max_time=4.0, sigma=10.0, beta=8./3, rho=28.0):

    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))

    def lorenz_deriv(x_y_z, t0, sigma=sigma, beta=beta, rho=rho):
        """Compute the time-derivative of a Lorenz system."""
        x, y, z = x_y_z
        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))

    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
</pre>

<div class="cellOOO border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>Let's call the function once to view the solutions. For this set of parameters, we see the trajectories swirling around two points, called attractors.</p>

</div>
</div>
</div>
<pre data-executable>
t, x_t = solve_lorenz(angle=0, N=10)
</pre>

<div class="cellOOO border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>Using IPython's <code>interactive</code> function, we can explore how the trajectories behave as we change the various parameters.</p>

</div>
</div>
</div>
<pre data-executable>
w = interactive(solve_lorenz, angle=(0.,360.), N=(0,50), sigma=(0.0,50.0), rho=(0.0,50.0))
display(w)
</pre>

<div class="cellOOO border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>The object returned by <code>interactive</code> is a <code>Widget</code> object and it has attributes that contain the current result and arguments:</p>

</div>
</div>
</div>
<pre data-executable>
t, x_t = w.result
</pre>

<pre data-executable>
w.kwargs
</pre>

<div class="cellOOO border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>After interacting with the system, we can take the result and perform further computations. In this case, we compute the average positions in $x$, $y$ and $z$.</p>

</div>
</div>
</div>
<pre data-executable>
xyz_avg = x_t.mean(axis=1)
</pre>

<pre data-executable>
xyz_avg.shape
</pre>

<div class="cellOOO border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>Creating histograms of the average positions (across different trajectories) show that on average the trajectories swirl about the attractors.</p>

</div>
</div>
</div>
<pre data-executable>
plt.hist(xyz_avg[:,0])
plt.title('Average $x(t)$')
</pre>

<pre data-executable>
plt.hist(xyz_avg[:,1])
plt.title('Average $y(t)$')
</pre>

<pre data-executable>

</pre>

## really-interactive-posts.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Really Interactive Blog Posts\n",
    "\n",
    "*This notebook first appeared as a [blog post](//betatim.github.io/posts/really-interactive-blog-posts) on [Tim Head](//betatim.github.io)'s blog.*\n",
    "\n",
    "*License: [MIT](http://opensource.org/licenses/MIT)*\n",
    "\n",
    "*(C) 2016, Tim Head.*\n",
    "*Feel free to use, distribute, and modify with the above attribution.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A few days ago I started making my [blog posts interactive](/posts/interactive-posts/).\n",
    "It was cool, but required you to surf to a different page for the interactive\n",
    "experience, while the original post was still non-interactive.\n",
    "\n",
    "[Alex](//alexpearce.me) pointed out that really you wanted it all in one\n",
    "page. Basically he was:\n",
    "\n",
    "<img src=\"/images/meh.gif\" width=\"480\" height=\"270\" />\n",
    "\n",
    "My blog setup follows [Jake Vanderplas'](https://jakevdp.github.io/blog/2013/05/07/migrating-from-octopress-to-pelican/) pretty closely. So I created a new [`liquid_tags`](https://github.com/getpelican/pelican-plugins/tree/master/liquid_tags) plugin\n",
    "that has its own template for `nbconvert` which generates HTML that [thebe](https://github.com/oreillymedia/thebe) understands.\n",
    "\n",
    "No downloading, no installing, no browsing to a separate page! Just interactive blog\n",
    "posts! (Scroll down to see it in action if you do not care how it was done.)\n",
    "\n",
    "\n",
    "## Do it yourself\n",
    "\n",
    "I am preparing a write up of how to modify your own [pelican](http://blog.getpelican.com/) site have an interactive section. For the keen and eager people, the most important part is using the following template with `nbconvert`:\n",
    "\n",
    "```\n",
    "{%- extends 'basic.tpl' -%}\n",
    "\n",
    "{% block codecell %}\n",
    "<pre data-executable>\n",
    "{{ cell.source }}\n",
    "</pre>\n",
    "{% endblock codecell %}\n",
    "\n",
    "{% block markdowncell scoped %}\n",
    "<div class=\"cellOOO border-box-sizing text_cell rendered\">\n",
    "{{ self.empty_in_prompt() }}\n",
    "<div class=\"inner_cell\">\n",
    "<div class=\"text_cell_render border-box-sizing rendered_html\">\n",
    "{{ cell.source  | markdown2html | strip_files_prefix }}\n",
    "</div>\n",
    "</div>\n",
    "</div>\n",
    "{%- endblock markdowncell %}\n",
    "```\n",
    "\n",
    "It embeds code cells in simple `<pre>` tags and modifies non-code cells so that they do not\n",
    "match the selectors used inside the notebook machinery. That is it. Then stick a bit of CSS and JS in the `<head>` of your web page and you are good to go (use the source of this one for inspiration).\n",
    "\n",
    "\n",
    "\n",
    "### Credits\n",
    "\n",
    "Compared to my previous post this setup now only relies on [thebe](https://github.com/oreillymedia/thebe), [tmpnb](https://tmpnb.org), and the kind people at [rackspace](https://developer.rackspace.com/) who sponsor the computing power for `tmpnb`.\n",
    "\n",
    "Below, the work of the jupyter development team, licensed under the 3 clause BSD license.\n",
    "\n",
    "Get in touch on twitter @[betatim](//twitter.com/betatim)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exploring the Lorenz System of Differential Equations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this Notebook we explore the Lorenz system of differential equations:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\dot{x} & = \\sigma(y-x) \\\\\n",
    "\\dot{y} & = \\rho x - y - xz \\\\\n",
    "\\dot{z} & = -\\beta z + xy\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "This is one of the classic systems in non-linear differential equations. It exhibits a range of different behaviors as the parameters ($\\sigma$, $\\beta$, $\\rho$) are varied."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we import the needed things from IPython, NumPy, Matplotlib and SciPy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from ipywidgets import interact, interactive\n",
    "from IPython.display import clear_output, display, HTML"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import integrate\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from matplotlib.colors import cnames\n",
    "from matplotlib import animation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing the trajectories and plotting the result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define a function that can integrate the differential equations numerically and then plot the solutions. This function has arguments that control the parameters of the differential equation ($\\sigma$, $\\beta$, $\\rho$), the numerical integration (`N`, `max_time`) and the visualization (`angle`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def solve_lorenz(N=10, angle=0.0, max_time=4.0, sigma=10.0, beta=8./3, rho=28.0):\n",
    "\n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_axes([0, 0, 1, 1], projection='3d')\n",
    "    ax.axis('off')\n",
    "\n",
    "    # prepare the axes limits\n",
    "    ax.set_xlim((-25, 25))\n",
    "    ax.set_ylim((-35, 35))\n",
    "    ax.set_zlim((5, 55))\n",
    "    \n",
    "    def lorenz_deriv(x_y_z, t0, sigma=sigma, beta=beta, rho=rho):\n",
    "        \"\"\"Compute the time-derivative of a Lorenz system.\"\"\"\n",
    "        x, y, z = x_y_z\n",
    "        return [sigma * (y - x), x * (rho - z) - y, x * y - beta * z]\n",
    "\n",
    "    # Choose random starting points, uniformly distributed from -15 to 15\n",
    "    np.random.seed(1)\n",
    "    x0 = -15 + 30 * np.random.random((N, 3))\n",
    "\n",
    "    # Solve for the trajectories\n",
    "    t = np.linspace(0, max_time, int(250*max_time))\n",
    "    x_t = np.asarray([integrate.odeint(lorenz_deriv, x0i, t)\n",
    "                      for x0i in x0])\n",
    "    \n",
    "    # choose a different color for each trajectory\n",
    "    colors = plt.cm.jet(np.linspace(0, 1, N))\n",
    "\n",
    "    for i in range(N):\n",
    "        x, y, z = x_t[i,:,:].T\n",
    "        lines = ax.plot(x, y, z, '-', c=colors[i])\n",
    "        plt.setp(lines, linewidth=2)\n",
    "\n",
    "    ax.view_init(30, angle)\n",
    "    plt.show()\n",
    "\n",
    "    return t, x_t"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's call the function once to view the solutions. For this set of parameters, we see the trajectories swirling around two points, called attractors. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAb4AAAEuCAYAAADx63eqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nKjLwSZIkSbXK/wOSG3SDerlRLQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1094486a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t, x_t = solve_lorenz(angle=0, N=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using IPython's `interactive` function, we can explore how the trajectories behave as we change the various parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAb4AAAEuCAYAAADx63eqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nKjLwSZIkSbXK/wOSG3SDerlRLQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1094d1f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(array([ 0.        ,  0.004004  ,  0.00800801,  0.01201201,  0.01601602,\n",
       "         0.02002002,  0.02402402,  0.02802803,  0.03203203,  0.03603604,\n",
       "         0.04004004,  0.04404404,  0.04804805,  0.05205205,  0.05605606,\n",
       "         0.06006006,  0.06406406,  0.06806807,  0.07207207,  0.07607608,\n",
       "         0.08008008,  0.08408408,  0.08808809,  0.09209209,  0.0960961 ,\n",
       "         0.1001001 ,  0.1041041 ,  0.10810811,  0.11211211,  0.11611612,\n",
       "         0.12012012,  0.12412412,  0.12812813,  0.13213213,  0.13613614,\n",
       "         0.14014014,  0.14414414,  0.14814815,  0.15215215,  0.15615616,\n",
       "         0.16016016,  0.16416416,  0.16816817,  0.17217217,  0.17617618,\n",
       "         0.18018018,  0.18418418,  0.18818819,  0.19219219,  0.1961962 ,\n",
       "         0.2002002 ,  0.2042042 ,  0.20820821,  0.21221221,  0.21621622,\n",
       "         0.22022022,  0.22422422,  0.22822823,  0.23223223,  0.23623624,\n",
       "         0.24024024,  0.24424424,  0.24824825,  0.25225225,  0.25625626,\n",
       "         0.26026026,  0.26426426,  0.26826827,  0.27227227,  0.27627628,\n",
       "         0.28028028,  0.28428428,  0.28828829,  0.29229229,  0.2962963 ,\n",
       "         0.3003003 ,  0.3043043 ,  0.30830831,  0.31231231,  0.31631632,\n",
       "         0.32032032,  0.32432432,  0.32832833,  0.33233233,  0.33633634,\n",
       "         0.34034034,  0.34434434,  0.34834835,  0.35235235,  0.35635636,\n",
       "         0.36036036,  0.36436436,  0.36836837,  0.37237237,  0.37637638,\n",
       "         0.38038038,  0.38438438,  0.38838839,  0.39239239,  0.3963964 ,\n",
       "         0.4004004 ,  0.4044044 ,  0.40840841,  0.41241241,  0.41641642,\n",
       "         0.42042042,  0.42442442,  0.42842843,  0.43243243,  0.43643644,\n",
       "         0.44044044,  0.44444444,  0.44844845,  0.45245245,  0.45645646,\n",
       "         0.46046046,  0.46446446,  0.46846847,  0.47247247,  0.47647648,\n",
       "         0.48048048,  0.48448448,  0.48848849,  0.49249249,  0.4964965 ,\n",
       "         0.5005005 ,  0.5045045 ,  0.50850851,  0.51251251,  0.51651652,\n",
       "         0.52052052,  0.52452452,  0.52852853,  0.53253253,  0.53653654,\n",
       "         0.54054054,  0.54454454,  0.54854855,  0.55255255,  0.55655656,\n",
       "         0.56056056,  0.56456456,  0.56856857,  0.57257257,  0.57657658,\n",
       "         0.58058058,  0.58458458,  0.58858859,  0.59259259,  0.5965966 ,\n",
       "         0.6006006 ,  0.6046046 ,  0.60860861,  0.61261261,  0.61661662,\n",
       "         0.62062062,  0.62462462,  0.62862863,  0.63263263,  0.63663664,\n",
       "         0.64064064,  0.64464464,  0.64864865,  0.65265265,  0.65665666,\n",
       "         0.66066066,  0.66466466,  0.66866867,  0.67267267,  0.67667668,\n",
       "         0.68068068,  0.68468468,  0.68868869,  0.69269269,  0.6966967 ,\n",
       "         0.7007007 ,  0.7047047 ,  0.70870871,  0.71271271,  0.71671672,\n",
       "         0.72072072,  0.72472472,  0.72872873,  0.73273273,  0.73673674,\n",
       "         0.74074074,  0.74474474,  0.74874875,  0.75275275,  0.75675676,\n",
       "         0.76076076,  0.76476476,  0.76876877,  0.77277277,  0.77677678,\n",
       "         0.78078078,  0.78478478,  0.78878879,  0.79279279,  0.7967968 ,\n",
       "         0.8008008 ,  0.8048048 ,  0.80880881,  0.81281281,  0.81681682,\n",
       "         0.82082082,  0.82482482,  0.82882883,  0.83283283,  0.83683684,\n",
       "         0.84084084,  0.84484484,  0.84884885,  0.85285285,  0.85685686,\n",
       "         0.86086086,  0.86486486,  0.86886887,  0.87287287,  0.87687688,\n",
       "         0.88088088,  0.88488488,  0.88888889,  0.89289289,  0.8968969 ,\n",
       "         0.9009009 ,  0.9049049 ,  0.90890891,  0.91291291,  0.91691692,\n",
       "         0.92092092,  0.92492492,  0.92892893,  0.93293293,  0.93693694,\n",
       "         0.94094094,  0.94494494,  0.94894895,  0.95295295,  0.95695696,\n",
       "         0.96096096,  0.96496496,  0.96896897,  0.97297297,  0.97697698,\n",
       "         0.98098098,  0.98498498,  0.98898899,  0.99299299,  0.996997  ,\n",
       "         1.001001  ,  1.00500501,  1.00900901,  1.01301301,  1.01701702,\n",
       "         1.02102102,  1.02502503,  1.02902903,  1.03303303,  1.03703704,\n",
       "         1.04104104,  1.04504505,  1.04904905,  1.05305305,  1.05705706,\n",
       "         1.06106106,  1.06506507,  1.06906907,  1.07307307,  1.07707708,\n",
       "         1.08108108,  1.08508509,  1.08908909,  1.09309309,  1.0970971 ,\n",
       "         1.1011011 ,  1.10510511,  1.10910911,  1.11311311,  1.11711712,\n",
       "         1.12112112,  1.12512513,  1.12912913,  1.13313313,  1.13713714,\n",
       "         1.14114114,  1.14514515,  1.14914915,  1.15315315,  1.15715716,\n",
       "         1.16116116,  1.16516517,  1.16916917,  1.17317317,  1.17717718,\n",
       "         1.18118118,  1.18518519,  1.18918919,  1.19319319,  1.1971972 ,\n",
       "         1.2012012 ,  1.20520521,  1.20920921,  1.21321321,  1.21721722,\n",
       "         1.22122122,  1.22522523,  1.22922923,  1.23323323,  1.23723724,\n",
       "         1.24124124,  1.24524525,  1.24924925,  1.25325325,  1.25725726,\n",
       "         1.26126126,  1.26526527,  1.26926927,  1.27327327,  1.27727728,\n",
       "         1.28128128,  1.28528529,  1.28928929,  1.29329329,  1.2972973 ,\n",
       "         1.3013013 ,  1.30530531,  1.30930931,  1.31331331,  1.31731732,\n",
       "         1.32132132,  1.32532533,  1.32932933,  1.33333333,  1.33733734,\n",
       "         1.34134134,  1.34534535,  1.34934935,  1.35335335,  1.35735736,\n",
       "         1.36136136,  1.36536537,  1.36936937,  1.37337337,  1.37737738,\n",
       "         1.38138138,  1.38538539,  1.38938939,  1.39339339,  1.3973974 ,\n",
       "         1.4014014 ,  1.40540541,  1.40940941,  1.41341341,  1.41741742,\n",
       "         1.42142142,  1.42542543,  1.42942943,  1.43343343,  1.43743744,\n",
       "         1.44144144,  1.44544545,  1.44944945,  1.45345345,  1.45745746,\n",
       "         1.46146146,  1.46546547,  1.46946947,  1.47347347,  1.47747748,\n",
       "         1.48148148,  1.48548549,  1.48948949,  1.49349349,  1.4974975 ,\n",
       "         1.5015015 ,  1.50550551,  1.50950951,  1.51351351,  1.51751752,\n",
       "         1.52152152,  1.52552553,  1.52952953,  1.53353353,  1.53753754,\n",
       "         1.54154154,  1.54554555,  1.54954955,  1.55355355,  1.55755756,\n",
       "         1.56156156,  1.56556557,  1.56956957,  1.57357357,  1.57757758,\n",
       "         1.58158158,  1.58558559,  1.58958959,  1.59359359,  1.5975976 ,\n",
       "         1.6016016 ,  1.60560561,  1.60960961,  1.61361361,  1.61761762,\n",
       "         1.62162162,  1.62562563,  1.62962963,  1.63363363,  1.63763764,\n",
       "         1.64164164,  1.64564565,  1.64964965,  1.65365365,  1.65765766,\n",
       "         1.66166166,  1.66566567,  1.66966967,  1.67367367,  1.67767768,\n",
       "         1.68168168,  1.68568569,  1.68968969,  1.69369369,  1.6976977 ,\n",
       "         1.7017017 ,  1.70570571,  1.70970971,  1.71371371,  1.71771772,\n",
       "         1.72172172,  1.72572573,  1.72972973,  1.73373373,  1.73773774,\n",
       "         1.74174174,  1.74574575,  1.74974975,  1.75375375,  1.75775776,\n",
       "         1.76176176,  1.76576577,  1.76976977,  1.77377377,  1.77777778,\n",
       "         1.78178178,  1.78578579,  1.78978979,  1.79379379,  1.7977978 ,\n",
       "         1.8018018 ,  1.80580581,  1.80980981,  1.81381381,  1.81781782,\n",
       "         1.82182182,  1.82582583,  1.82982983,  1.83383383,  1.83783784,\n",
       "         1.84184184,  1.84584585,  1.84984985,  1.85385385,  1.85785786,\n",
       "         1.86186186,  1.86586587,  1.86986987,  1.87387387,  1.87787788,\n",
       "         1.88188188,  1.88588589,  1.88988989,  1.89389389,  1.8978979 ,\n",
       "         1.9019019 ,  1.90590591,  1.90990991,  1.91391391,  1.91791792,\n",
       "         1.92192192,  1.92592593,  1.92992993,  1.93393393,  1.93793794,\n",
       "         1.94194194,  1.94594595,  1.94994995,  1.95395395,  1.95795796,\n",
       "         1.96196196,  1.96596597,  1.96996997,  1.97397397,  1.97797798,\n",
       "         1.98198198,  1.98598599,  1.98998999,  1.99399399,  1.997998  ,\n",
       "         2.002002  ,  2.00600601,  2.01001001,  2.01401401,  2.01801802,\n",
       "         2.02202202,  2.02602603,  2.03003003,  2.03403403,  2.03803804,\n",
       "         2.04204204,  2.04604605,  2.05005005,  2.05405405,  2.05805806,\n",
       "         2.06206206,  2.06606607,  2.07007007,  2.07407407,  2.07807808,\n",
       "         2.08208208,  2.08608609,  2.09009009,  2.09409409,  2.0980981 ,\n",
       "         2.1021021 ,  2.10610611,  2.11011011,  2.11411411,  2.11811812,\n",
       "         2.12212212,  2.12612613,  2.13013013,  2.13413413,  2.13813814,\n",
       "         2.14214214,  2.14614615,  2.15015015,  2.15415415,  2.15815816,\n",
       "         2.16216216,  2.16616617,  2.17017017,  2.17417417,  2.17817818,\n",
       "         2.18218218,  2.18618619,  2.19019019,  2.19419419,  2.1981982 ,\n",
       "         2.2022022 ,  2.20620621,  2.21021021,  2.21421421,  2.21821822,\n",
       "         2.22222222,  2.22622623,  2.23023023,  2.23423423,  2.23823824,\n",
       "         2.24224224,  2.24624625,  2.25025025,  2.25425425,  2.25825826,\n",
       "         2.26226226,  2.26626627,  2.27027027,  2.27427427,  2.27827828,\n",
       "         2.28228228,  2.28628629,  2.29029029,  2.29429429,  2.2982983 ,\n",
       "         2.3023023 ,  2.30630631,  2.31031031,  2.31431431,  2.31831832,\n",
       "         2.32232232,  2.32632633,  2.33033033,  2.33433433,  2.33833834,\n",
       "         2.34234234,  2.34634635,  2.35035035,  2.35435435,  2.35835836,\n",
       "         2.36236236,  2.36636637,  2.37037037,  2.37437437,  2.37837838,\n",
       "         2.38238238,  2.38638639,  2.39039039,  2.39439439,  2.3983984 ,\n",
       "         2.4024024 ,  2.40640641,  2.41041041,  2.41441441,  2.41841842,\n",
       "         2.42242242,  2.42642643,  2.43043043,  2.43443443,  2.43843844,\n",
       "         2.44244244,  2.44644645,  2.45045045,  2.45445445,  2.45845846,\n",
       "         2.46246246,  2.46646647,  2.47047047,  2.47447447,  2.47847848,\n",
       "         2.48248248,  2.48648649,  2.49049049,  2.49449449,  2.4984985 ,\n",
       "         2.5025025 ,  2.50650651,  2.51051051,  2.51451451,  2.51851852,\n",
       "         2.52252252,  2.52652653,  2.53053053,  2.53453453,  2.53853854,\n",
       "         2.54254254,  2.54654655,  2.55055055,  2.55455455,  2.55855856,\n",
       "         2.56256256,  2.56656657,  2.57057057,  2.57457457,  2.57857858,\n",
       "         2.58258258,  2.58658659,  2.59059059,  2.59459459,  2.5985986 ,\n",
       "         2.6026026 ,  2.60660661,  2.61061061,  2.61461461,  2.61861862,\n",
       "         2.62262262,  2.62662663,  2.63063063,  2.63463463,  2.63863864,\n",
       "         2.64264264,  2.64664665,  2.65065065,  2.65465465,  2.65865866,\n",
       "         2.66266266,  2.66666667,  2.67067067,  2.67467467,  2.67867868,\n",
       "         2.68268268,  2.68668669,  2.69069069,  2.69469469,  2.6986987 ,\n",
       "         2.7027027 ,  2.70670671,  2.71071071,  2.71471471,  2.71871872,\n",
       "         2.72272272,  2.72672673,  2.73073073,  2.73473473,  2.73873874,\n",
       "         2.74274274,  2.74674675,  2.75075075,  2.75475475,  2.75875876,\n",
       "         2.76276276,  2.76676677,  2.77077077,  2.77477477,  2.77877878,\n",
       "         2.78278278,  2.78678679,  2.79079079,  2.79479479,  2.7987988 ,\n",
       "         2.8028028 ,  2.80680681,  2.81081081,  2.81481481,  2.81881882,\n",
       "         2.82282282,  2.82682683,  2.83083083,  2.83483483,  2.83883884,\n",
       "         2.84284284,  2.84684685,  2.85085085,  2.85485485,  2.85885886,\n",
       "         2.86286286,  2.86686687,  2.87087087,  2.87487487,  2.87887888,\n",
       "         2.88288288,  2.88688689,  2.89089089,  2.89489489,  2.8988989 ,\n",
       "         2.9029029 ,  2.90690691,  2.91091091,  2.91491491,  2.91891892,\n",
       "         2.92292292,  2.92692693,  2.93093093,  2.93493493,  2.93893894,\n",
       "         2.94294294,  2.94694695,  2.95095095,  2.95495495,  2.95895896,\n",
       "         2.96296296,  2.96696697,  2.97097097,  2.97497497,  2.97897898,\n",
       "         2.98298298,  2.98698699,  2.99099099,  2.99499499,  2.998999  ,\n",
       "         3.003003  ,  3.00700701,  3.01101101,  3.01501502,  3.01901902,\n",
       "         3.02302302,  3.02702703,  3.03103103,  3.03503504,  3.03903904,\n",
       "         3.04304304,  3.04704705,  3.05105105,  3.05505506,  3.05905906,\n",
       "         3.06306306,  3.06706707,  3.07107107,  3.07507508,  3.07907908,\n",
       "         3.08308308,  3.08708709,  3.09109109,  3.0950951 ,  3.0990991 ,\n",
       "         3.1031031 ,  3.10710711,  3.11111111,  3.11511512,  3.11911912,\n",
       "         3.12312312,  3.12712713,  3.13113113,  3.13513514,  3.13913914,\n",
       "         3.14314314,  3.14714715,  3.15115115,  3.15515516,  3.15915916,\n",
       "         3.16316316,  3.16716717,  3.17117117,  3.17517518,  3.17917918,\n",
       "         3.18318318,  3.18718719,  3.19119119,  3.1951952 ,  3.1991992 ,\n",
       "         3.2032032 ,  3.20720721,  3.21121121,  3.21521522,  3.21921922,\n",
       "         3.22322322,  3.22722723,  3.23123123,  3.23523524,  3.23923924,\n",
       "         3.24324324,  3.24724725,  3.25125125,  3.25525526,  3.25925926,\n",
       "         3.26326326,  3.26726727,  3.27127127,  3.27527528,  3.27927928,\n",
       "         3.28328328,  3.28728729,  3.29129129,  3.2952953 ,  3.2992993 ,\n",
       "         3.3033033 ,  3.30730731,  3.31131131,  3.31531532,  3.31931932,\n",
       "         3.32332332,  3.32732733,  3.33133133,  3.33533534,  3.33933934,\n",
       "         3.34334334,  3.34734735,  3.35135135,  3.35535536,  3.35935936,\n",
       "         3.36336336,  3.36736737,  3.37137137,  3.37537538,  3.37937938,\n",
       "         3.38338338,  3.38738739,  3.39139139,  3.3953954 ,  3.3993994 ,\n",
       "         3.4034034 ,  3.40740741,  3.41141141,  3.41541542,  3.41941942,\n",
       "         3.42342342,  3.42742743,  3.43143143,  3.43543544,  3.43943944,\n",
       "         3.44344344,  3.44744745,  3.45145145,  3.45545546,  3.45945946,\n",
       "         3.46346346,  3.46746747,  3.47147147,  3.47547548,  3.47947948,\n",
       "         3.48348348,  3.48748749,  3.49149149,  3.4954955 ,  3.4994995 ,\n",
       "         3.5035035 ,  3.50750751,  3.51151151,  3.51551552,  3.51951952,\n",
       "         3.52352352,  3.52752753,  3.53153153,  3.53553554,  3.53953954,\n",
       "         3.54354354,  3.54754755,  3.55155155,  3.55555556,  3.55955956,\n",
       "         3.56356356,  3.56756757,  3.57157157,  3.57557558,  3.57957958,\n",
       "         3.58358358,  3.58758759,  3.59159159,  3.5955956 ,  3.5995996 ,\n",
       "         3.6036036 ,  3.60760761,  3.61161161,  3.61561562,  3.61961962,\n",
       "         3.62362362,  3.62762763,  3.63163163,  3.63563564,  3.63963964,\n",
       "         3.64364364,  3.64764765,  3.65165165,  3.65565566,  3.65965966,\n",
       "         3.66366366,  3.66766767,  3.67167167,  3.67567568,  3.67967968,\n",
       "         3.68368368,  3.68768769,  3.69169169,  3.6956957 ,  3.6996997 ,\n",
       "         3.7037037 ,  3.70770771,  3.71171171,  3.71571572,  3.71971972,\n",
       "         3.72372372,  3.72772773,  3.73173173,  3.73573574,  3.73973974,\n",
       "         3.74374374,  3.74774775,  3.75175175,  3.75575576,  3.75975976,\n",
       "         3.76376376,  3.76776777,  3.77177177,  3.77577578,  3.77977978,\n",
       "         3.78378378,  3.78778779,  3.79179179,  3.7957958 ,  3.7997998 ,\n",
       "         3.8038038 ,  3.80780781,  3.81181181,  3.81581582,  3.81981982,\n",
       "         3.82382382,  3.82782783,  3.83183183,  3.83583584,  3.83983984,\n",
       "         3.84384384,  3.84784785,  3.85185185,  3.85585586,  3.85985986,\n",
       "         3.86386386,  3.86786787,  3.87187187,  3.87587588,  3.87987988,\n",
       "         3.88388388,  3.88788789,  3.89189189,  3.8958959 ,  3.8998999 ,\n",
       "         3.9039039 ,  3.90790791,  3.91191191,  3.91591592,  3.91991992,\n",
       "         3.92392392,  3.92792793,  3.93193193,  3.93593594,  3.93993994,\n",
       "         3.94394394,  3.94794795,  3.95195195,  3.95595596,  3.95995996,\n",
       "         3.96396396,  3.96796797,  3.97197197,  3.97597598,  3.97997998,\n",
       "         3.98398398,  3.98798799,  3.99199199,  3.995996  ,  4.        ]),\n",
       " array([[[ -2.48933986e+00,   6.60973480e+00,  -1.49965688e+01],\n",
       "         [ -2.14077645e+00,   6.18646806e+00,  -1.48962127e+01],\n",
       "         [ -1.82130748e+00,   5.82299967e+00,  -1.47853208e+01],\n",
       "         ..., \n",
       "         [  6.87667416e+00,   1.07734499e+01,   1.78286316e+01],\n",
       "         [  7.03431517e+00,   1.10115546e+01,   1.79410297e+01],\n",
       "         [  7.19515729e+00,   1.12517722e+01,   1.80659207e+01]],\n",
       " \n",
       "        [[ -5.93002282e+00,  -1.05973233e+01,  -1.22298422e+01],\n",
       "         [ -6.13136261e+00,  -1.15193465e+01,  -1.18344052e+01],\n",
       "         [ -6.36138540e+00,  -1.24619735e+01,  -1.14104771e+01],\n",
       "         ..., \n",
       "         [ -1.11085203e+01,  -1.62261151e+01,   2.32341935e+01],\n",
       "         [ -1.13121656e+01,  -1.63640151e+01,   2.37150767e+01],\n",
       "         [ -1.15128567e+01,  -1.64827701e+01,   2.42098140e+01]],\n",
       " \n",
       "        [[ -9.41219366e+00,  -4.63317819e+00,  -3.09697577e+00],\n",
       "         [ -9.24717733e+00,  -5.76936651e+00,  -2.87083263e+00],\n",
       "         [ -9.13260659e+00,  -6.87477643e+00,  -2.60897637e+00],\n",
       "         ..., \n",
       "         [  8.94933599e+00,   1.00204877e+01,   2.61339939e+01],\n",
       "         [  8.99188828e+00,   1.00458891e+01,   2.62149083e+01],\n",
       "         [  9.03371359e+00,   1.00685518e+01,   2.62975123e+01]],\n",
       " \n",
       "        ..., \n",
       "        [[  1.40478473e+01,  -5.59727466e+00,   5.76967847e+00],\n",
       "         [  1.33015844e+01,  -4.35137818e+00,   5.43762841e+00],\n",
       "         [  1.26324566e+01,  -3.15868945e+00,   5.18607122e+00],\n",
       "         ..., \n",
       "         [ -5.62183444e+00,  -9.08227752e+00,   1.57576353e+01],\n",
       "         [ -5.76241216e+00,  -9.32397964e+00,   1.57989149e+01],\n",
       "         [ -5.90705639e+00,  -9.57059699e+00,   1.58506576e+01]],\n",
       " \n",
       "        [[  1.12916746e+01,   1.18381999e+01,  -1.24486737e+01],\n",
       "         [  1.13481065e+01,   1.36039497e+01,  -1.17430178e+01],\n",
       "         [  1.14710812e+01,   1.53431579e+01,  -1.09606825e+01],\n",
       "         ..., \n",
       "         [ -1.47677316e-02,  -1.23193351e-02,   1.01977111e+01],\n",
       "         [ -1.46914304e-02,  -1.33208729e-02,   1.00894066e+01],\n",
       "         [ -1.46573919e-02,  -1.43208005e-02,   9.98225246e+00]],\n",
       " \n",
       "        [[ -1.38283565e+01,  -9.90508741e+00,   1.13442751e+01],\n",
       "         [ -1.36915606e+01,  -1.07690154e+01,   1.17903119e+01],\n",
       "         [ -1.35933180e+01,  -1.15964765e+01,   1.22727276e+01],\n",
       "         ..., \n",
       "         [  1.61306741e+01,   1.93584734e+01,   3.43088188e+01],\n",
       "         [  1.62473985e+01,   1.88446346e+01,   3.51764615e+01],\n",
       "         [  1.63382575e+01,   1.82747191e+01,   3.60076113e+01]]]))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "w = interactive(solve_lorenz, angle=(0.,360.), N=(0,50), sigma=(0.0,50.0), rho=(0.0,50.0))\n",
    "display(w)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The object returned by `interactive` is a `Widget` object and it has attributes that contain the current result and arguments:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "t, x_t = w.result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'N': 10,\n",
       " 'angle': 0.0,\n",
       " 'beta': 2.6666666666666665,\n",
       " 'max_time': 4.0,\n",
       " 'rho': 28.0,\n",
       " 'sigma': 10.0}"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w.kwargs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After interacting with the system, we can take the result and perform further computations. In this case, we compute the average positions in $x$, $y$ and $z$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "xyz_avg = x_t.mean(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 3)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xyz_avg.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Creating histograms of the average positions (across different trajectories) show that on average the trajectories swirl about the attractors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x109d07160>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAEMCAYAAADUEk3/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109c18978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(xyz_avg[:,0])\n",
    "plt.title('Average $x(t)$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x109df9048>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAEMCAYAAADUEk3/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQJekRhjoktQIA12SGmGgS1Ij/j8QYH02MxsJPQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109d55160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(xyz_avg[:,1])\n",
    "plt.title('Average $y(t)$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}

## thebe.tpl
{%- extends 'basic.tpl' -%}

{% block header %}
<head>
  <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/codemirror/5.10.0/codemirror.min.css">

  <script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/1.11.0/jquery.min.js" type="text/javascript"></script>
  <script type="text/javascript" src="https://cdn.rawgit.com/oreillymedia/thebe/17fe0971303cac24d7e806c8f1bc8ba3c0c40b23/static/main-bu\
ilt.js"></script>
  <script>
    $(function(){
      new Thebe({url:"https://tmpnb.org/",
                 kernel_name: "python3"});
    });
  </script>
</head>
{% endblock header %}

{% block codecell %}
<pre data-executable>
{{ cell.source }}
</pre>
{% endblock codecell %}

{% block markdowncell scoped %}
<div class="cellOOO border-box-sizing text_cell rendered">
{{ self.empty_in_prompt() }}
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
{{ cell.source  | markdown2html | strip_files_prefix }}
</div>
</div>
</div>
{%- endblock markdowncell %}
	# Convert your notebook to an interactive webpage
	#
	# Attached a notebook (really-interactive-posts.ipynb) and the generated
	# output (really-interactive-posts.html). The thebe.tpl template file is
	# at the very end of the gist.

	$ jupyter nbconvert --template thebe.tpl --to html <notebook.ipynb>


	# You can open the generated webpage locally file://... howerver some
	# resources will not load properly. Best to open it from a webserver:

	$ python3 -m http.server

	# or if you'd rather have a local https server (credit to: https://gist.github.com/dergachev/7028596)
	# generate certificate with the following command:

	$ openssl req -new -x509 -keyout server.pem -out server.pem -days 365 -nodes
	$ echo "import BaseHTTPServer, SimpleHTTPServer
	import ssl

	httpd = BaseHTTPServer.HTTPServer(('localhost', 4443), SimpleHTTPServer.SimpleHTTPRequestHandler)
	httpd.socket = ssl.wrap_socket (httpd.socket, certfile='./server.pem', server_side=True)
	httpd.serve_forever()" > simple-https-server.py

	# run with:

	$ python simple-https-server.py

	# In your browser, visit:
	# https://localhost:4443

	<head>
	<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/codemirror/5.10.0/codemirror.min.css">

	<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/1.11.0/jquery.min.js" type="text/javascript"></script>
	<script type="text/javascript" src="https://cdn.rawgit.com/oreillymedia/thebe/17fe0971303cac24d7e806c8f1bc8ba3c0c40b23/static/main-built.js"></script>
	<script>
	$(function(){
	new Thebe({url:"https://tmpnb.org/",
	kernel_name: "python3"});
	});
	</script>
	</head>

	<div class="cellOOO border-box-sizing text_cell rendered">
	<div class="prompt input_prompt">
	</div>
	<div class="inner_cell">
	<div class="text_cell_render border-box-sizing rendered_html">
	<h1 id="Really-Interactive-Blog-Posts">Really Interactive Blog Posts<a class="anchor-link" href="#Really-Interactive-Blog-Posts">¶</a></h1><p><em>This notebook first appeared as a <a href="//betatim.github.io/posts/really-interactive-blog-posts">blog post</a> on <a href="//betatim.github.io">Tim Head</a>'s blog.</em></p>
	<p><em>License: <a href="http://opensource.org/licenses/MIT">MIT</a></em></p>
	<p><em>(C) 2016, Tim Head.</em>
	<em>Feel free to use, distribute, and modify with the above attribution.</em></p>

	</div>
	</div>
	</div>
	<div class="cellOOO border-box-sizing text_cell rendered">
	<div class="prompt input_prompt">
	</div>
	<div class="inner_cell">
	<div class="text_cell_render border-box-sizing rendered_html">
	<p>A few days ago I started making my <a href="/posts/interactive-posts/">blog posts interactive</a>.
	It was cool, but required you to surf to a different page for the interactive
	experience, while the original post was still non-interactive.</p>
	<p><a href="//alexpearce.me">Alex</a> pointed out that really you wanted it all in one
	page. Basically he was:</p>
	<p><img src="/images/meh.gif" width="480" height="270" /></p>
	<p>My blog setup follows <a href="https://jakevdp.github.io/blog/2013/05/07/migrating-from-octopress-to-pelican/">Jake Vanderplas'</a> pretty closely. So I created a new <a href="https://github.com/getpelican/pelican-plugins/tree/master/liquid_tags"><code>liquid_tags</code></a> plugin
	that has its own template for <code>nbconvert</code> which generates HTML that <a href="https://github.com/oreillymedia/thebe">thebe</a> understands.</p>
	<p>No downloading, no installing, no browsing to a separate page! Just interactive blog
	posts! (Scroll down to see it in action if you do not care how it was done.)</p>
	<h2 id="Do-it-yourself">Do it yourself<a class="anchor-link" href="#Do-it-yourself">¶</a></h2><p>I am preparing a write up of how to modify your own <a href="http://blog.getpelican.com/">pelican</a> site have an interactive section. For the keen and eager people, the most important part is using the following template with <code>nbconvert</code>:</p>

	<pre><code>{%- extends 'basic.tpl' -%}

	{% block codecell %}
	<pre data-executable>
	{{ cell.source }}
	</pre>
	{% endblock codecell %}

	{% block markdowncell scoped %}
	<div class="cellOOO border-box-sizing text_cell rendered">
	{{ self.empty_in_prompt() }}
	<div class="inner_cell">
	<div class="text_cell_render border-box-sizing rendered_html">
	{{ cell.source \| markdown2html \| strip_files_prefix }}
	</div>
	</div>
	</div>
	{%- endblock markdowncell %}</code></pre>
	<p>It embeds code cells in simple <code><pre></code> tags and modifies non-code cells so that they do not
	match the selectors used inside the notebook machinery. That is it. Then stick a bit of CSS and JS in the <code><head></code> of your web page and you are good to go (use the source of this one for inspiration).</p>
	<h3 id="Credits">Credits<a class="anchor-link" href="#Credits">¶</a></h3><p>Compared to my previous post this setup now only relies on <a href="https://github.com/oreillymedia/thebe">thebe</a>, <a href="https://tmpnb.org">tmpnb</a>, and the kind people at <a href="https://developer.rackspace.com/">rackspace</a> who sponsor the computing power for <code>tmpnb</code>.</p>
	<p>Below, the work of the jupyter development team, licensed under the 3 clause BSD license.</p>
	<p>Get in touch on twitter @<a href="//twitter.com/betatim">betatim</a>.</p>

	</div>
	</div>
	</div>
	<div class="cellOOO border-box-sizing text_cell rendered">
	<div class="prompt input_prompt">
	</div>
	<div class="inner_cell">
	<div class="text_cell_render border-box-sizing rendered_html">
	<h1 id="Exploring-the-Lorenz-System-of-Differential-Equations">Exploring the Lorenz System of Differential Equations<a class="anchor-link" href="#Exploring-the-Lorenz-System-of-Differential-Equations">¶</a></h1>
	</div>
	</div>
	</div>
	<div class="cellOOO border-box-sizing text_cell rendered">
	<div class="prompt input_prompt">
	</div>
	<div class="inner_cell">
	<div class="text_cell_render border-box-sizing rendered_html">
	<p>In this Notebook we explore the Lorenz system of differential equations:</p>
	$$
	\begin{aligned}
	\dot{x} & = \sigma(y-x) \\
	\dot{y} & = \rho x - y - xz \\
	\dot{z} & = -\beta z + xy
	\end{aligned}
	$$<p>This is one of the classic systems in non-linear differential equations. It exhibits a range of different behaviors as the parameters ($\sigma$, $\beta$, $\rho$) are varied.</p>

	</div>
	</div>
	</div>
	<div class="cellOOO border-box-sizing text_cell rendered">
	<div class="prompt input_prompt">
	</div>
	<div class="inner_cell">
	<div class="text_cell_render border-box-sizing rendered_html">
	<h2 id="Imports">Imports<a class="anchor-link" href="#Imports">¶</a></h2>
	</div>
	</div>
	</div>
	<div class="cellOOO border-box-sizing text_cell rendered">
	<div class="prompt input_prompt">
	</div>
	<div class="inner_cell">
	<div class="text_cell_render border-box-sizing rendered_html">
	<p>First, we import the needed things from IPython, NumPy, Matplotlib and SciPy.</p>

	</div>
	</div>
	</div>
	<pre data-executable>
	%matplotlib inline
	</pre>

	<pre data-executable>
	from ipywidgets import interact, interactive
	from IPython.display import clear_output, display, HTML
	</pre>

	<pre data-executable>
	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
	</pre>

	<div class="cellOOO border-box-sizing text_cell rendered">
	<div class="prompt input_prompt">
	</div>
	<div class="inner_cell">
	<div class="text_cell_render border-box-sizing rendered_html">
	<h2 id="Computing-the-trajectories-and-plotting-the-result">Computing the trajectories and plotting the result<a class="anchor-link" href="#Computing-the-trajectories-and-plotting-the-result">¶</a></h2>
	</div>
	</div>
	</div>
	<div class="cellOOO border-box-sizing text_cell rendered">
	<div class="prompt input_prompt">
	</div>
	<div class="inner_cell">
	<div class="text_cell_render border-box-sizing rendered_html">
	<p>We define a function that can integrate the differential equations numerically and then plot the solutions. This function has arguments that control the parameters of the differential equation ($\sigma$, $\beta$, $\rho$), the numerical integration (<code>N</code>, <code>max_time</code>) and the visualization (<code>angle</code>).</p>

	</div>
	</div>
	</div>
	<pre data-executable>
	def solve_lorenz(N=10, angle=0.0, max_time=4.0, sigma=10.0, beta=8./3, rho=28.0):

	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))

	def lorenz_deriv(x_y_z, t0, sigma=sigma, beta=beta, rho=rho):
	"""Compute the time-derivative of a Lorenz system."""
	x, y, z = x_y_z
	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))

	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
	</pre>

	<div class="cellOOO border-box-sizing text_cell rendered">
	<div class="prompt input_prompt">
	</div>
	<div class="inner_cell">
	<div class="text_cell_render border-box-sizing rendered_html">
	<p>Let's call the function once to view the solutions. For this set of parameters, we see the trajectories swirling around two points, called attractors.</p>

	</div>
	</div>
	</div>
	<pre data-executable>
	t, x_t = solve_lorenz(angle=0, N=10)
	</pre>

	<div class="cellOOO border-box-sizing text_cell rendered">
	<div class="prompt input_prompt">
	</div>
	<div class="inner_cell">
	<div class="text_cell_render border-box-sizing rendered_html">
	<p>Using IPython's <code>interactive</code> function, we can explore how the trajectories behave as we change the various parameters.</p>

	</div>
	</div>
	</div>
	<pre data-executable>
	w = interactive(solve_lorenz, angle=(0.,360.), N=(0,50), sigma=(0.0,50.0), rho=(0.0,50.0))
	display(w)
	</pre>

	<div class="cellOOO border-box-sizing text_cell rendered">
	<div class="prompt input_prompt">
	</div>
	<div class="inner_cell">
	<div class="text_cell_render border-box-sizing rendered_html">
	<p>The object returned by <code>interactive</code> is a <code>Widget</code> object and it has attributes that contain the current result and arguments:</p>

	</div>
	</div>
	</div>
	<pre data-executable>
	t, x_t = w.result
	</pre>

	<pre data-executable>
	w.kwargs
	</pre>

	<div class="cellOOO border-box-sizing text_cell rendered">
	<div class="prompt input_prompt">
	</div>
	<div class="inner_cell">
	<div class="text_cell_render border-box-sizing rendered_html">
	<p>After interacting with the system, we can take the result and perform further computations. In this case, we compute the average positions in $x$, $y$ and $z$.</p>

	</div>
	</div>
	</div>
	<pre data-executable>
	xyz_avg = x_t.mean(axis=1)
	</pre>

	<pre data-executable>
	xyz_avg.shape
	</pre>

	<div class="cellOOO border-box-sizing text_cell rendered">
	<div class="prompt input_prompt">
	</div>
	<div class="inner_cell">
	<div class="text_cell_render border-box-sizing rendered_html">
	<p>Creating histograms of the average positions (across different trajectories) show that on average the trajectories swirl about the attractors.</p>

	</div>
	</div>
	</div>
	<pre data-executable>
	plt.hist(xyz_avg[:,0])
	plt.title('Average $x(t)$')
	</pre>

	<pre data-executable>
	plt.hist(xyz_avg[:,1])
	plt.title('Average $y(t)$')
	</pre>

	<pre data-executable>

	</pre>
	{%- extends 'basic.tpl' -%}

	{% block header %}
	<head>
	<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/codemirror/5.10.0/codemirror.min.css">

	<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/1.11.0/jquery.min.js" type="text/javascript"></script>
	<script type="text/javascript" src="https://cdn.rawgit.com/oreillymedia/thebe/17fe0971303cac24d7e806c8f1bc8ba3c0c40b23/static/main-bu\
	ilt.js"></script>
	<script>
	$(function(){
	new Thebe({url:"https://tmpnb.org/",
	kernel_name: "python3"});
	});
	</script>
	</head>
	{% endblock header %}

	{% block codecell %}
	<pre data-executable>
	{{ cell.source }}
	</pre>
	{% endblock codecell %}

	{% block markdowncell scoped %}
	<div class="cellOOO border-box-sizing text_cell rendered">
	{{ self.empty_in_prompt() }}
	<div class="inner_cell">
	<div class="text_cell_render border-box-sizing rendered_html">
	{{ cell.source \| markdown2html \| strip_files_prefix }}
	</div>
	</div>
	</div>
	{%- endblock markdowncell %}