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<section id="strange-attractors-py-non-linear-ordinary-differential-equations">
<h1>05-strange-attractors.py - Non-linear ordinary differential equations.<a class="headerlink" href="#strange-attractors-py-non-linear-ordinary-differential-equations" title="Permalink to this heading">¶</a></h1>
<section id="oscilloscope-part-of-the-tutorial">
<h2>Oscilloscope part of the tutorial<a class="headerlink" href="#oscilloscope-part-of-the-tutorial" title="Permalink to this heading">¶</a></h2>
<p>A strange attractor is a system of three non-linear ordinary
differential equations. These differential equations define a
continuous-time dynamical system that exhibits chaotic dynamics
associated with the fractal properties of the attractor.</p>
<p>There is three strange attractors in the library, the Rossler,
the Lorenz and the ChenLee objects. Each one can output stereo
signal if the <cite>stereo</cite> argument is set to True.</p>
<p>Use the “voice” slider of the window “Input interpolator” to
interpolate between the three sources.</p>
</section>
<section id="audio-part-of-the-tutorial">
<h2>Audio part of the tutorial<a class="headerlink" href="#audio-part-of-the-tutorial" title="Permalink to this heading">¶</a></h2>
<p>It’s possible to create very interesting LFO with strange
attractors. The last part of this tutorial shows the use of
Lorenz’s output to drive the frequency of two sine wave oscillators.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <a class="sphinx-codeautolink-a" href="../../api/alphabetical.html#module-pyo" title="pyo"><span class="nn">pyo</span></a> <span class="kn">import</span> <span class="o">*</span>
<span class="n">s</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/classes/server.html#pyo.Server" title="pyo.lib.server.Server"><span class="n">Server</span></a><span class="p">()</span><span class="o">.</span><span class="n">boot</span><span class="p">()</span>
<span class="c1">### Oscilloscope ###</span>
<span class="c1"># LFO applied to the `chaos` attribute</span>
<span class="n">lfo</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/classes/generators.html#pyo.Sine" title="pyo.lib.generators.Sine"><span class="n">Sine</span></a><span class="p">(</span><span class="mf">0.2</span><span class="p">)</span><span class="o">.</span><span class="n">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="c1"># Rossler attractor</span>
<a class="sphinx-codeautolink-a" href="../../api/classes/generators.html#pyo.Rossler" title="pyo.lib.generators.Rossler"><span class="n">n1</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/classes/generators.html#pyo.Rossler" title="pyo.lib.generators.Rossler"><span class="n">Rossler</span></a><span class="p">(</span><span class="n">pitch</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">chaos</span><span class="o">=</span><span class="n">lfo</span><span class="p">,</span> <span class="n">stereo</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="c1"># Lorenz attractor</span>
<a class="sphinx-codeautolink-a" href="../../api/classes/generators.html#pyo.Lorenz" title="pyo.lib.generators.Lorenz"><span class="n">n2</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/classes/generators.html#pyo.Lorenz" title="pyo.lib.generators.Lorenz"><span class="n">Lorenz</span></a><span class="p">(</span><span class="n">pitch</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">chaos</span><span class="o">=</span><span class="n">lfo</span><span class="p">,</span> <span class="n">stereo</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="c1"># ChenLee attractor</span>
<a class="sphinx-codeautolink-a" href="../../api/classes/generators.html#pyo.ChenLee" title="pyo.lib.generators.ChenLee"><span class="n">n3</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/classes/generators.html#pyo.ChenLee" title="pyo.lib.generators.ChenLee"><span class="n">ChenLee</span></a><span class="p">(</span><span class="n">pitch</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">chaos</span><span class="o">=</span><span class="n">lfo</span><span class="p">,</span> <span class="n">stereo</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="c1"># Interpolates between input objects to produce a single output</span>
<a class="sphinx-codeautolink-a" href="../../api/classes/pan.html#pyo.Selector" title="pyo.lib.pan.Selector"><span class="n">sel</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/classes/pan.html#pyo.Selector" title="pyo.lib.pan.Selector"><span class="n">Selector</span></a><span class="p">([</span><a class="sphinx-codeautolink-a" href="../../api/classes/generators.html#pyo.Rossler" title="pyo.lib.generators.Rossler"><span class="n">n1</span></a><span class="p">,</span> <a class="sphinx-codeautolink-a" href="../../api/classes/generators.html#pyo.Lorenz" title="pyo.lib.generators.Lorenz"><span class="n">n2</span></a><span class="p">,</span> <a class="sphinx-codeautolink-a" href="../../api/classes/generators.html#pyo.ChenLee" title="pyo.lib.generators.ChenLee"><span class="n">n3</span></a><span class="p">])</span>
<span class="n">sel</span><span class="o">.</span><span class="n">ctrl</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s2">"Input interpolator (0=Rossler, 1=Lorenz, 2=ChenLee)"</span><span class="p">)</span>
<span class="c1"># Displays the waveform of the chosen attractor</span>
<a class="sphinx-codeautolink-a" href="../../api/classes/analysis.html#pyo.Scope" title="pyo.lib.analysis.Scope"><span class="n">sc</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/classes/analysis.html#pyo.Scope" title="pyo.lib.analysis.Scope"><span class="n">Scope</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="../../api/classes/pan.html#pyo.Selector" title="pyo.lib.pan.Selector"><span class="n">sel</span></a><span class="p">)</span>
<span class="c1">### Audio ###</span>
<span class="c1"># Lorenz with very low pitch value that acts as a LFO</span>
<a class="sphinx-codeautolink-a" href="../../api/classes/generators.html#pyo.Lorenz" title="pyo.lib.generators.Lorenz"><span class="n">freq</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/classes/generators.html#pyo.Lorenz" title="pyo.lib.generators.Lorenz"><span class="n">Lorenz</span></a><span class="p">(</span><span class="mf">0.005</span><span class="p">,</span> <span class="n">chaos</span><span class="o">=</span><span class="mf">0.7</span><span class="p">,</span> <span class="n">stereo</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">mul</span><span class="o">=</span><span class="mi">250</span><span class="p">,</span> <span class="n">add</span><span class="o">=</span><span class="mi">500</span><span class="p">)</span>
<span class="n">a</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/classes/generators.html#pyo.Sine" title="pyo.lib.generators.Sine"><span class="n">Sine</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="../../api/classes/generators.html#pyo.Lorenz" title="pyo.lib.generators.Lorenz"><span class="n">freq</span></a><span class="p">,</span> <span class="n">mul</span><span class="o">=</span><span class="mf">0.3</span><span class="p">)</span><span class="o">.</span><span class="n">out</span><span class="p">()</span>
<span class="n">s</span><span class="o">.</span><span class="n">gui</span><span class="p">(</span><span class="nb">locals</span><span class="p">())</span>
</pre></div>
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