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<p>Hi again,</p>
<p>Here is a small code doing the graphic job:</p>
<pre style="font-family:Monospaced;font-style:normal;font-size:17.0;"><span style="color:rgb(176,24,19);">function</span> <span style="color:rgb(131,67,16);font-weight:bold;">X</span><span style="color:rgb(92,92,92);">=</span><span style="color:rgb(0,0,0);text-decoration:underline;">anglePath</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(131,67,16);font-weight:bold;">r</span><span style="color:rgb(0,0,0);">, </span><span style="color:rgb(131,67,16);font-weight:bold;">th</span><span style="color:rgb(74,85,219);">)</span>
<span style="color:rgb(0,0,0);">cumth</span> <span style="color:rgb(92,92,92);">=</span> <span style="color:rgb(50,185,185);">cumsum</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(131,67,16);font-weight:bold;">th</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(131,67,16);font-weight:bold;">X</span> <span style="color:rgb(92,92,92);">=</span> <span style="color:rgb(50,185,185);">cumsum</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(74,85,219);">[</span><span style="color:rgb(188,143,143);">0</span> <span style="color:rgb(131,67,16);font-weight:bold;">r</span><span style="color:rgb(92,92,92);">.*</span><span style="color:rgb(50,185,185);">cos</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">cumth</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(0,0,0);">;</span><span style="color:rgb(188,143,143);">0</span> <span style="color:rgb(131,67,16);font-weight:bold;">r</span><span style="color:rgb(92,92,92);">.*</span><span style="color:rgb(50,185,185);">sin</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(0,0,0);">cumth</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(74,85,219);">]</span><span style="color:rgb(0,0,0);">,</span> <span style="color:rgb(188,143,143);">2</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(160,32,240);">end</span>
<span style="color:rgb(176,24,19);">function</span> <span style="color:rgb(131,67,16);font-weight:bold;">N</span><span style="color:rgb(92,92,92);">=</span><span style="color:rgb(0,0,0);text-decoration:underline;">collatz</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(131,67,16);font-weight:bold;">n</span><span style="color:rgb(74,85,219);">)</span>
<span style="color:rgb(131,67,16);font-weight:bold;">N</span> <span style="color:rgb(92,92,92);">=</span> <span style="color:rgb(131,67,16);font-weight:bold;">n</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(160,32,240);">while</span> <span style="color:rgb(131,67,16);font-weight:bold;">n</span><span style="color:rgb(92,92,92);"><></span><span style="color:rgb(188,143,143);">1</span>
<span style="color:rgb(160,32,240);">if</span> <span style="color:rgb(0,0,0);">modulo</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(131,67,16);font-weight:bold;">n</span><span style="color:rgb(0,0,0);">,</span><span style="color:rgb(188,143,143);">2</span><span style="color:rgb(74,85,219);">)</span> <span style="color:rgb(92,92,92);">==</span> <span style="color:rgb(188,143,143);">0</span>
<span style="color:rgb(131,67,16);font-weight:bold;">n</span> <span style="color:rgb(92,92,92);">=</span> <span style="color:rgb(131,67,16);font-weight:bold;">n</span><span style="color:rgb(92,92,92);">/</span><span style="color:rgb(188,143,143);">2</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(160,32,240);">else</span>
<span style="color:rgb(131,67,16);font-weight:bold;">n</span> <span style="color:rgb(92,92,92);">=</span> <span style="color:rgb(188,143,143);">3</span><span style="color:rgb(92,92,92);">*</span><span style="color:rgb(131,67,16);font-weight:bold;">n</span><span style="color:rgb(92,92,92);">+</span><span style="color:rgb(188,143,143);">1</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(160,32,240);">end</span>
<span style="color:rgb(131,67,16);font-weight:bold;">N</span> <span style="color:rgb(92,92,92);">=</span> <span style="color:rgb(74,85,219);">[</span><span style="color:rgb(131,67,16);font-weight:bold;">n</span> <span style="color:rgb(131,67,16);font-weight:bold;">N</span><span style="color:rgb(74,85,219);">]</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(160,32,240);">end</span>
<span style="color:rgb(160,32,240);">end</span>
<span style="color:rgb(0,0,0);">a</span><span style="color:rgb(92,92,92);">=</span><span style="color:rgb(188,143,143);">0.08</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(0,0,0);">e</span><span style="color:rgb(92,92,92);">=</span><span style="color:rgb(188,143,143);">1.2</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(0,0,0);">clf</span>
<span style="color:rgb(0,0,0);">gcf</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(92,92,92);">.</span><span style="color:rgb(170,170,170);">color_map</span><span style="color:rgb(92,92,92);">=</span><span style="color:rgb(0,0,0);">graycolormap</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(188,143,143);">128</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(160,32,240);">for</span> <span style="color:rgb(0,0,0);">i</span><span style="color:rgb(92,92,92);">=</span><span style="color:rgb(188,143,143);">1</span><span style="color:rgb(255,170,0);">:</span><span style="color:rgb(188,143,143);">100</span>
<span style="color:rgb(131,67,16);font-weight:bold;">r</span><span style="color:rgb(92,92,92);">=</span><span style="color:rgb(0,0,0);text-decoration:underline;">collatz</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(50,185,185);">ceil</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(50,185,185);">rand</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(92,92,92);">*</span><span style="color:rgb(188,143,143);">2000000000</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(131,67,16);font-weight:bold;">X</span><span style="color:rgb(92,92,92);">=</span><span style="color:rgb(0,0,0);text-decoration:underline;">anglePath</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(131,67,16);font-weight:bold;">r</span><span style="color:rgb(92,92,92);">./</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(188,143,143);">1</span><span style="color:rgb(92,92,92);">+</span><span style="color:rgb(131,67,16);font-weight:bold;">r</span><span style="color:rgb(92,92,92);">.^</span><span style="color:rgb(188,143,143);">1.2</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(0,0,0);">,</span><span style="color:rgb(0,0,0);">a</span><span style="color:rgb(92,92,92);">*</span><span style="color:rgb(218,112,214);">%pi</span><span style="color:rgb(92,92,92);">*</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(188,143,143);">0.35</span><span style="color:rgb(92,92,92);">-</span><span style="color:rgb(0,0,0);">modulo</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(131,67,16);font-weight:bold;">r</span><span style="color:rgb(0,0,0);">,</span><span style="color:rgb(188,143,143);">2</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(0,0,0);">plot</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(188,143,143);">0.01</span><span style="color:rgb(92,92,92);">+</span><span style="color:rgb(131,67,16);font-weight:bold;">X</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(188,143,143);">1</span><span style="color:rgb(0,0,0);">,</span><span style="color:rgb(255,170,0);">:</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(0,0,0);">,</span><span style="color:rgb(92,92,92);">-</span><span style="color:rgb(188,143,143);">0.01</span><span style="color:rgb(92,92,92);">+</span><span style="color:rgb(131,67,16);font-weight:bold;">X</span><span style="color:rgb(74,85,219);">(</span><span style="color:rgb(188,143,143);">2</span><span style="color:rgb(0,0,0);">,</span><span style="color:rgb(255,170,0);">:</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(74,85,219);">)</span><span style="color:rgb(0,0,0);">;</span>
<span style="color:rgb(160,32,240);">end
<img moz-do-not-send="false" src="cid:part1.Q9bQt94p.vO2efLK3@utc.fr" alt="collatz" width="498" height="351">
</span></pre>
<pre class="moz-signature" cols="72">--
Stéphane Mottelet
Ingénieur de recherche
EA 4297 Transformations Intégrées de la Matière Renouvelable
Département Génie des Procédés Industriels
Sorbonne Universités - Université de Technologie de Compiègne
CS 60319, 60203 Compiègne cedex
Tel : +33(0)344234688
<a class="moz-txt-link-freetext" href="http://www.utc.fr/~mottelet" moz-do-not-send="true">http://www.utc.fr/~mottelet</a>
</pre>
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