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      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
      <footer alignment="Center" color="#a9a9a9">&amp;[PAGENUM] / &amp;[COUNT]</footer>
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    <text lang="eng">
      <p bold="true">Planetary spot system</p>
    </text>
  </region>
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    <text lang="eng">
      <p>The system can be built to isolate the center spot to make it bigger,and the satellites smaller.  </p>
    </text>
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  <region id="2" left="18" top="63" width="56" height="45" color="#000000" bgColor="#ffffff" fontSize="10">
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      <description active="true" position="Right" lang="eng">
        <p>'N' number of satellitesradius position satellites</p>
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        <e type="operand">6</e>
        <e type="operator" args="2">:</e>
        <e type="operand">r</e>
        <e type="operand">π</e>
        <e type="operator" args="2">:</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
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    <math>
      <description active="true" position="Right" lang="eng">
        <p>radius center spotradius satellites</p>
      </description>
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        <e type="operand">r0</e>
        <e type="operand">1.25</e>
        <e type="operator" args="2">:</e>
        <e type="operand">r1</e>
        <e type="operand">0.625</e>
        <e type="operator" args="2">:</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
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    <math decimalPlaces="4">
      <description active="true" position="Right" lang="eng">
        <p>position center spot</p>
      </description>
      <input>
        <e type="operand">x0</e>
        <e type="operand">0</e>
        <e type="operator" args="2">:</e>
        <e type="operand">y0</e>
        <e type="operand">0</e>
        <e type="operator" args="2">:</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="4">mat</e>
      </input>
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    <math decimalPlaces="4">
      <description active="true" position="Top" lang="eng">
        <p>Center Planet ...  raduis r0 @ x0, y0</p>
      </description>
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        <e type="operand">y</e>
        <e type="operand">x0</e>
        <e type="operand">y0</e>
        <e type="operand">r0</e>
        <e type="function" args="5">f0</e>
        <e type="operand">255</e>
        <e type="operand">x</e>
        <e type="operand">x0</e>
        <e type="operator" args="2">-</e>
        <e type="operand">r0</e>
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        <e type="bracket">(</e>
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        <e type="operand">y</e>
        <e type="operand">y0</e>
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        <e type="operand">r0</e>
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        <e type="bracket">(</e>
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        <e type="operator" args="1">-</e>
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      <description active="true" position="Top" lang="eng">
        <p>Satellites  ...  raduis r1 @ N locations xs, ys</p>
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        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="operand">xs</e>
        <e type="operand">ys</e>
        <e type="operand">r1</e>
        <e type="function" args="5">f1</e>
        <e type="operand">255</e>
        <e type="operand">x</e>
        <e type="operand">xs</e>
        <e type="operator" args="2">-</e>
        <e type="operand">r1</e>
        <e type="operator" args="2">/</e>
        <e type="bracket">(</e>
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        <e type="operand">ys</e>
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        <e type="operand">1</e>
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      <description active="true" position="Top" lang="eng">
        <p>The complete Planetary system: Planet + Satellites</p>
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        <e type="operand">y</e>
        <e type="function" args="2">Φ</e>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="operand">x0</e>
        <e type="operand">y0</e>
        <e type="operand">r0</e>
        <e type="function" args="5">f0</e>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="operand">r</e>
        <e type="operand">2</e>
        <e type="operand">π</e>
        <e type="operator" args="2">*</e>
        <e type="operand">j</e>
        <e type="operator" args="2">*</e>
        <e type="operand">N</e>
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        <e type="function" preserve="true" args="1">cos</e>
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        <e type="operand">r</e>
        <e type="operand">2</e>
        <e type="operand">π</e>
        <e type="operator" args="2">*</e>
        <e type="operand">j</e>
        <e type="operator" args="2">*</e>
        <e type="operand">N</e>
        <e type="operator" args="2">/</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operator" args="2">*</e>
        <e type="operand">r1</e>
        <e type="function" args="5">f1</e>
        <e type="operand">j</e>
        <e type="operand">0</e>
        <e type="operand">N</e>
        <e type="operand">1</e>
        <e type="operator" args="2">-</e>
        <e type="function" preserve="true" args="4">sum</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
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    <math optimize="2" decimalPlaces="6">
      <description active="true" position="Top" lang="eng">
        <p>... typical setup for symmetric Φ(x,y).</p>
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        <e type="operand">y</e>
        <e type="function" args="2">Φ</e>
        <e type="operand">L</e>
        <e type="operand">H</e>
        <e type="operand">n</e>
        <e type="function" args="4">Sym</e>
        <e type="operand">U</e>
        <e type="operand">0</e>
        <e type="operator" args="2">:</e>
        <e type="operand">dx</e>
        <e type="operand">H</e>
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        <e type="operand">n</e>
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        <e type="operand">i</e>
        <e type="operand">1</e>
        <e type="operand">n</e>
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        <e type="operand">U</e>
        <e type="operand">i</e>
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        <e type="operand">L</e>
        <e type="operand">dx</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
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        <e type="bracket">(</e>
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        <e type="operand" style="string">symmetric Gaussian</e>
        <e type="operand">r</e>
        <e type="operand">1</e>
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        <e type="operand">i</e>
        <e type="operand">1</e>
        <e type="operand">n</e>
        <e type="operand">1</e>
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        <e type="bracket">(</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">c</e>
        <e type="operand">1</e>
        <e type="operator" args="2">:</e>
        <e type="operand">j</e>
        <e type="operand">1</e>
        <e type="operand">n</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">M</e>
        <e type="operand">r</e>
        <e type="operand">c</e>
        <e type="function" preserve="true" args="3">el</e>
        <e type="operand">U</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">U</e>
        <e type="operand">j</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="function" args="2">Φ</e>
        <e type="function" preserve="true" args="1">eval</e>
        <e type="operator" args="2">:</e>
        <e type="operand">c</e>
        <e type="operand">c</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
        <e type="function" preserve="true" args="3">for</e>
        <e type="operand">r</e>
        <e type="operand">r</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">line</e>
        <e type="function" preserve="true" args="3">for</e>
        <e type="operand">M</e>
        <e type="operand">6</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="8">line</e>
        <e type="operator" args="2">:</e>
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        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="function" args="2">Φ</e>
        <e type="operand">5</e>
        <e type="operator" args="1">-</e>
        <e type="operand">5</e>
        <e type="operand">64</e>
        <e type="function" args="4">Sym</e>
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      </input>
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        <e type="operand">Planet</e>
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        <e type="operand">spot</e>
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      <input>
        <e type="operand">Planet</e>
      </input>
    </image>
  </region>
  <region id="14" left="459" top="675" width="146" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="1">
      <input>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="1">time</e>
        <e type="operand">t0</e>
        <e type="operator" args="2">-</e>
      </input>
      <contract>
        <e type="operand" style="unit">min</e>
      </contract>
      <result action="numeric">
        <e type="operand">1</e>
      </result>
    </math>
  </region>
</regions>