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  6.     <title>11.5.¬† IFS Fractal</title>
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  20.         <tr>
  21.           <th colspan="3" align="center">11.5.¬†
  22.     <span lang="en" xml:lang="en">IFS Fractal</span>
  23.   </th>
  24.         </tr>
  25.         <tr>
  26.           <td width="20%" align="left"><a accesskey="p" href="plug-in-flame.html"><img src="../images/prev.png" alt="Prev" /></a>¬†</td>
  27.           <th width="60%" align="center">11.¬†
  28.     <span lang="en" xml:lang="en">Rendering Filters</span>
  29.   </th>
  30.           <td width="20%" align="right">¬†<a accesskey="n" href="plug-in-diffraction.html"><img src="../images/next.png" alt="Next" /></a></td>
  31.         </tr>
  32.       </table>
  33.       <hr />
  34.     </div>
  35.     <div class="sect2" lang="en" xml:lang="en">
  36.       <div class="titlepage">
  37.         <div>
  38.           <div>
  39.             <h3 class="title"><a id="plug-in-ifsfractal"></a>11.5.¬†
  40.     <span lang="en" xml:lang="en">IFS Fractal</span>
  41.   </h3>
  42.           </div>
  43.           <div>
  44.             <div class="revhistory">
  45.               <table border="1" width="100%" summary="Revision history">
  46.                 <tr>
  47.                   <th align="left" valign="top" colspan="3">
  48.                     <b>Revision History</b>
  49.                   </th>
  50.                 </tr>
  51.                 <tr>
  52.                   <td align="left">Revision $Revision: 2442 $</td>
  53.                   <td align="left">2006-12-16</td>
  54.                   <td align="left">j.h</td>
  55.                 </tr>
  56.               </table>
  57.             </div>
  58.           </div>
  59.         </div>
  60.       </div>
  61.       <a id="id2770507" class="indexterm"></a>
  62.       <a id="id2770525" class="indexterm"></a>
  63.       <div class="mediaobject">
  64.         <img src="../images/filters/filters-render-ifsfractal.png" />
  65.       </div>
  66.       <div class="sect3" lang="en" xml:lang="en">
  67.         <div class="titlepage">
  68.           <div>
  69.             <div>
  70.               <h4 class="title"><a id="id2770549"></a>11.5.1.¬†
  71.       <span lang="en" xml:lang="en">Overview</span>
  72.     </h4>
  73.             </div>
  74.           </div>
  75.         </div>
  76.         <div class="figure">
  77.           <a id="id2770560"></a>
  78.           <p class="title">
  79.             <b>Figure¬†16.237.¬†
  80.         <span lang="en" xml:lang="en">Applying example for the IFS Compose filter</span>
  81.       </b>
  82.           </p>
  83.           <div class="figure-contents">
  84.             <div class="mediaobject">
  85.               <img src="../images/filters/examples/render-taj-ifscompose.jpg" alt="Applying example for the IFS Compose filter" />
  86.               <div class="caption">
  87.                 <p>Filter ‚Äú<span class="quote">IFS Fractal</span>‚Äù applied</p>
  88.               </div>
  89.             </div>
  90.           </div>
  91.         </div>
  92.         <br class="figure-break" />
  93.         <p>
  94.       You can find this filter through
  95.       <span class="guimenu">Filte<span class="accel">r</span>s</span> ‚Üí <span class="guisubmenu"><span class="accel">R</span>ender</span> ‚Üí <span class="guisubmenu"><span class="accel">N</span>ature</span> ‚Üí <span class="guimenuitem"><span class="accel">I</span>FS fractal</span>
  96.     </p>
  97.         <p>
  98.       This fractal-based plug-in is truly wonderful! With this
  99.       versatile instrument, you can create amazingly naturalistic
  100.       organic shapes, like leaves, flowers, branches, or even whole
  101.       trees.  (‚Äú<span class="quote">IFS</span>‚Äù stands for ‚Äú<span class="quote">Iterated Function System
  102.       </span>‚Äù.)
  103.     </p>
  104.         <p>
  105.       The key to use this plug-in lies in making very small and precise
  106.       movements in fractal space. The outcome is always hard to predict, and
  107.       you have to be extremely gentle when you change the pattern. If you make
  108.       a component triangle too big, or if you move it too far (even ever so
  109.       slightly), the preview screen will black out, or more commonly, you'll
  110.       get stuck with a big shapeless particle cloud.
  111.     </p>
  112.         <p>
  113.       A word of advice: When you have found a pattern you want to work with,
  114.       make only small changes, and stick to variations of that pattern. It's
  115.       all too easy to lose a good thing. Contrary to what you might believe,
  116.       it's really much easier to create a leaf or a tree with IFS Compose than
  117.       to make a defined geometrical pattern (where you actually know what
  118.       you're doing, and end up with the pattern you had in mind).
  119.     </p>
  120.         <p>
  121.       For a brief introduction to IFS's see Foley and van Dam, et
  122.       al,. <em class="citetitle">Computer Graphics, Principles and
  123.       Practice</em><a class="xref" href="bibliography.html#bibliography-books-foley01" title="Computer Graphics, Principles and Practice">[<abbr class="abbrev">FOLEY01</abbr>]</a>.
  124.     </p>
  125.       </div>
  126.       <div class="sect3" lang="en" xml:lang="en">
  127.         <div class="titlepage">
  128.           <div>
  129.             <div>
  130.               <h4 class="title"><a id="id2770712"></a>11.5.2.¬†
  131.       <span lang="en" xml:lang="en">Options</span>
  132.     </h4>
  133.             </div>
  134.           </div>
  135.         </div>
  136.         <div class="variablelist">
  137.           <dl>
  138.             <dt>
  139.               <span class="term">The Main Interface</span>
  140.             </dt>
  141.             <dd>
  142.               <p>
  143.             The plug-in interface consists of the compose area to the left, a
  144.             preview screen to the right, and some tabs and option buttons at
  145.             the bottom of the dialog. The Default setting (in the preview
  146.             window) is three equilateral triangles. (This gives rise to a
  147.             fractal pattern called the
  148.             <span class="emphasis"><em>Sierpinski Triangle</em></span>).
  149.           </p>
  150.             </dd>
  151.             <dt>
  152.               <span class="term">Toolbar</span>
  153.             </dt>
  154.             <dd>
  155.               <p>
  156.             Some tools are directly visible in this tool bar:
  157.             <span class="guibutton">Move</span>,
  158.             <span class="guibutton">Rotate</span>, <span class="guibutton">Stretch</span>,
  159.             <span class="guibutton">New</span>,
  160.             <span class="guibutton">Delete</span>, <span class="guibutton">Undo</span>
  161.             , <span class="guibutton">Redo</span>,
  162.             <span class="guibutton">Select All</span>.
  163.             You can see others, if your window is not wide enough, by
  164.             clicking on the drop-down list button on the right of tool bar:
  165.             <span class="guibutton">Recenter</span>  and
  166.             <span class="guibutton">Render Options</span> where you have have
  167.             several parameters:
  168.           </p>
  169.               <div class="variablelist">
  170.                 <dl>
  171.                   <dt>
  172.                     <span class="term">Render Options</span>
  173.                   </dt>
  174.                   <dd>
  175.                     <div class="variablelist">
  176.                       <dl>
  177.                         <dt>
  178.                           <span class="term">Memory</span>
  179.                         </dt>
  180.                         <dd>
  181.                           <p>
  182.                         Enables you to speed up rendering time. This is
  183.                         especially useful when working with a large spot
  184.                         radius; just remember to use even multiples of the
  185.                         default value: 4096, 8192, 16384, ...
  186.                       </p>
  187.                         </dd>
  188.                         <dt>
  189.                           <span class="term">Iterations</span>
  190.                         </dt>
  191.                         <dd>
  192.                           <p>
  193.                         Determines how many times the fractal will repeat
  194.                         itself. (A high value for Subdivide and Iterations is
  195.                         for obvious reasons a waste of process time unless
  196.                         your image is very large.)
  197.                       </p>
  198.                         </dd>
  199.                         <dt>
  200.                           <span class="term">Subdivide</span>
  201.                         </dt>
  202.                         <dd>
  203.                           <p>Controls the level of detail.</p>
  204.                         </dd>
  205.                         <dt>
  206.                           <span class="term">Spot Radius</span>
  207.                         </dt>
  208.                         <dd>
  209.                           <p>
  210.                         Determines the density of the
  211.                         ‚Äú<span class="quote">brushstrokes</span>‚Äù
  212.                         in the rendered image. A low spot radius is good for
  213.                         thin particle clouds or spray, while a high spot
  214.                         radius produces thick, solid color strokes much like
  215.                         watercolor painting. Be careful not to use too much
  216.                         spot radius -- it takes a lot of time to render.
  217.                       </p>
  218.                         </dd>
  219.                       </dl>
  220.                     </div>
  221.                   </dd>
  222.                 </dl>
  223.               </div>
  224.             </dd>
  225.             <dt>
  226.               <span class="term">Spatial Transformation</span>
  227.             </dt>
  228.             <dd>
  229.               <p>
  230.             Gives you information on the active fractal, and allows you to
  231.             type a value instead of changing it manually. Changing parameters
  232.             with the mouse isn't very accurate, so this is a useful option
  233.             when you need to be exact.
  234.           </p>
  235.             </dd>
  236.             <dt>
  237.               <span class="term">Color transformation</span>
  238.             </dt>
  239.             <dd>
  240.               <div class="figure">
  241.                 <a id="id2770975"></a>
  242.                 <p class="title">
  243.                   <b>Figure¬†16.238.¬†
  244.               <span lang="en" xml:lang="en">
  245.                 ‚Äú<span class="quote">Color transformation</span>‚Äù tab options
  246.               </span>
  247.             </b>
  248.                 </p>
  249.                 <div class="figure-contents">
  250.                   <div class="mediaobject">
  251.                     <img src="../images/filters/options-render-ifscompose2.png" alt="Color transformation tab options" />
  252.                   </div>
  253.                 </div>
  254.               </div>
  255.               <br class="figure-break" />
  256.               <div class="variablelist">
  257.                 <dl>
  258.                   <dt>
  259.                     <span class="term">Simple color transformation</span>
  260.                   </dt>
  261.                   <dd>
  262.                     <p>
  263.                   Changes the color of the currently selected fractal
  264.                   component (default is the foreground color in the toolbox)
  265.                   to a color of your choice.
  266.                 </p>
  267.                   </dd>
  268.                   <dt>
  269.                     <span class="term">Full color transformation</span>
  270.                   </dt>
  271.                   <dd>
  272.                     <p>
  273.                   Like the Simple color transformation but this time you can
  274.                   manage the color transformation for each color channel and
  275.                   for the alpha channel (shown as a black channel).
  276.                 </p>
  277.                   </dd>
  278.                   <dt>
  279.                     <span class="term">Scale Hue/Value</span>
  280.                   </dt>
  281.                   <dd>
  282.                     <p>
  283.                   When you have many fractals with different colors, the
  284.                   colors blend into each other. So even if you set
  285.                   ‚Äú<span class="quote">pure red</span>‚Äù for a fractal, it might actually
  286.                   be quite blue in some places, while another ‚Äú<span class="quote">red
  287.                   </span>‚Äù fractal might have a lot of yellow in it. Scale
  288.                   Hue/Value changes the color strength of the active
  289.                   fractal, or how influential that fractal color should be.
  290.                 </p>
  291.                   </dd>
  292.                 </dl>
  293.               </div>
  294.             </dd>
  295.             <dt>
  296.               <span class="term">Relative Probability</span>
  297.             </dt>
  298.             <dd>
  299.               <p>
  300.             Determines influence or total impact of a certain fractal.
  301.           </p>
  302.             </dd>
  303.           </dl>
  304.         </div>
  305.       </div>
  306.       <div class="sect3" lang="en" xml:lang="en">
  307.         <div class="titlepage">
  308.           <div>
  309.             <div>
  310.               <h4 class="title"><a id="id2771112"></a>11.5.3.¬†
  311.       <span lang="en" xml:lang="en">A Brief Tutorial</span>
  312.     </h4>
  313.             </div>
  314.           </div>
  315.         </div>
  316.         <p>
  317.       This is a rather complex plug-in, so to help you understand it, we'll
  318.       guide you through an example where you'll create a leaf or branch.
  319.     </p>
  320.         <p>
  321.       Many forms of life, and especially plants, are built like
  322.       mathematical fractals, i.e., a shape that reproduces or repeats
  323.       itself indefinitely into the smallest detail. You can easily
  324.       reproduce the shape of a leaf or a branch by using four (or
  325.       more) fractals. Three fractals make up the tip and sides of the
  326.       leaf, and the fourth represents the stem.
  327.     </p>
  328.         <div class="orderedlist">
  329.           <ol type="1">
  330.             <li>
  331.               <p>
  332.           Before invoking the filter: Select
  333.           <span class="guimenu">File</span> ‚Üí <span class="guimenuitem">New Image</span>
  334.           Add a transparent layer with
  335.           <span class="guimenu">Layers</span> ‚Üí <span class="guisubmenu">Layers and Channels</span> ‚Üí <span class="guimenuitem">New Layer</span>
  336.           Set the foreground color in the toolbox to black, and
  337.           set the background to white.
  338.         </p>
  339.             </li>
  340.             <li>
  341.               <p>
  342.           Open IFS Compose. Start by rotating the right and bottom triangles,
  343.           so that they point upward. You'll now be able to see the outline of
  344.           what's going to be the tip and sides of the leaf. (If you have
  345.           problems, it may help to know that the three vertices of a triangle
  346.           are not equivalent.)<a id="id2771215" class="indexterm"></a>
  347.         </p>
  348.               <div class="figure">
  349.                 <a id="id2771231"></a>
  350.                 <p class="title">
  351.                   <b>Figure¬†16.239.¬†
  352.             <span lang="en" xml:lang="en">Tutorial Step 2</span>
  353.           </b>
  354.                 </p>
  355.                 <div class="figure-contents">
  356.                   <div class="mediaobject">
  357.                     <img src="../images/filters/examples/ifscompose-tut1.png" alt="Tutorial Step 2" />
  358.                     <div class="caption">
  359.                       <p>
  360.                 Start by rotating triangles 2 and 3, trying to keep them nearly
  361.                 the same size.
  362.               </p>
  363.                     </div>
  364.                   </div>
  365.                 </div>
  366.               </div>
  367.               <br class="figure-break" />
  368.             </li>
  369.             <li>
  370.               <p>
  371.           To make the leaf symmetrical, adjust the bottom triangle to
  372.           point slightly to the left, and the right triangle to point
  373.           slightly to the right.
  374.         </p>
  375.             </li>
  376.             <li>
  377.               <p>
  378.           Press <span class="guibutton">New</span> to add a component to the
  379.           composition. This is going to be the stem of the leaf, so we
  380.           need to make it long and thin. Press
  381.           <span class="guibutton">Stretch</span>, and drag to
  382.           stretch the new triangle. Don't be alarmed if this messes up
  383.           the image, just use <span class="guibutton">Scale</span> to adjust
  384.           the size of the overlong
  385.           triangle. You'll probably also have to move and rotate the
  386.           new fractal to make it look convincing.
  387.         </p>
  388.               <div class="figure">
  389.                 <a id="id2771314"></a>
  390.                 <p class="title">
  391.                   <b>Figure¬†16.240.¬†
  392.             <span lang="en" xml:lang="en">Tutorial Step 3</span>
  393.           </b>
  394.                 </p>
  395.                 <div class="figure-contents">
  396.                   <div class="mediaobject">
  397.                     <img src="../images/filters/examples/ifscompose-tut2.png" alt="Tutorial Step 3" />
  398.                     <div class="caption">
  399.                       <p>
  400.                 Add a fourth component, then stretch, scale, and move it
  401.                 as shown.
  402.               </p>
  403.                     </div>
  404.                   </div>
  405.                 </div>
  406.               </div>
  407.               <br class="figure-break" />
  408.             </li>
  409.             <li>
  410.               <p>
  411.           You still have to make it look more leaf-like. Increase the
  412.           size of the top triangle, until you think it's thick and
  413.           leafy enough. Adjust all fractals until you're happy with
  414.           the shape. Right-click to get the pop-up menu, and choose
  415.           <span class="guibutton">Select all</span>. Now all components are
  416.           selected, and you can scale
  417.           and rotate the entire leaf.
  418.         </p>
  419.               <div class="figure">
  420.                 <a id="id2771373"></a>
  421.                 <p class="title">
  422.                   <b>Figure¬†16.241.¬†
  423.             <span lang="en" xml:lang="en">Tutorial Step 4</span>
  424.           </b>
  425.                 </p>
  426.                 <div class="figure-contents">
  427.                   <div class="mediaobject">
  428.                     <img src="../images/filters/examples/ifscompose-tut3.png" alt="Tutorial Step 4" />
  429.                     <div class="caption">
  430.                       <p>
  431.                 Enlarge component 1, arrange the other components
  432.                 appropriately, then select all, scale and rotate.
  433.               </p>
  434.                     </div>
  435.                   </div>
  436.                 </div>
  437.               </div>
  438.               <br class="figure-break" />
  439.             </li>
  440.             <li>
  441.               <p>
  442.           The final step is to adjust color. Click on the
  443.           <span class="guibutton">Color Transformation</span> tab, and choose
  444.           a different color for each fractal. To do this, check
  445.           <span class="guibutton">Simple</span> and press the right color
  446.           square. A color circle appears, where you can click or
  447.           select to choose a color.
  448.         </p>
  449.               <div class="figure">
  450.                 <a id="id2771437"></a>
  451.                 <p class="title">
  452.                   <b>Figure¬†16.242.¬†
  453.             <span lang="en" xml:lang="en">Tutorial Step 5</span>
  454.           </b>
  455.                 </p>
  456.                 <div class="figure-contents">
  457.                   <div class="mediaobject">
  458.                     <img src="../images/filters/examples/ifscompose-tut4.png" alt="Tutorial Step 5" />
  459.                     <div class="caption">
  460.                       <p>
  461.                 Assign a brownish color to component 4, and various shades
  462.                 of green to the other components.
  463.               </p>
  464.                     </div>
  465.                   </div>
  466.                 </div>
  467.               </div>
  468.               <br class="figure-break" />
  469.             </li>
  470.             <li>
  471.               <p>
  472.           Press OK to apply the image, and voil√†, you've just made a
  473.           perfect fractal leaf! Now that you've got the hang of it,
  474.           you'll just have to experiment and make your own
  475.           designs. All plant-imitating fractals (be they oak trees,
  476.           ferns or straws) are more or less made in this fashion,
  477.           which is leaves around a stem (or several stems). You just
  478.           have to twist another way, stretch and turn a little or add
  479.           a few more fractals to get a totally different plant.
  480.         </p>
  481.             </li>
  482.           </ol>
  483.         </div>
  484.       </div>
  485.     </div>
  486.     <div class="navfooter">
  487.       <hr />
  488.       <table width="100%" summary="Navigation footer">
  489.         <tr>
  490.           <td width="40%" align="left"><a accesskey="p" href="plug-in-flame.html"><img src="../images/prev.png" alt="Prev" /></a>¬†</td>
  491.           <td width="20%" align="center">
  492.             <a accesskey="u" href="filters-render.html">
  493.               <img src="../images/up.png" alt="Up" />
  494.             </a>
  495.           </td>
  496.           <td width="40%" align="right">¬†<a accesskey="n" href="plug-in-diffraction.html"><img src="../images/next.png" alt="Next" /></a></td>
  497.         </tr>
  498.         <tr>
  499.           <td width="40%" align="left" valign="top"><a accesskey="p" href="plug-in-flame.html">11.4.¬†
  500.     <span lang="en" xml:lang="en">Flame</span>
  501.   </a>¬†</td>
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  506.           </td>
  507.           <td width="40%" align="right" valign="top">¬†<a accesskey="n" href="plug-in-diffraction.html">11.6.¬†
  508.     <span lang="en" xml:lang="en">Diffraction Patterns</span>
  509.   </a></td>
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  512.     </div>
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  515.