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              <c val="#800080">Instant "Art"</c>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Some of the functions in this Extension Pack allow you to create images that bear some resemblance to various schools of modern art. A few are illustrated here.</p>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Three random images are smoothed and quantized to generate contours with a given level; the red, green, and blue components of these images are combined to get an interesting layered color image.</p>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">The most efficient way to make random arrays is to apply a random number function to an empty array using <f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">Mathcad</inlineAttr></f>'s vectorize operator.</p>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Each random array is filtered using the FFT, and the result quantized. The variable <f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">levels</inlineAttr></f> is set below.</p>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Now view the result:</p>
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          </ml:apply>
        </inputs>
        <outputs />
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    <region region-id="1607" left="6" top="786.75" width="305.25" height="28.5" align-x="6" align-y="798" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">The integer<b><sp /></b><f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">N controls the degree of smoothing; higher N</inlineAttr></f> gives less smoothing.</p>
      </text>
    </region>
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      <math optimize="false" disable-calc="false">
        <ml:globalDefine>
          <ml:id xml:space="preserve">N</ml:id>
          <ml:real>3</ml:real>
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      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">The variable <f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">levels</inlineAttr></f> sets the number of levels in each color:</p>
      </text>
    </region>
    <region region-id="1610" left="36" top="870.75" width="47.25" height="15.75" align-x="68.25" align-y="882" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
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          <ml:id xml:space="preserve">levels</ml:id>
          <ml:real>8</ml:real>
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    <region region-id="1611" left="6" top="894.75" width="318" height="28.5" align-x="6" align-y="906" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">To recompute with the sam<f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">e N</inlineAttr></f> and <f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">levels but new random images, click the definition of L </inlineAttr></f>below and press <b>[F9]</b> to recompute.</p>
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          <ml:id xml:space="preserve">L</ml:id>
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      <pageBreak />
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">
          <b>
            <c val="#800000">HSV Stripes and Plaids</c>
          </b>
        </p>
      </text>
      <indexes>
        <phrase>hsv stripes and plaids</phrase>
      </indexes>
    </region>
    <region region-id="1614" left="6" top="1002.75" width="313.5" height="57" align-x="6" align-y="1014" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Pretty patterns of random stripes reminiscent of the paintings of Gene Davis result when the columns of the hue matrix in an HSV image are divided into sections of random length and filled with a random hue value. The following arithmetic carries out this scheme.</p>
      </text>
      <indexes>
        <phrase>Davis, Gene</phrase>
      </indexes>
    </region>
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        <ml:define>
          <ml:apply>
            <ml:indexer />
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            <ml:real>0</ml:real>
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        <ml:define>
          <ml:id xml:space="preserve">M</ml:id>
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            <ml:localDefine>
              <ml:id xml:space="preserve">m</ml:id>
              <ml:real>0</ml:real>
            </ml:localDefine>
            <ml:localDefine>
              <ml:apply>
                <ml:indexer />
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              </ml:apply>
              <ml:real>0</ml:real>
            </ml:localDefine>
            <ml:localDefine>
              <ml:id xml:space="preserve">m</ml:id>
              <ml:apply>
                <ml:plus />
                <ml:id xml:space="preserve">m</ml:id>
                <ml:real>1</ml:real>
              </ml:apply>
            </ml:localDefine>
            <ml:while>
              <ml:apply>
                <ml:lessOrEqual />
                <ml:apply>
                  <ml:indexer />
                  <ml:id xml:space="preserve">M</ml:id>
                  <ml:apply>
                    <ml:minus />
                    <ml:id xml:space="preserve">m</ml:id>
                    <ml:real>1</ml:real>
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                </ml:apply>
                <ml:real>160</ml:real>
              </ml:apply>
              <ml:program>
                <ml:localDefine>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id xml:space="preserve">M</ml:id>
                    <ml:id xml:space="preserve">m</ml:id>
                  </ml:apply>
                  <ml:apply>
                    <ml:plus />
                    <ml:apply>
                      <ml:plus />
                      <ml:apply>
                        <ml:indexer />
                        <ml:id xml:space="preserve">M</ml:id>
                        <ml:apply>
                          <ml:minus />
                          <ml:id xml:space="preserve">m</ml:id>
                          <ml:real>1</ml:real>
                        </ml:apply>
                      </ml:apply>
                      <ml:real>1</ml:real>
                    </ml:apply>
                    <ml:apply>
                      <ml:id xml:space="preserve">floor</ml:id>
                      <ml:apply>
                        <ml:id xml:space="preserve">rnd</ml:id>
                        <ml:real>12</ml:real>
                      </ml:apply>
                    </ml:apply>
                  </ml:apply>
                </ml:localDefine>
                <ml:localDefine>
                  <ml:id xml:space="preserve">m</ml:id>
                  <ml:apply>
                    <ml:plus />
                    <ml:id xml:space="preserve">m</ml:id>
                    <ml:real>1</ml:real>
                  </ml:apply>
                </ml:localDefine>
              </ml:program>
            </ml:while>
            <ml:localDefine>
              <ml:apply>
                <ml:indexer />
                <ml:id xml:space="preserve">M</ml:id>
                <ml:id xml:space="preserve">m</ml:id>
              </ml:apply>
              <ml:apply>
                <ml:plus />
                <ml:apply>
                  <ml:plus />
                  <ml:apply>
                    <ml:indexer />
                    <ml:id xml:space="preserve">M</ml:id>
                    <ml:apply>
                      <ml:minus />
                      <ml:id xml:space="preserve">m</ml:id>
                      <ml:real>1</ml:real>
                    </ml:apply>
                  </ml:apply>
                  <ml:real>1</ml:real>
                </ml:apply>
                <ml:apply>
                  <ml:id xml:space="preserve">floor</ml:id>
                  <ml:apply>
                    <ml:id xml:space="preserve">rnd</ml:id>
                    <ml:real>12</ml:real>
                  </ml:apply>
                </ml:apply>
              </ml:apply>
            </ml:localDefine>
            <ml:id xml:space="preserve">M</ml:id>
          </ml:program>
        </ml:define>
      </math>
      <rendering item-idref="25" />
    </region>
    <region region-id="1620" left="6" top="1272.75" width="324" height="57" align-x="6" align-y="1284" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">The vector <f family="Times New Roman" charset="0"><b><inlineAttr line-through="false">M</inlineAttr></b></f><f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false"> contains the boundaries between the stripes. Random hues, one for each stripe, are assigned in the vector </inlineAttr></f><f family="Times New Roman" charset="0"><b><inlineAttr line-through="false">H</inlineAttr></b></f>. The<b> hist</b> function picks out the hue corresponding to each column, so this hue can be multiplied by a column of 1's.</p>
      </text>
      <indexes>
        <phrase>hist function</phrase>
      </indexes>
    </region>
    <region region-id="1631" left="36" top="1338.75" width="101.25" height="15.75" align-x="49.5" align-y="1350" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:id xml:space="preserve">n</ml:id>
          <ml:range>
            <ml:real>0</ml:real>
            <ml:apply>
              <ml:minus />
              <ml:apply>
                <ml:id xml:space="preserve">rows</ml:id>
                <ml:id xml:space="preserve">M</ml:id>
              </ml:apply>
              <ml:real>2</ml:real>
            </ml:apply>
          </ml:range>
        </ml:define>
      </math>
      <rendering item-idref="26" />
    </region>
    <region region-id="1632" left="162" top="1338.75" width="99" height="17.25" align-x="172.5" align-y="1350" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedUDScalar">
          <ml:id xml:space="preserve">i</ml:id>
          <ml:range>
            <ml:real>0</ml:real>
            <ml:apply>
              <ml:indexer />
              <ml:id xml:space="preserve">M</ml:id>
              <ml:apply>
                <ml:minus />
                <ml:apply>
                  <ml:id xml:space="preserve">rows</ml:id>
                  <ml:id xml:space="preserve">M</ml:id>
                </ml:apply>
                <ml:real>1</ml:real>
              </ml:apply>
            </ml:apply>
          </ml:range>
        </ml:define>
      </math>
      <rendering item-idref="27" />
    </region>
    <region region-id="1633" left="288" top="1344.75" width="32.25" height="17.25" align-x="303.75" align-y="1356" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:apply>
            <ml:indexer />
            <ml:id xml:space="preserve">u</ml:id>
            <ml:id xml:space="preserve">i</ml:id>
          </ml:apply>
          <ml:real>1</ml:real>
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      </math>
      <rendering item-idref="28" />
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    <region region-id="1634" left="36" top="1368.75" width="75" height="17.25" align-x="57.75" align-y="1380" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedBIUnit">
          <ml:apply>
            <ml:indexer />
            <ml:id xml:space="preserve">H</ml:id>
            <ml:id xml:space="preserve">n</ml:id>
          </ml:apply>
          <ml:apply>
            <ml:id xml:space="preserve">rnd</ml:id>
            <ml:real>360</ml:real>
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        </ml:define>
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      <rendering item-idref="29" />
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    <region region-id="1635" left="162" top="1364.25" width="123.75" height="20.25" align-x="192.75" align-y="1380" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:apply>
            <ml:matcol />
            <ml:id xml:space="preserve">HI</ml:id>
            <ml:id xml:space="preserve">i</ml:id>
          </ml:apply>
          <ml:apply>
            <ml:mult style="default" />
            <ml:id xml:space="preserve">u</ml:id>
            <ml:parens>
              <ml:apply>
                <ml:mult style="default" />
                <ml:apply>
                  <ml:id xml:space="preserve">hist</ml:id>
                  <ml:sequence>
                    <ml:id xml:space="preserve">M</ml:id>
                    <ml:apply>
                      <ml:mult style="default" />
                      <ml:id xml:space="preserve">a</ml:id>
                      <ml:id xml:space="preserve">i</ml:id>
                    </ml:apply>
                  </ml:sequence>
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                <ml:id xml:space="preserve">H</ml:id>
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      <rendering item-idref="30" />
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    <region region-id="1636" left="6" top="1392.75" width="326.25" height="42.75" align-x="6" align-y="1404" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">To give the saturation and value some variety, the same process is repeated on these components, biasing the values toward the high end of the scale:</p>
      </text>
    </region>
    <region region-id="1637" left="36" top="1446.75" width="99" height="17.25" align-x="56.25" align-y="1458" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedBIUnit">
          <ml:apply>
            <ml:indexer />
            <ml:id xml:space="preserve">S</ml:id>
            <ml:id xml:space="preserve">n</ml:id>
          </ml:apply>
          <ml:apply>
            <ml:plus />
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            <ml:apply>
              <ml:id xml:space="preserve">rnd</ml:id>
              <ml:real>56</ml:real>
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          </ml:apply>
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      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:apply>
            <ml:matcol />
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            <ml:id xml:space="preserve">i</ml:id>
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          <ml:apply>
            <ml:mult style="default" />
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                <ml:mult style="default" />
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                  <ml:id xml:space="preserve">hist</ml:id>
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                      <ml:id xml:space="preserve">a</ml:id>
                      <ml:id xml:space="preserve">i</ml:id>
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                <ml:id xml:space="preserve">S</ml:id>
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      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedBIUnit">
          <ml:apply>
            <ml:indexer />
            <ml:id xml:space="preserve">V</ml:id>
            <ml:id xml:space="preserve">n</ml:id>
          </ml:apply>
          <ml:apply>
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            <ml:apply>
              <ml:id xml:space="preserve">rnd</ml:id>
              <ml:real>56</ml:real>
            </ml:apply>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="33" />
    </region>
    <region region-id="1640" left="162" top="1472.25" width="123.75" height="20.25" align-x="192.75" align-y="1488" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:apply>
            <ml:matcol />
            <ml:id xml:space="preserve">VI</ml:id>
            <ml:id xml:space="preserve">i</ml:id>
          </ml:apply>
          <ml:apply>
            <ml:mult style="default" />
            <ml:id xml:space="preserve">u</ml:id>
            <ml:parens>
              <ml:apply>
                <ml:mult style="default" />
                <ml:apply>
                  <ml:id xml:space="preserve">hist</ml:id>
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                    <ml:id xml:space="preserve">M</ml:id>
                    <ml:apply>
                      <ml:mult style="default" />
                      <ml:id xml:space="preserve">a</ml:id>
                      <ml:id xml:space="preserve">i</ml:id>
                    </ml:apply>
                  </ml:sequence>
                </ml:apply>
                <ml:id xml:space="preserve">V</ml:id>
              </ml:apply>
            </ml:parens>
          </ml:apply>
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      </math>
      <rendering item-idref="34" />
    </region>
    <region region-id="1641" left="6" top="1506.75" width="289.5" height="71.25" align-x="6" align-y="1518" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">The <b>H</b>, <b>S</b>, and <b>V</b> matrices are recombined for viewing. To turn the stripes into plaid, we average each matrix with its transpose. To generate a new random stripe pattern and the associated plaid, click in the definition of <f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">K</inlineAttr></f> below and then press <b>[F9]</b> to recalculate.</p>
      </text>
    </region>
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      <pageBreak />
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    <region region-id="1669" left="12" top="1602" width="129" height="157.5" align-x="75.75" align-y="1602" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <component hide-arguments="false" clsid-buddy="8442da2d-08d7-45ad-a4a6-f28bee6ae06a" item-idref="35" disable-calc="false">
        <inputs>
          <ml:apply>
            <ml:id xml:space="preserve">augment3</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">HI</ml:id>
              <ml:id xml:space="preserve">SI</ml:id>
              <ml:id xml:space="preserve">VI</ml:id>
            </ml:sequence>
          </ml:apply>
        </inputs>
        <outputs />
      </component>
      <rendering item-idref="36" />
    </region>
    <region region-id="1670" left="174" top="1602" width="209.25" height="181.5" align-x="237.75" align-y="1602" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <component hide-arguments="false" clsid-buddy="8442da2d-08d7-45ad-a4a6-f28bee6ae06a" item-idref="37" disable-calc="false">
        <inputs>
          <ml:apply>
            <ml:id xml:space="preserve">augment3</ml:id>
            <ml:sequence>
              <ml:apply>
                <ml:div />
                <ml:apply>
                  <ml:plus />
                  <ml:id xml:space="preserve">HI</ml:id>
                  <ml:apply>
                    <ml:transpose />
                    <ml:id xml:space="preserve">HI</ml:id>
                  </ml:apply>
                </ml:apply>
                <ml:real>2</ml:real>
              </ml:apply>
              <ml:apply>
                <ml:div />
                <ml:apply>
                  <ml:plus />
                  <ml:id xml:space="preserve">SI</ml:id>
                  <ml:apply>
                    <ml:transpose />
                    <ml:id xml:space="preserve">SI</ml:id>
                  </ml:apply>
                </ml:apply>
                <ml:real>2</ml:real>
              </ml:apply>
              <ml:apply>
                <ml:div />
                <ml:apply>
                  <ml:plus />
                  <ml:id xml:space="preserve">VI</ml:id>
                  <ml:apply>
                    <ml:transpose />
                    <ml:id xml:space="preserve">VI</ml:id>
                  </ml:apply>
                </ml:apply>
                <ml:real>2</ml:real>
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