mandel.html
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<div align="center"><font size="3"><b><font color="#FFFFFF">Applet
Tutorials: Mandelbrot</font></b></font></div>
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<td><b><font size="3" color="#FFFFFF">Mandelbrot Applet</font></b></td>
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<td><center><img src="images/mandel1.jpg" width="130" height="131"></center></td>
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<p>This applet visualises the Mandelbrot set onto a complex
plane. </p>
<p><b>[Def. Mandelbrot set]</b></p>
<p>The Mandelbrot set <b>M</b> consists of all of those
(complex) <b>c</b>-values for which the corresponding
orbit of <b>0</b> under <b>z^2 + c</b> does not escape
to infinity.</p>
<p>Although it is not possible to determine if certain
<b>c</b>-values lies in the Mandelbrot set, as the number
of iteration increases (to infinite), the closer boundary
of <b>M</b> can be plotted.</p>
<p><font size="3">[For more <a href="../Applet/mandel2/mandel.txt">technical
information</a> about the available parameters, click
<a href="../Applet/mandel2/mandel.txt">here</a>.]</font></p>
<hr width="90%">
<p><font size="3">Most parameters are self-explanatory
and you can always see brief description of each parameter
by moving the mouse pointer over the wizard. </font></p>
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<td width="46%"><img src="images/mandel2.gif" width="156" height="130"></td>
<td width="54%"><font size="3">First of all, define
the "<b>Width</b>" and "<b>Height</b>"
of the applet area and select a value for "<b>Resolution</b>."
Resolution is the magnification rate of the internal
image size. </font> </td>
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<p><font size="3">For example, the value 3 gives
three times as big image size as the internal
image has. So, it works as a zooming parameter.</font>
</p>
<p><font size="3">As for colouring of the boundary
of <b>M</b>, 27 palettes are available. Choose
a palette number and explore the result.</font></p>
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<td width="47%"><img src="images/mandel3.gif" width="159" height="216"></td>
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<p><font size="3">Look at the bottom of the left
picture. Determine "<b>StartX</b>" and
"<b>StartY</b>" values. These are the
initial values with which recursive calculation
of <b>z(n+1)=z(n)^2 + c</b> (z=x+yi) begins. </font></p>
<p><font size="3"><b>Xmin</b> and <b>Ymax</b> determine
normal XY complex plane scrolling values, while
<b>Xmax</b> and <b>Y min</b> give XY magnification
rate.</font></p>
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<p><font size="3">We have only discussed about the Mandelbrot
specific parameters. For generic parameters, please
read <a href="wizard.html">wizard</a> section.</font></p>
<p><font size="3">Proceed to<a href="wizard.html#4"> </a>
<a href="wizard.html#5">the expert menu</a>.</font></p>
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