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<a name="Definitions-for-complex-fractals"></a>
<div class="header">
<p>
Next: <a href="maxima_275.html#Definitions-for-Koch-snowflakes" accesskey="n" rel="next">Definitions for Koch snowflakes</a>, Previous: <a href="maxima_273.html#Definitions-for-IFS-fractals" accesskey="p" rel="previous">Definitions for IFS fractals</a>, Up: <a href="maxima_toc.html#Top" accesskey="u" rel="up">Top</a> [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_423.html#Function-and-Variable-Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Definitions-for-complex-fractals-1"></a>
<h3 class="section">60.3 Definitions for complex fractals</h3>
<a name="mandelbrot_005fset"></a><a name="Item_003a-fractals_002fdeffn_002fmandelbrot_005fset"></a><dl>
<dt><a name="index-mandelbrot_005fset"></a>Function: <strong>mandelbrot_set</strong> <em>(<var>x</var>, <var>y</var>)</em></dt>
<dd>
<p>Mandelbrot set.
</p>
<p>Example:
</p>
<p>This program is time consuming because it must make a lot of operations;
the computing time is also related with the number of grid points.
</p>
<div class="example">
<pre class="example">(%i1) load("fractals")$
(%i2) plot3d (mandelbrot_set, [x, -2.5, 1], [y, -1.5, 1.5],
[gnuplot_preamble, "set view map"],
[gnuplot_pm3d, true],
[grid, 150, 150])$
</pre></div>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Package-fractals">Package fractals</a>
·</div>
</dd></dl>
<a name="julia_005fset"></a><a name="Item_003a-fractals_002fdeffn_002fjulia_005fset"></a><dl>
<dt><a name="index-julia_005fset"></a>Function: <strong>julia_set</strong> <em>(<var>x</var>, <var>y</var>)</em></dt>
<dd>
<p>Julia sets.
</p>
<p>This program is time consuming because it must make a lot of operations;
the computing time is also related with the number of grid points.
</p>
<p>Example:
</p>
<div class="example">
<pre class="example">(%i1) load("fractals")$
(%i2) plot3d (julia_set, [x, -2, 1], [y, -1.5, 1.5],
[gnuplot_preamble, "set view map"],
[gnuplot_pm3d, true],
[grid, 150, 150])$
</pre></div>
<p>See also <code><a href="#julia_005fparameter">julia_parameter</a></code>.
</p>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Package-fractals">Package fractals</a>
·</div>
</dd></dl>
<a name="julia_005fparameter"></a><a name="Item_003a-fractals_002fdefvr_002fjulia_005fparameter"></a><dl>
<dt><a name="index-julia_005fparameter"></a>Optional variable: <strong>julia_parameter</strong></dt>
<dd><p>Default value: <code><a href="maxima_18.html#g_t_0025i">%i</a></code>
</p>
<p>Complex parameter for Julia fractals.
Its default value is <code><a href="maxima_18.html#g_t_0025i">%i</a></code>; we suggest the values <code>-.745+%i*.113002</code>,
<code>-.39054-%i*.58679</code>, <code>-.15652+%i*1.03225</code>, <code>-.194+%i*.6557</code> and
<code>.011031-%i*.67037</code>.
</p>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Package-fractals">Package fractals</a>
·</div>
</dd></dl>
<a name="julia_005fsin"></a><a name="Item_003a-fractals_002fdeffn_002fjulia_005fsin"></a><dl>
<dt><a name="index-julia_005fsin"></a>Function: <strong>julia_sin</strong> <em>(<var>x</var>, <var>y</var>)</em></dt>
<dd>
<p>While function <code>julia_set</code> implements the transformation <code>julia_parameter+z^2</code>,
function <code>julia_sin</code> implements <code>julia_parameter*sin(z)</code>. See source code
for more details.
</p>
<p>This program runs slowly because it calculates a lot of sines.
</p>
<p>Example:
</p>
<p>This program is time consuming because it must make a lot of operations;
the computing time is also related with the number of grid points.
</p>
<div class="example">
<pre class="example">(%i1) load("fractals")$
(%i2) julia_parameter:1+.1*%i$
(%i3) plot3d (julia_sin, [x, -2, 2], [y, -3, 3],
[gnuplot_preamble, "set view map"],
[gnuplot_pm3d, true],
[grid, 150, 150])$
</pre></div>
<p>See also <code><a href="#julia_005fparameter">julia_parameter</a></code>.
</p>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Package-fractals">Package fractals</a>
·</div>
</dd></dl>
<a name="Item_003a-fractals_002fnode_002fDefinitions-for-Koch-snowflakes"></a><hr>
<div class="header">
<p>
Next: <a href="maxima_275.html#Definitions-for-Koch-snowflakes" accesskey="n" rel="next">Definitions for Koch snowflakes</a>, Previous: <a href="maxima_273.html#Definitions-for-IFS-fractals" accesskey="p" rel="previous">Definitions for IFS fractals</a>, Up: <a href="maxima_toc.html#Top" accesskey="u" rel="up">Top</a> [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_423.html#Function-and-Variable-Index" title="Index" rel="index">Index</a>]</p>
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