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<a name="Definitions-for-IFS-fractals"></a>
<div class="header">
<p>
Next: <a href="maxima_274.html#Definitions-for-complex-fractals" accesskey="n" rel="next">Definitions for complex fractals</a>, Previous: <a href="maxima_272.html#Introduction-to-fractals" accesskey="p" rel="previous">Introduction to fractals</a>, Up: <a href="maxima_271.html#fractals_002dpkg" accesskey="u" rel="up">fractals-pkg</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-IFS-fractals-1"></a>
<h3 class="section">60.2 Definitions for IFS fractals</h3>
<p>Some fractals can be generated by iterative applications
of contractive affine transformations in a random way; see
</p>
<p>Hoggar S. G., "Mathematics for computer graphics", Cambridge University
Press 1994.
</p>
<p>We define a list with several contractive affine transformations,
and we randomly select the transformation in a recursive way.
The probability of the choice of a transformation must be related
with the contraction ratio.
</p>
<p>You can change the transformations and find another fractal
</p>
<a name="sierpinskiale"></a><a name="Item_003a-fractals_002fdeffn_002fsierpinskiale"></a><dl>
<dt><a name="index-sierpinskiale"></a>Function: <strong>sierpinskiale</strong> <em>(<var>n</var>)</em></dt>
<dd>
<p>Sierpinski Triangle: 3 contractive maps; .5 contraction constant and translations;
all maps have the same contraction ratio. Argument <var>n</var> must be great enough, 10000 or greater.
</p>
<p>Example:
</p>
<div class="example">
<pre class="example">(%i1) load("fractals")$
(%i2) n: 10000$
(%i3) plot2d([discrete,sierpinskiale(n)], [style,dots])$
</pre></div>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Package-fractals">Package fractals</a>
·</div>
</dd></dl>
<a name="treefale"></a><a name="Item_003a-fractals_002fdeffn_002ftreefale"></a><dl>
<dt><a name="index-treefale"></a>Function: <strong>treefale</strong> <em>(<var>n</var>)</em></dt>
<dd>
<p>3 contractive maps all with the same contraction ratio.
Argument <var>n</var> must be great enough, 10000 or greater.
</p>
<p>Example:
</p>
<div class="example">
<pre class="example">(%i1) load("fractals")$
(%i2) n: 10000$
(%i3) plot2d([discrete,treefale(n)], [style,dots])$
</pre></div>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Package-fractals">Package fractals</a>
·</div>
</dd></dl>
<a name="fernfale"></a><a name="Item_003a-fractals_002fdeffn_002ffernfale"></a><dl>
<dt><a name="index-fernfale"></a>Function: <strong>fernfale</strong> <em>(<var>n</var>)</em></dt>
<dd>
<p>4 contractive maps, the probability to choice a transformation must be related
with the contraction ratio. Argument <var>n</var> must be great enough, 10000 or greater.
</p>
<p>Example:
</p>
<div class="example">
<pre class="example">(%i1) load("fractals")$
(%i2) n: 10000$
(%i3) plot2d([discrete,fernfale(n)], [style,dots])$
</pre></div>
<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-complex-fractals"></a><hr>
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<p>
Next: <a href="maxima_274.html#Definitions-for-complex-fractals" accesskey="n" rel="next">Definitions for complex fractals</a>, Previous: <a href="maxima_272.html#Introduction-to-fractals" accesskey="p" rel="previous">Introduction to fractals</a>, Up: <a href="maxima_271.html#fractals_002dpkg" accesskey="u" rel="up">fractals-pkg</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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