Cleaning out my disk

M

Magnus Henriksson

Hi all,

While getting ready to get rid of an old computer of mine, I came across
this transform that I wrote a few years ago (around 2002 I think). I did
it just to prove that it could be done, so the more mathematically
inclined will no doubt find better ways to do this.

I thought some of you might get a kick out of it.

Do this:

1) Run it trough your favorite XSLT 1.0 processor, output to file. I
recommend a really fast processor, such as SAXON. The transform does not
depend on any input source, so you can use whatever you have lying
around. Wait for it...

2) Open the result in a browser. Wait for it...


Here is the transform:

-- begin mandel.xsl --

<?xml version="1.0" encoding="utf-8"?>

<xsl:stylesheet version="1.0"
xmlns:xsl="http://www.w3.org/1999/XSL/Transform">

<xsl:eek:utput method="html"
indent="yes"
encoding="iso-8859-1"/>

<!-- The area to calculate -->
<xsl:param name="minX" select="-2"/>
<xsl:param name="maxX" select="1.25"/>
<xsl:param name="minY" select="-1.25"/>
<xsl:param name="maxY" select="1.75"/>

<!-- Maximum number of iterations -->
<xsl:param name="maxIterations" select="100"/>

<!-- Cell size -->
<xsl:param name="cellSize" select="1"/>

<!-- Number of rows -->
<xsl:param name="rowsMax" select="300"/>

<xsl:variable name="dy" select="($maxY - $minY) div $rowsMax"/>
<xsl:variable name="cellsMax" select="($maxX - $minX) div $dy"/>
<xsl:variable name="dx" select="($maxX - $minX) div $cellsMax"/>

<xsl:template match="/">
<html>
<head>
<title>XSLT Mandelbrot Set</title>
</head>
<body>
<table cellspacing="0"
cellpadding="0"
border="0"
bgcolor="black">
<xsl:call-template name="Rows"/>
</table>
</body>
</html>
</xsl:template>

<xsl:template name="Rows">
<xsl:param name="rowNumber" select="0"/>
<xsl:if test="$rowNumber &lt; $rowsMax">
<xsl:message>
<xsl:value-of select="concat('Row ', $rowNumber + 1, ' of ',
$rowsMax)"/>
</xsl:message>
<tr>
<xsl:call-template name="Cells">
<xsl:with-param name="rowNumber" select="$rowNumber"/>
</xsl:call-template>
</tr>
<xsl:call-template name="Rows">
<xsl:with-param name="rowNumber" select="$rowNumber + 1"/>
</xsl:call-template>
</xsl:if>
</xsl:template>

<xsl:template name="Cells">
<xsl:param name="cellNumber" select="0"/>
<xsl:param name="rowNumber"/>
<xsl:if test="$cellNumber &lt; $cellsMax">
<td width="{$cellSize}" height="{$cellSize}">
<xsl:call-template name="CellColor">
<xsl:with-param name="cx" select="$minX + ($cellNumber * $dx)"/>
<xsl:with-param name="cy" select="$minY + ($rowNumber * $dy)"/>
</xsl:call-template>
</td>
<xsl:call-template name="Cells">
<xsl:with-param name="cellNumber" select="$cellNumber + 1"/>
<xsl:with-param name="rowNumber" select="$rowNumber"/>
</xsl:call-template>
</xsl:if>
</xsl:template>

<xsl:template name="CellColor">
<xsl:param name="iteration" select="0"/>
<xsl:param name="cx"/>
<xsl:param name="cy"/>
<xsl:param name="a0" select="0"/>
<xsl:param name="b0" select="0"/>
<xsl:variable name="a1" select="($a0 * $a0) - ($b0 * $b0) + $cx"/>
<xsl:variable name="b1" select="2 * ($a0 * $b0) + $cy"/>
<xsl:variable name="zLength" select="($a1 * $a1) + ($b1 * $b1)"/>
<xsl:if test="$zLength &gt; 4">
<xsl:variable name="color">
<xsl:call-template name="Dec2Hex">
<xsl:with-param name="dec" select="round((16777215 div
$maxIterations) * $iteration)"/>
</xsl:call-template>
</xsl:variable>
<xsl:variable name="padding"
select="6 - string-length($color)"/>
<xsl:variable name="paddedColor"
select="concat(substring('000000',1,$padding), $color)"/>
<xsl:attribute name="bgcolor">
<xsl:value-of select="concat('#',$paddedColor)"/>
</xsl:attribute>
</xsl:if>
<xsl:if test="$iteration &lt; $maxIterations and $zLength &lt;= 4">
<xsl:call-template name="CellColor">
<xsl:with-param name="iteration" select="$iteration + 1"/>
<xsl:with-param name="cx" select="$cx"/>
<xsl:with-param name="cy" select="$cy"/>
<xsl:with-param name="a0" select="$a1"/>
<xsl:with-param name="b0" select="$b1"/>
</xsl:call-template>
</xsl:if>
</xsl:template>

<xsl:template name="Dec2Hex">
<xsl:param name="dec" select="0"/>
<xsl:variable name="div" select="floor($dec div 16)"/>
<xsl:variable name="rem" select="$dec - ($div * 16)"/>
<xsl:choose>
<xsl:when test="$dec = 0">0</xsl:when>
<xsl:when test="$dec = 1">1</xsl:when>
<xsl:when test="$dec = 2">2</xsl:when>
<xsl:when test="$dec = 3">3</xsl:when>
<xsl:when test="$dec = 4">4</xsl:when>
<xsl:when test="$dec = 5">5</xsl:when>
<xsl:when test="$dec = 6">6</xsl:when>
<xsl:when test="$dec = 7">7</xsl:when>
<xsl:when test="$dec = 8">8</xsl:when>
<xsl:when test="$dec = 9">9</xsl:when>
<xsl:when test="$dec = 10">A</xsl:when>
<xsl:when test="$dec = 11">B</xsl:when>
<xsl:when test="$dec = 12">C</xsl:when>
<xsl:when test="$dec = 13">D</xsl:when>
<xsl:when test="$dec = 14">E</xsl:when>
<xsl:when test="$dec = 15">F</xsl:when>
<xsl:eek:therwise>
<xsl:call-template name="Dec2Hex">
<xsl:with-param name="dec" select="$div"/>
</xsl:call-template>
</xsl:eek:therwise>
</xsl:choose>
<xsl:if test="$div">
<xsl:call-template name="Dec2Hex">
<xsl:with-param name="dec" select="$rem"/>
</xsl:call-template>
</xsl:if>
</xsl:template>

</xsl:stylesheet>

-- end mandel.xsl --

Other mildly interesting values of the parameters are:

minX = 0.2
maxX = 0.4
minY = 0.5
maxY = 0.7

and

minX = 0.3
maxX = 0.4
minY = 0.5
maxY = 0.6

and

minX = 0.32
maxX = 0.35
minY = 0.52
maxY = 0.55

The smaller the area, the longer it will take. For really small areas it
seems like the processor gets stuck.


// Magnus
 
J

Joseph Kesselman

And I thought merely solving the eight-queens problem in XSLT was a
terrifying concept... <grin/>

Are you willing to officially put that into the public domain so we can
pass it around?
 
M

Magnus Henriksson

Joseph said:
And I thought merely solving the eight-queens problem in XSLT was a
terrifying concept... <grin/>

Are you willing to officially put that into the public domain so we can
pass it around?
Click to expand...

I hereby abandon any property rights to the XSLT code in message
[email protected].

// Magnus
 
R

roy axenov

Magnus Henriksson wrote:

[XSLT Mandelbrot Set Explorer]
I thought some of you might get a kick out of it.
Click to expand...

I sure did.
1) Run it trough your favorite XSLT 1.0 processor, output
to file. I recommend a really fast processor, such as
SAXON.
Click to expand...

libxslt-based PHP5 module worked well enough for me. (And I
didn't even have to juggle the files around - my web-based
toolkit handles that for me and displays the transformation
result in an iframe.)

I guess this post is a bit pointless, but I just wanted to
say that this is wonderful stuff. Hats off.
 

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