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		<title>A New Algorithm for Rendering Kissing Schottky Groups - Versionsgeschichte</title>
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		<id>http://de.evo-art.org/index.php?title=A_New_Algorithm_for_Rendering_Kissing_Schottky_Groups&amp;diff=33156&amp;oldid=prev</id>
		<title>Gubachelier: /* Bibtex */</title>
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				<updated>2016-12-27T19:45:11Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Bibtex&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;col class=&#039;diff-content&#039; /&gt;
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				&lt;td colspan=&#039;2&#039; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Nächstältere Version&lt;/td&gt;
				&lt;td colspan=&#039;2&#039; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Version vom 27. Dezember 2016, 19:45 Uhr&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l24&quot; &gt;Zeile 24:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Zeile 24:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&amp;#160; publisher&amp;#160;  = {Tessellations Publishing},&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&amp;#160; publisher&amp;#160;  = {Tessellations Publishing},&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&amp;#160; address&amp;#160; &amp;#160;  = {Phoenix, Arizona},&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&amp;#160; address&amp;#160; &amp;#160;  = {Phoenix, Arizona},&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&amp;#160; url&amp;#160; &amp;#160; &amp;#160; &amp;#160;  = {http://de.evo-art.org/index.php?title=A_New_Algorithm_for_Rendering_Kissing_Schottky_Groups},&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&amp;#160; url&amp;#160; &amp;#160; &amp;#160; &amp;#160;  = {http://de.evo-art.org/index.php?title=A_New_Algorithm_for_Rendering_Kissing_Schottky_Groups },&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&amp;#160; note&amp;#160; &amp;#160; &amp;#160; &amp;#160; = {Available online at \url{http://archive.bridgesmathart.org/2016/bridges2016-367.html}}&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&amp;#160; note&amp;#160; &amp;#160; &amp;#160; &amp;#160; = {Available online at \url{http://archive.bridgesmathart.org/2016/bridges2016-367.html}}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160; }&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160; }&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Used References ==&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Used References ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Gubachelier</name></author>	</entry>

	<entry>
		<id>http://de.evo-art.org/index.php?title=A_New_Algorithm_for_Rendering_Kissing_Schottky_Groups&amp;diff=33106&amp;oldid=prev</id>
		<title>Gubachelier: Die Seite wurde neu angelegt: „ == Reference == Kento Nakamura and Kazushi Ahara: A New Algorithm for Rendering Kissing Schottky Groups. In: Bridges 2016, Pages 367–370.   == DOI =…“</title>
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				<updated>2016-12-27T09:44:19Z</updated>
		
		<summary type="html">&lt;p&gt;Die Seite wurde neu angelegt: „ == Reference == Kento Nakamura and Kazushi Ahara: &lt;a href=&quot;/index.php?title=A_New_Algorithm_for_Rendering_Kissing_Schottky_Groups&quot; title=&quot;A New Algorithm for Rendering Kissing Schottky Groups&quot;&gt;A New Algorithm for Rendering Kissing Schottky Groups&lt;/a&gt;. In: &lt;a href=&quot;/index.php?title=Bridges_2016&quot; title=&quot;Bridges 2016&quot;&gt;Bridges 2016&lt;/a&gt;, Pages 367–370.   == DOI =…“&lt;/p&gt;
&lt;p&gt;&lt;b&gt;Neue Seite&lt;/b&gt;&lt;/p&gt;&lt;div&gt;&lt;br /&gt;
== Reference ==&lt;br /&gt;
Kento Nakamura and Kazushi Ahara: [[A New Algorithm for Rendering Kissing Schottky Groups]]. In: [[Bridges 2016]], Pages 367–370. &lt;br /&gt;
&lt;br /&gt;
== DOI ==&lt;br /&gt;
&lt;br /&gt;
== Abstract ==&lt;br /&gt;
In this paper, we present an algorithm for drawing images of Schottky groups. This algorithm is called an Iterated&lt;br /&gt;
Inversion System (IIS). It is easy to parallelize and renders images fast. It can be used to render 2-dimensional kissing&lt;br /&gt;
Schottky groups and also 3-dimensional kissing Schottky groups.&lt;br /&gt;
&lt;br /&gt;
== Extended Abstract ==&lt;br /&gt;
&lt;br /&gt;
== Bibtex == &lt;br /&gt;
 @inproceedings{bridges2016:367,&lt;br /&gt;
  author      = {Kento Nakamura and Kazushi Ahara},&lt;br /&gt;
  title       = {A New Algorithm for Rendering Kissing Schottky Groups},&lt;br /&gt;
  pages       = {367--370},&lt;br /&gt;
  booktitle   = {Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture},&lt;br /&gt;
  year        = {2016},&lt;br /&gt;
  editor      = {Eve Torrence, Bruce Torrence, Carlo S\&amp;#039;equin, Douglas McKenna, Krist\&amp;#039;of Fenyvesi and Reza Sarhangi},&lt;br /&gt;
  isbn        = {978-1-938664-19-9},&lt;br /&gt;
  issn        = {1099-6702},&lt;br /&gt;
  publisher   = {Tessellations Publishing},&lt;br /&gt;
  address     = {Phoenix, Arizona},&lt;br /&gt;
  url         = {http://de.evo-art.org/index.php?title=A_New_Algorithm_for_Rendering_Kissing_Schottky_Groups},&lt;br /&gt;
  note        = {Available online at \url{http://archive.bridgesmathart.org/2016/bridges2016-367.html}}&lt;br /&gt;
 }&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Used References ==&lt;br /&gt;
[1] David Mumford, Caroline Series, David Wright, Indra’s Pearls (2002), Cambridge University Press.&lt;br /&gt;
&lt;br /&gt;
[2] Kazushi Ahara, Yoshiaki Araki, Sphairahedral Approach to Parameterize Visible Three Dimensional&lt;br /&gt;
Quasi-Fuchsian Fractals (2003), http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?&lt;br /&gt;
tp=&amp;amp;arnumber=1214471&amp;amp;isnumber=27295, IEEE Computer Graphics International&lt;br /&gt;
&lt;br /&gt;
[3] Knighty, Another 3D Kleinian,&lt;br /&gt;
http://www.fractalforums.com/ifs-iterated-function-systems/&lt;br /&gt;
another-3d-kleinian/ (as of Jan. 10 2016)&lt;br /&gt;
&lt;br /&gt;
[4] Mikael H Christensen, Distance Estimated 3D Fractals (Part I), http://blog.hvidtfeldts.net/&lt;br /&gt;
index.php/2011/06/distance-estimated-3d-fractals-part-i/ (as of Jan. 10 2016)&lt;br /&gt;
&lt;br /&gt;
[5] Kento Nakamura as soma arc, Indra’s Bubbles&lt;br /&gt;
https://www.shadertoy.com/view/XsGGWG (as of March 4 2016)&lt;br /&gt;
&lt;br /&gt;
[6] Kento Nakamura as soma-arc, Iterated Inversion System in GitHub,&lt;br /&gt;
https://github.com/soma-arc/IteratedInversionSystem (as of March 4 2016)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Links ==&lt;br /&gt;
=== Full Text === &lt;br /&gt;
http://archive.bridgesmathart.org/2016/bridges2016-367.pdf&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[intern file]]&lt;br /&gt;
&lt;br /&gt;
=== Sonstige Links ===&lt;br /&gt;
http://archive.bridgesmathart.org/2016/bridges2016-367.html&lt;/div&gt;</summary>
		<author><name>Gubachelier</name></author>	</entry>

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