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	<title>Complex Dynamics &#187; noneuclidean</title>
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	<description>what&#039;s next</description>
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		<title>Visualizing hyperbolic symmetries using WebGL (aka a hyperbolic doodler in your browser)</title>
		<link>http://www.brainjam.ca/wp/2011/02/visualizing-hyperbolic-symmetries-using-webgl/</link>
		<comments>http://www.brainjam.ca/wp/2011/02/visualizing-hyperbolic-symmetries-using-webgl/#comments</comments>
		<pubDate>Sat, 19 Feb 2011 19:59:21 +0000</pubDate>
		<dc:creator>admin</dc:creator>
				<category><![CDATA[Uncategorized]]></category>
		<category><![CDATA[noneuclidean]]></category>
		<category><![CDATA[WebGL]]></category>

		<guid isPermaLink="false">http://www.brainjam.ca/wp/?p=192</guid>
		<description><![CDATA[I&#8217;ve long been fascinated by non-Euclidean tessellations and symmetries. The most widely known examples of these are the circle limit images by M.C. Escher.  I&#8217;ve always wanted to create an interactive way of producing these images, and with the advent &#8230; <a href="http://www.brainjam.ca/wp/2011/02/visualizing-hyperbolic-symmetries-using-webgl/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p>I&#8217;ve long been fascinated by <a href="http://www.brainjam.ca/tessellations.htm">non-Euclidean tessellations and symmetries.</a> The most widely known examples of these are the <a href="http://euler.slu.edu/escher/index.php/Escher's_Circle_Limit_Exploration">circle limit images by M.C. Escher</a>.  I&#8217;ve always wanted to create an interactive way of producing these images, and with the advent of <a href="http://en.wikipedia.org/wiki/WebGL">WebGL</a> I&#8217;ve made some preliminary steps to doing this in the browser.</p>
<p>To see what I&#8217;ve done, you need a <a href="http://www.khronos.org/webgl/wiki/Getting_a_WebGL_Implementation">WebGL-capable browser</a>.  Hopefully it will work for you, but your platform may not be capable of supporting WebGL. (There are some more setup and troubleshooting tips at the <a href="http://learningwebgl.com/blog/?p=11">Learning WebGL website</a>.)</p>
<p>The current experiments are a <a href="http://www.brainjam.ca/circlelimit/hyperbolicdoodler.htm">hyperbolic doodler</a> and a <a href="http://www.brainjam.ca/circlelimit/kaleidoscope.htm">hyperbolic kaleidoscope</a>.  In the scheme of things, they are just minor variations of one another.  In both cases, things happen when you drag the mouse across the disk (dragging slower is better, at least until you get the hang of what&#8217;s going on).  In the doodler, you get a trail of white dots which is reflected across hyperbolic lines to get an infinite symmetry going all the way to the border of the disk.  The occasional colored shape is thrown in for a splash of color.  In the kaleidoscope, you get the same trail of dots, and more frequent colored shapes, along with a movement effect.  The impression you get is of throwing confetti into a hyperbolic mirrored chamber.</p>
<p>These are preliminary experiments.  I hope to do a lot more to increase control and expressiveness (and to let you save your work), but the project is on a bit of hiatus as I do a paying gig.  So I&#8217;ve posted this in the interim.</p>
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		<title>SeaDragon &#8211; Microsoft does something right</title>
		<link>http://www.brainjam.ca/wp/2010/01/seadragon-microsoft-does-something-right/</link>
		<comments>http://www.brainjam.ca/wp/2010/01/seadragon-microsoft-does-something-right/#comments</comments>
		<pubDate>Mon, 11 Jan 2010 18:06:18 +0000</pubDate>
		<dc:creator>admin</dc:creator>
				<category><![CDATA[Uncategorized]]></category>
		<category><![CDATA[math]]></category>
		<category><![CDATA[noneuclidean]]></category>
		<category><![CDATA[tessellations]]></category>

		<guid isPermaLink="false">http://www.brainjam.ca/wp/?p=88</guid>
		<description><![CDATA[In the past year, I&#8217;ve experimented with different ways to visualize non-Euclidean tessellations.  Mainly, I&#8217;ve made movies with simple zooms or animations. But sometimes I think I want something more interactive, so that viewers can explore tessellations as they wish, &#8230; <a href="http://www.brainjam.ca/wp/2010/01/seadragon-microsoft-does-something-right/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p>In the past year, I&#8217;ve experimented with different ways to visualize non-Euclidean tessellations.  Mainly, I&#8217;ve made movies with simple zooms or animations. But sometimes I think I want something more interactive, so that viewers can explore tessellations as they wish, as opposed to watching them fly by.</p>
<p>Last year, I dabbled with creating some ways of interactively zooming into images using the browser.  Here are some examples, <a href="http://www.brainjam.ca/noneuclidean/slideshow/slideshow.htm">one using Javascript</a>, and <a href="http://www.brainjam.ca/noneuclidean/tile8.13/map.htm">another using Google Maps</a>.  The first one was kind of a Javascript learning project for me, as was the second.  Both suffer from latency problems.</p>
<p>Then I discovered Seadragon.com, a Microsoft site for creating and hosting zoomable images.  Seadragon technology comes in various flavors, including one that uses pure Javascript, and another that uses Silverlight.  The functionality is similar to the zooming functionality of Google Maps, but has a nicer feel.  An example, using one of my images, can be found at <a href="http://seadragon.com/view/4bj">http://seadragon.com/view/4bj</a>, or seen below.</p>
<p><script src="http://seadragon.com/embed/4bj.js?width=auto&#038;height=400px"></script></p>
<p>Note that there are controls for zooming in and out, and for using the full browser window.  You pan by clicking and dragging on the image.  The controls have a nice springy physics to them, and interactivity feels like real time.  And even though you may not be able to exactly contr0l the zoom levels as finely as you like, the zoom transitions are continuous.  The original image was  24000 x 13500 (324 megapixels) </p>
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