<?xml version="1.0" encoding="UTF-8"?>
<rss version="2.0"
	xmlns:content="http://purl.org/rss/1.0/modules/content/"
	xmlns:wfw="http://wellformedweb.org/CommentAPI/"
	xmlns:dc="http://purl.org/dc/elements/1.1/"
	xmlns:atom="http://www.w3.org/2005/Atom"
	xmlns:sy="http://purl.org/rss/1.0/modules/syndication/"
	xmlns:slash="http://purl.org/rss/1.0/modules/slash/"
	>

<channel>
	<title>odd number</title>
	<atom:link href="http://www.oddnumber.co.uk/feed/" rel="self" type="application/rss+xml" />
	<link>http://www.oddnumber.co.uk</link>
	<description>Christopher Henden - constructions, words</description>
	<lastBuildDate>Sun, 09 Oct 2011 11:01:22 +0000</lastBuildDate>
	<language>en</language>
	<sy:updatePeriod>hourly</sy:updatePeriod>
	<sy:updateFrequency>1</sy:updateFrequency>
	<generator>http://wordpress.org/?v=3.0</generator>
		<item>
		<title>Things I saw at Tate Britain yesterday</title>
		<link>http://www.oddnumber.co.uk/2011/10/09/things-i-saw-at-tate-britain-yesterday/</link>
		<comments>http://www.oddnumber.co.uk/2011/10/09/things-i-saw-at-tate-britain-yesterday/#comments</comments>
		<pubDate>Sun, 09 Oct 2011 11:01:22 +0000</pubDate>
		<dc:creator>admin</dc:creator>
				<category><![CDATA[geographical]]></category>
		<category><![CDATA[painting]]></category>

		<guid isPermaLink="false">http://www.oddnumber.co.uk/?p=1933</guid>
		<description><![CDATA[John Martin &#8211; attempts at huge, Biblical scale become a distraction from the architectural fantasies being destroyed in passing. One of his most peaceful paintings is of the city of Babylon being destroyed by the Persians. But they have only &#8230; <a href="http://www.oddnumber.co.uk/2011/10/09/things-i-saw-at-tate-britain-yesterday/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p><a href="http://blog.tate.org.uk/?p=8052">John Martin</a> &#8211; attempts at huge, Biblical scale become a distraction from the architectural fantasies being destroyed in passing. One of his most peaceful paintings is of the city of Babylon being destroyed by the Persians. But they have only just arrived. What really absorbs is the invented architectures, stretching as far as the eye can see. The  invaders arriving on their boats have a job on their hands.</p>
<p>His maps of planned sewage and circular underground railways show a desire to wreak the same transformation on his physical landscape. A different sense of scale, and of genuinely apocalyptic change, arises from seeing Wood Lane and Porto Bello farms on the maps, linked to urban territory by lanes across fields.</p>
<p>Round the corner, one of Paul Noble&#8217;s pencil drawings matches these paintings both in size and carefully constructed fantasy. The people in John Martin&#8217;s paintings are either there to show jaw-dropping scale, or to be flung around by cataclysmic forces, or to be lonely witnesses as the Last Man Alive. For Paul Noble they are completely absent, <a href="http://www.artnet.com/magazine/reviews/kardon/kardon3-17-2.asp">represented only by ladders to be climbed, or mechanisms to be operated.</a></p>
<p>Lynn Chadwick&#8217;s <a href="http://www.tate.org.uk/servlet/ViewWork?workid=2120&amp;roomid=6642">Dragonfly</a> and neighbouring <a href="http://www.tate.org.uk/servlet/ViewWork?cgroupid=999999961&#038;workid=78613&#038;searchid=9524">stabiles</a> have no references to people. Together with Nuam Gabo&#8217;s plastic sculptures in the next room it&#8217;s possible to see how geometrical and biological constructions can be an end in themselves.</p>
]]></content:encoded>
			<wfw:commentRss>http://www.oddnumber.co.uk/2011/10/09/things-i-saw-at-tate-britain-yesterday/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Islands of Wales</title>
		<link>http://www.oddnumber.co.uk/2011/10/01/islands-of-wales/</link>
		<comments>http://www.oddnumber.co.uk/2011/10/01/islands-of-wales/#comments</comments>
		<pubDate>Sat, 01 Oct 2011 20:46:28 +0000</pubDate>
		<dc:creator>admin</dc:creator>
				<category><![CDATA[geographical]]></category>

		<guid isPermaLink="false">http://www.oddnumber.co.uk/?p=1928</guid>
		<description><![CDATA[Here&#8217;s a list of islands around Wales, pulled from Geonames with some Java jiggery-pokery. The plan is to keep exploring the geography of this list, with inspiration from Judith Schalansky&#8217;s Atlas of Remote Islands. Wikipedia offers a A Companion Guide &#8230; <a href="http://www.oddnumber.co.uk/2011/10/01/islands-of-wales/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p>Here&#8217;s a <a href="http://www.oddnumber.co.uk/islands/list.html">list of islands around Wales</a>, pulled from Geonames with some Java jiggery-pokery.</p>
<p>The plan is to keep exploring the geography of this list, with inspiration from Judith Schalansky&#8217;s <a href="http://www.amazon.co.uk/Atlas-Remote-Islands-Fifty-Visited/dp/1846143489">Atlas of Remote Islands</a>.</p>
<p>Wikipedia offers a <a href="http://en.wikipedia.org/wiki/Book:Atlas_of_Remote_Islands">A Companion Guide to Atlas of Remote Islands</a>, which is an interesting concept in itself. I was constantly looking on Wikipedia when reading through <a href="http://en.wikipedia.org/wiki/Wolf_Hall">Wolf Hall</a>, if only because my knowledge of English history was so poor. A book often seems closely symbiotic to the author&#8217;s diligent research (see <a href="http://www.guardian.co.uk/books/2011/sep/09/anna-funder-writing-editing-fact-checkers">Anna Funder on All That I Am</a>). It makes sense that a book becomes a kind of boat in the rising oceans of data. A Wikipedia book is <a href="http://en.wikipedia.org/wiki/Wikipedia:Books">a collection of Wikipedia articles that can be easily saved, rendered electronically in PDF, ZIM or OpenDocument format, or ordered as a printed book</a>. But the idea of a conventional book being the skeleton of such accumulated, formatted data is something else again.</p>
<p>For example, I would like to take the <a href="http://www.oddnumber.co.uk/2011/09/20/the-scale-of-the-world-2666/">text of 2666</a>, and run it through a <a href="http://edina.ac.uk/projects/geoxwalk/geoparser.html">geoparser</a>, to gain a sense of both the novel&#8217;s sprawl and density. The book then becomes a navigation of meaning through all those points in space.</p>
]]></content:encoded>
			<wfw:commentRss>http://www.oddnumber.co.uk/2011/10/01/islands-of-wales/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>The scale of the world (2666)</title>
		<link>http://www.oddnumber.co.uk/2011/09/20/the-scale-of-the-world-2666/</link>
		<comments>http://www.oddnumber.co.uk/2011/09/20/the-scale-of-the-world-2666/#comments</comments>
		<pubDate>Tue, 20 Sep 2011 17:43:18 +0000</pubDate>
		<dc:creator>admin</dc:creator>
				<category><![CDATA[geographical]]></category>

		<guid isPermaLink="false">http://www.oddnumber.co.uk/?p=1917</guid>
		<description><![CDATA[Some thoughts on Roberto Bolaño&#8217;s novel 2666. Map of Ciudad Juarez cc-by-sa Open Street Map Films and books purposefully shrink the world, connecting continents with the efficiency of budget flights. Thrillers act out tour guides, triggering our holiday memories, interrupting &#8230; <a href="http://www.oddnumber.co.uk/2011/09/20/the-scale-of-the-world-2666/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p>Some thoughts on Roberto Bolaño&#8217;s novel <a href="http://en.wikipedia.org/wiki/2666_(novel)">2666</a>.</p>
<p><a href="http://www.oddnumber.co.uk/wp-content/uploads/2011/09/ciudad-juarez2.png"><img src="http://www.oddnumber.co.uk/wp-content/uploads/2011/09/ciudad-juarez2.png" alt="" title="Ciudad Juarez" width="806" height="284" class="alignnone size-full wp-image-1919" /></a><br />
<small>Map of Ciudad Juarez <a href="http://creativecommons.org/licenses/by-sa/2.0/">cc-by-sa</a> <a href="http://www.openstreetmap.org/?lat=31.7418&#038;lon=-106.495&#038;zoom=14&#038;layers=C">Open Street Map</a></small></p>
<p>Films and books purposefully shrink the world, connecting continents with the efficiency of budget flights. Thrillers act out tour guides, triggering our holiday memories, interrupting the tourists at their cafe tables. Protaganists effortlessly move their havoc from one tourist destination to another, the globe becoming a series of themed computer game levels to quickly conquer. This restricted environment enables novels to be built on an improbable, but familiar foundation of coinciding events and characters. It makes possible the easy encounters and plot twists which make stories work. We consider ourselves sophisticated as we use literary novels to familiar with alien places, moving deeper than a city break can ever take us.</p>
<p>2666 has a similar global reach, spanning two continents. But it does the opposite. The world is returned to its true scale.<br />
<span id="more-1917"></span></p>
<h3>Disappearance</h3>
<p>The long book directly shows how its protagonists can disappear. The first part is based on the mystery of a writer&#8217;s true identity, which is never solved. The upset of the Second World War shows how families are split, people are never seen again. A mother loses all sight of her son, and her brother too. Life becomes a series of fleeting encounters. We use history to merge details of the war into one huge, horrible sequence of events &#8211; but Bolano shows how solders on the Eastern front experienced a wholly different, incommunicable reality to those on the West.</p>
<p>Later we glimpse Archimboldi using the internet to search for old names, &#8220;forgotten occurrences&#8221; &#8211; we don&#8217;t know if he succeeds.</p>
<h3>Anonymity</h3>
<p>The unending, relentless series of murdered women in Santa Theresa manifests as endless lists of names and place names. We can only guiltily scan, ignore, skip, generalise, fusing all into one, reacting with the disinterest of a newspaper reader. It&#8217;s like reading a phone directory &#8211; except that this matters, as it&#8217;s people, who we should care about. The book is a barely concealed documentary, based on real killings in Ciudad Juarez. Perhaps only for a reader in the UK, the sheer unfamiliarity of Latin American names renders them meaningless all the same, easily dismissed and indistinguishable.</p>
<h3>Distance</h3>
<p>A single city is centre stage, but is bewilderingly vast, with murdered girls appearing without a hope of finding a connection. Detectives follow the threads, to find them bewilderingly short. The victims don&#8217;t have long enough stories to form a join &#8211; they are too busy working for the <a href="http://en.wikipedia.org/wiki/Maquiladora">Maquiladoras</a> (low wage factories assembling products to be sent over the border to the USA)</p>
<p>Santa Theresa is ignored in Mexico, let alone the USA, which it almost touches. It is surrounded by desert, or unthinkably vast rubbish dumps, which are mistaken for mountains. Drug lords proceed in cavalcades of expensive cars to their remote ranches, where they orgy uninterrupted.</p>
<p>The American counterpart of the city is rarely mentioned, except as the border which attracts hopeful migrants. When a visitor from the other half disappears, the Sheriff is determined to find out what happened. He makes progress, doggedly following a lead to its end &#8211; he gets somewhere, but in the scale of things, it&#8217;s nowhere.</p>
<ul>
<li><a href="http://www.google.com/maps?q=Ciudad+Juarez,+Mexico&#038;hl=en&#038;ll=31.731087,-106.462669&#038;spn=0.077673,0.163937&#038;sll=37.0625,-95.677068&#038;sspn=36.999937,83.935547&#038;vpsrc=6&#038;t=h&#038;z=13">Ciudad Juarez on Google Maps</a></li>
<li><a href="http://en.wikipedia.org/wiki/Female_homicides_in_Ciudad_Juárez">The murders in Ciudad Juarez</a> (Wikipedia)</li>
<li><a href="http://en.wikipedia.org/wiki/Maquiladora">Maquiladoras</a></li>
</ul>
]]></content:encoded>
			<wfw:commentRss>http://www.oddnumber.co.uk/2011/09/20/the-scale-of-the-world-2666/feed/</wfw:commentRss>
		<slash:comments>1</slash:comments>
		</item>
		<item>
		<title>12 solutions for e2342s</title>
		<link>http://www.oddnumber.co.uk/2011/07/31/12-solutions-for-e2342s/</link>
		<comments>http://www.oddnumber.co.uk/2011/07/31/12-solutions-for-e2342s/#comments</comments>
		<pubDate>Sun, 31 Jul 2011 18:39:08 +0000</pubDate>
		<dc:creator>admin</dc:creator>
				<category><![CDATA[Uncategorized]]></category>

		<guid isPermaLink="false">http://www.oddnumber.co.uk/?p=1875</guid>
		<description><![CDATA[]]></description>
			<content:encoded><![CDATA[<p><a href="http://www.oddnumber.co.uk/wp-content/uploads/2011/07/e2342s.jpg"><img src="http://www.oddnumber.co.uk/wp-content/uploads/2011/07/e2342s-806x1024.jpg" alt="" title="e2342s" width="640" height="813" class="alignnone size-large wp-image-1876" /></a></p>
]]></content:encoded>
			<wfw:commentRss>http://www.oddnumber.co.uk/2011/07/31/12-solutions-for-e2342s/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Cogcloud</title>
		<link>http://www.oddnumber.co.uk/2011/05/08/cogcloud/</link>
		<comments>http://www.oddnumber.co.uk/2011/05/08/cogcloud/#comments</comments>
		<pubDate>Sun, 08 May 2011 16:18:53 +0000</pubDate>
		<dc:creator>admin</dc:creator>
				<category><![CDATA[interactive]]></category>
		<category><![CDATA[maths]]></category>

		<guid isPermaLink="false">http://www.oddnumber.co.uk/?p=1807</guid>
		<description><![CDATA[The last day has been spent spinning cogs &#8211; a first engagement with processing.js. An initial cog is generated, then new ones are added with random radii. Some jiggling about establishes the number of teeth, and the corresponding radius, position &#8230; <a href="http://www.oddnumber.co.uk/2011/05/08/cogcloud/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p><a href="http://www.oddnumber.co.uk/projects/cogs/"><img src="http://www.oddnumber.co.uk/wp-content/uploads/2011/05/cogcloud1.png" alt="" title="cogcloud screenshot" width="599" height="251" class="alignnone size-full wp-image-1810" /></a></p>
<p>The last day has been spent <a href="http://www.oddnumber.co.uk/projects/cogs/">spinning cogs</a> &#8211; a first engagement with <a href="http://processingjs.org/">processing.js</a>.</p>
<p>An initial cog is generated, then new ones are added with random radii. Some jiggling about establishes the number of teeth, and the corresponding radius, position and speed needed to mesh with one of the existing cogs. If you would like a new combination of cogs, please click on the active area.</p>
]]></content:encoded>
			<wfw:commentRss>http://www.oddnumber.co.uk/2011/05/08/cogcloud/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Remaining lines</title>
		<link>http://www.oddnumber.co.uk/2011/05/01/remaining-lines/</link>
		<comments>http://www.oddnumber.co.uk/2011/05/01/remaining-lines/#comments</comments>
		<pubDate>Sun, 01 May 2011 11:19:36 +0000</pubDate>
		<dc:creator>admin</dc:creator>
				<category><![CDATA[passingthrough]]></category>
		<category><![CDATA[drawing]]></category>

		<guid isPermaLink="false">http://www.oddnumber.co.uk/?p=1800</guid>
		<description><![CDATA[A few scribbles from the beaches of the Lleyn Peninsula.]]></description>
			<content:encoded><![CDATA[<p><a href="http://www.flickr.com/photos/30791144@N06/5675512626/" title="Bardsey far by c.j.henden, on Flickr"><img src="http://farm6.static.flickr.com/5184/5675512626_9ff01dd7d8.jpg" width="500" height="354" alt="Bardsey far"></a></p>
<p>A few <a href="http://www.flickr.com/search/?q=lleynpeninsula&#038;d=taken-20110413-20110501&#038;ss=2&#038;ct=5&#038;mt=all&#038;w=30791144%40N06&#038;adv=1">scribbles</a> from the beaches of the Lleyn Peninsula.</p>
]]></content:encoded>
			<wfw:commentRss>http://www.oddnumber.co.uk/2011/05/01/remaining-lines/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Ongoing rooftops</title>
		<link>http://www.oddnumber.co.uk/2011/04/25/ongoing-rooftops/</link>
		<comments>http://www.oddnumber.co.uk/2011/04/25/ongoing-rooftops/#comments</comments>
		<pubDate>Mon, 25 Apr 2011 09:25:57 +0000</pubDate>
		<dc:creator>admin</dc:creator>
				<category><![CDATA[painting]]></category>

		<guid isPermaLink="false">http://www.oddnumber.co.uk/?p=1790</guid>
		<description><![CDATA[A painting is underway. As it&#8217;s unlikely to be finished soon, here are a few closeups, which currently are more interesting than the entirety: I&#8217;m going to keep coaxing it into existence, but despite the expanse of Easter time, there &#8230; <a href="http://www.oddnumber.co.uk/2011/04/25/ongoing-rooftops/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p>A painting is underway. As it&#8217;s unlikely to be finished soon, here are a few closeups, which currently are more interesting than the entirety:<br />
<a href="http://www.oddnumber.co.uk/wp-content/uploads/2011/04/roofs2.jpg"><img src="http://www.oddnumber.co.uk/wp-content/uploads/2011/04/roofs2.jpg" alt="" title="roofs2" width="640" height="428" class="alignnone size-full wp-image-1791" /></a></p>
<p><a href="http://www.oddnumber.co.uk/wp-content/uploads/2011/04/roofs1.jpg"><img src="http://www.oddnumber.co.uk/wp-content/uploads/2011/04/roofs1.jpg" alt="" title="roofs1" width="640" height="428" class="alignnone size-full wp-image-1792" /></a></p>
<p>I&#8217;m going to keep coaxing it into existence, but despite the expanse of Easter time, there are many other things to do.</p>
]]></content:encoded>
			<wfw:commentRss>http://www.oddnumber.co.uk/2011/04/25/ongoing-rooftops/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>The spurge is broadcasting</title>
		<link>http://www.oddnumber.co.uk/2011/03/20/the-spurge-is-broadcasting/</link>
		<comments>http://www.oddnumber.co.uk/2011/03/20/the-spurge-is-broadcasting/#comments</comments>
		<pubDate>Sun, 20 Mar 2011 09:59:40 +0000</pubDate>
		<dc:creator>admin</dc:creator>
				<category><![CDATA[Uncategorized]]></category>

		<guid isPermaLink="false">http://www.oddnumber.co.uk/?p=1758</guid>
		<description><![CDATA[]]></description>
			<content:encoded><![CDATA[<p><a href="http://www.oddnumber.co.uk/wp-content/uploads/2011/03/spurge.jpg"><img src="http://www.oddnumber.co.uk/wp-content/uploads/2011/03/spurge-1024x492.jpg" alt="Communicating on organic channels" title="Communicating on organic channels" width="640" height="307" class="alignnone size-large wp-image-1759" /></a></p>
]]></content:encoded>
			<wfw:commentRss>http://www.oddnumber.co.uk/2011/03/20/the-spurge-is-broadcasting/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>The impossibility of capturing the sea</title>
		<link>http://www.oddnumber.co.uk/2011/03/19/the-impossibility-of-capturing-the-sea/</link>
		<comments>http://www.oddnumber.co.uk/2011/03/19/the-impossibility-of-capturing-the-sea/#comments</comments>
		<pubDate>Sat, 19 Mar 2011 23:46:04 +0000</pubDate>
		<dc:creator>admin</dc:creator>
				<category><![CDATA[Uncategorized]]></category>

		<guid isPermaLink="false">http://www.oddnumber.co.uk/?p=1756</guid>
		<description><![CDATA[Anselm Kiefer has always held an unquestionable appeal. Reading today&#8217;s Guardian interview, I am told why. He is &#8220;almost theatrically&#8221; serious: Putting a Euclidean diagram on a seascape is about the impossibility of capturing the sea. The sea is always &#8230; <a href="http://www.oddnumber.co.uk/2011/03/19/the-impossibility-of-capturing-the-sea/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p>Anselm Kiefer has always held an unquestionable appeal. Reading today&#8217;s Guardian interview, I am told why. He is &#8220;almost theatrically&#8221; serious:</p>
<blockquote><p>Putting a Euclidean diagram on a seascape is about the impossibility of capturing the sea. The sea is always fluid. The geometrical figure gives the impression of fixing it at a certain moment. It&#8217;s the same as us imposing constellations on the sky which, of course, are completely crazy and nothing to do with the stars. It is just for us to feel more comfortable. To construct an illusion for ourselves that we have brought order to chaos. We haven&#8217;t. I might have been born into a very literal state of chaos, but in fact that state is true of all of us.</p></blockquote>
]]></content:encoded>
			<wfw:commentRss>http://www.oddnumber.co.uk/2011/03/19/the-impossibility-of-capturing-the-sea/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Isometric colouring challenge &#8211; solution</title>
		<link>http://www.oddnumber.co.uk/2011/01/03/isometric-colouring-challenge-solution/</link>
		<comments>http://www.oddnumber.co.uk/2011/01/03/isometric-colouring-challenge-solution/#comments</comments>
		<pubDate>Mon, 03 Jan 2011 17:44:02 +0000</pubDate>
		<dc:creator>admin</dc:creator>
				<category><![CDATA[maths]]></category>

		<guid isPermaLink="false">http://www.oddnumber.co.uk/?p=1660</guid>
		<description><![CDATA[The previous post contained a fiendish Christmas challenge sent to me by the basket-weaving Gareth Williams. Here&#8217;s my vague strategy together with the coloured in solution. First attempt: start colouring&#8230; perhaps it could be solved as I went along. But &#8230; <a href="http://www.oddnumber.co.uk/2011/01/03/isometric-colouring-challenge-solution/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p>The <a href="http://www.oddnumber.co.uk/2011/01/03/isometric-colouring-challenge/">previous post</a> contained a fiendish Christmas challenge sent to me by the basket-weaving Gareth Williams.</p>
<p>Here&#8217;s my vague strategy together with the coloured in solution.<br />
<span id="more-1660"></span></p>
<p>First attempt: start colouring&#8230; perhaps it could be solved as I went along. But that soon ended in stuckness.</p>
<p>A map can be represented as a <a href="http://en.wikipedia.org/wiki/Planar_graph">planar graph</a>. Which means a graph without any overlapping edges. Each shape can be represented by a node, and any other shapes it neighbours can be connected by a edge. I only did this with the obvious pattern &#8211; it&#8217;s possible to do the whole page, but that would be a crazy mess.<br />
<a href="http://www.oddnumber.co.uk/wp-content/uploads/2011/01/graph.png"><img src="http://www.oddnumber.co.uk/wp-content/uploads/2011/01/graph.png" alt="" title="graph" width="554" height="289"  /></a><br />
<br />
Each shape in the main pattern has six neighbours. It&#8217;s fairly easy once you have the graph to see a way of colouring them without any colours being adjacent:</p>
<p><a href="http://www.oddnumber.co.uk/wp-content/uploads/2011/01/graph-coloured.png"><img src="http://www.oddnumber.co.uk/wp-content/uploads/2011/01/graph-coloured.png" alt="" title="graph-coloured" width="554" height="289"  /></a></p>
<p></p>
<p>There are then two problems: the non-patterned join between the three directions of the pattern, and the join between the pattern and the margin &#8211; which is one of the four colours. </p>
<p>It&#8217;s best to start with the complex shapes formed by the join, as many of them have more than six neighbours. I did try making graphs out of the larger ones. This helped in visualising the problem, but became too complicated to think through systematically. </p>
<p>Only three colours are needed for the above graph (including the margin), which means the fourth colour can be used for the complex join shapes, any mess caused by the meeting with the margin, and other emergencies. </p>
<p>Colouring it in was straightforward except for the combined join points and margin, which required some juggling:<br />
<a href="http://www.oddnumber.co.uk/wp-content/uploads/2011/01/3-way-grid-coloured-small.png"><img src="http://www.oddnumber.co.uk/wp-content/uploads/2011/01/3-way-grid-coloured-small.png" alt="" title="3-way-grid-coloured-small" width="566" height="800" class="alignleft size-full wp-image-1661" /></a></p>
]]></content:encoded>
			<wfw:commentRss>http://www.oddnumber.co.uk/2011/01/03/isometric-colouring-challenge-solution/feed/</wfw:commentRss>
		<slash:comments>2</slash:comments>
		</item>
	</channel>
</rss>

