When I woke up this morning for some reason I was thinking about Polytope Tetris, my N-D Tetris game, and specifically generating Tetris pieces in various number of dimensions. When I first wrote PTT I thought that as the number of dimensions increased you could end up with an infinite number of non-equivalent crazy Tetris pieces. However this morning I realized that because you only get four blocks per piece there are only a possible three joints in a single Tetris piece which means that you only need three dimensions to represent all possible distinct N-D Tetris pieces.
Below is the table of the various possible pieces per number of dimensions and sorted by the number of joints in the piece. Notice that the 'J' and 'L' become equivalent in 3D because you can rotate the 'J' through the third dimension to make it an 'L'. The same happens for 'S' and 'Z' in 3D, and 'S+' and 'Z+' in 4D.
| Joints | Name | 1D | 2D | 3D | + |
|---|---|---|---|---|---|
| 1 | I |
|
|
|
|
| 2 | J |
|
|
|
|
| L |
|
||||
| 3 | O |
|
|
|
|
| T |
|
|
|
||
| S |
|
|
|
||
| Z |
|
||||
| T+ |
|
|
|||
| S+ |
|
|
|||
| Z+ |
|
||||
| Total | 1 | 7 | 8 | 7 |
As a consequence of not realizing there's a finite and small number of N-D Tetris pieces, I wrote code that would randomly generate pieces for a specified number of dimensions by wandering through Tetris space. This consists of first marking the current spot, then randomly picking a direction (a dimension and either forward or backward), going in that direction until hitting a previously unvisited spot and repeating until four spots are marked, forming a Tetris piece. However this morning I realized that continuing in the same direction until reaching am unvisited spot means I can't generate the 'T+' piece. I think the better way to go is keep the list of all possible pieces, pick one randomly, and rotate it randomly through the available dimensions. Doing this will also allow me to give distinct pieces their own specific color (like the classic Tetris games do) rather than picking the color randomly like I do now.
![['Neverending story' by Alexandre Duret-Lutz. A framed photo of books with the droste effect applied. Licensed under creative commons.]](http://farm1.static.flickr.com/90/252757784_3de44cbeb4_m_d.jpg)
Information about URI Fragments, the portion of URIs
that follow the '#' at the end and that are used to navigate within a document, is scattered throughout various documents which I usually have to hunt down. Instead I'll link to them all here.
Definitions. Fragments are defined in the URI RFC which states that they're used to identify a secondary resource that is related to the primary resource identified by the URI as a subset of the primary, a view of the primary, or some other resource described by the primary. The interpretation of a fragment is based on the mime type of the primary resource. Tim Berners-Lee notes that determining fragment meaning from mime type is a problem because a single URI may contain a single fragment, however over HTTP a single URI can result in the same logical resource represented in different mime types. So there's one fragment but multiple mime types and so multiple interpretations of the one fragment. The URI RFC says that if an author has a single resource available in multiple mime types then the author must ensure that the various representations of a single resource must all resolve fragments to the same logical secondary resource. Depending on which mime types you're dealing with this is either not easy or not possible.
HTTP. In HTTP when URIs are used, the fragment is not included. The General Syntax section of the HTTP standard says it uses the definitions of 'URI-reference' (which includes the fragment), 'absoluteURI', and 'relativeURI' (which don't include the fragment) from the URI RFC. However, the 'URI-reference' term doesn't actually appear in the BNF for the protocol. Accordingly the headers like 'Request-URI', 'Content-Location', 'Location', and 'Referer' which include URIs are defined with 'absoluteURI' or 'relativeURI' and don't include the fragment. This is in keeping with the original fragment definition which says that the fragment is used as a view of the original resource and consequently only needed for resolution on the client. Additionally, the URI RFC explicitly notes that not including the fragment is a privacy feature such that page authors won't be able to stop clients from viewing whatever fragments the client chooses. This seems like an odd claim given that if the author wanted to selectively restrict access to portions of documents there are other options for them like breaking out the parts of a single resource to which the author wishes to restrict access into separate resources.
HTML. In HTML, the HTML mime type RFC defines HTML's fragment use which consists of fragments referring to elements with a corresponding 'id' attribute or one of a particular set of elements with a corresponding 'name' attribute. The HTML spec discusses fragment use additionally noting that the names and ids must be unique in the document and that they must consist of only US-ASCII characters. The ID and NAME attributes are further restricted in section 6 to only consist of alphanumerics, the hyphen, period, colon, and underscore. This is a subset of the characters allowed in the URI fragment so no encoding is discussed since technically its not needed. However, practically speaking, browsers like FireFox and Internet Explorer allow for names and ids containing characters outside of the defined set including characters that must be percent-encoded to appear in a URI fragment. The interpretation of percent-encoded characters in fragments for HTML documents is not consistent across browsers (or in some cases within the same browser) especially for the percent-encoded percent.
Text. Text/plain recently got a fragment definition that allows fragments to refer to particular lines or characters within a text document. The scheme no longer includes regular expressions, which disappointed me at first, but in retrospect is probably good idea for increasing the adoption of this fragment scheme and for avoiding the potential for ubiquitous DoS via regex. One of the authors also notes this on his blog. I look forward to the day when this scheme is widely implemented.
XML. XML has the XPointer framework to define its fragment structure as noted by the XML mime type definition. XPointer consists of a general scheme that contains subschemes that identify a subset of an XML document. Its too bad such a thing wasn't adopted for URI fragments in general to solve the problem of a single resource with multiple mime type representations. I wrote more about XPointer when I worked on hacking XPointer into IE.
SVG and MPEG. Through the Media Fragments Working Group I found a couple more fragment scheme definitions. SVG's fragment scheme is defined in the SVG documentation and looks similar to XML's. MPEG has one defined but I could only find it as an ISO document "Text of ISO/IEC FCD 21000-17 MPEG-12 FID" and not as an RFC which is a little disturbing.
AJAX. AJAX websites have used fragments as an escape hatch for two issues that I've seen. The first is getting a unique URL for versions of a page that are produced on the client by script. The fragment may be changed by script without forcing the page to reload. This goes outside the rules of the standards by using HTML fragments in a fashion not called out by the HTML spec. but it does seem to be inline with the spirit of the fragment in that it is a subview of the original resource and interpretted client side. The other hack-ier use of the fragment in AJAX is for cross domain communication. The basic idea is that different frames or windows may not communicate in normal fashions if they have different domains but they can view each other's URLs and accordingly can change their own fragments in order to send a message out to those who know where to look. IMO this is not inline with the spirit of the fragment but is rather a cool hack.
I now have search and an archive available for my site. I previously tried to setup crappy search by cheating using Yahoo Pipes and now
instead I have a slightly less crappy search that works over all of the content that I've produced on my blog, uploaded to flickr or youtube, or added to delicious.
You can now read my first LiveJournal blog post or, for probably much more entertainment value, view all the photos and videos of Cadbury by searching for 'bunny'.
The search is only slightly less lame because although it searches over all my content, I still implemented it myself rather than getting a professional package. Also, the feed supports the same search and archive as my homepage so you can subscribe to a feed of Cadbury if you're so inclined and just skip all this other boring stuff. My homepage and feed implement the OpenSearch response elements and I've got an OpenSearch search provider (source) as well.
The Goodwin family, except for Michelle who is taking a class trip to Washington DC and New York, was in Seattle this week. Sarah and I met up with them for dinner last night at the Icon Grill. I enjoy the Icon Grill in general and last night was no exception especially having dinner with the Goodwins which was a lot of fun. It was particularly cold and at one point snowed. The Goodwin's are seeing all the classic tourist attractions in Seattle some of which are depicted in the following 1962 Seattle's Worlds Fair postcard. The postcard is featured on Paleo-Future and unsurprisingly the 1962 Worlds Fair favored Seattle's Space Needle and monorail.
![[Icon Grill front. Licensed under under Creative Commons. By Troy B Thompson]](http://farm1.static.flickr.com/17/22461595_7fb7e702c4_m_d.jpg)
![[Seattle's Worlds Fair Postcard]](http://bp0.blogger.com/_sGYULzoQCgA/R7NOl8B8s2I/AAAAAAAABX4/0gPURFTR4X4/s400/Seattle_Fair_Olympia_Brewing_PC_001.jpg)
Some rights reserved