In my Intro to Algorithms course in college the Fibonacci sequence was used as the example algorithm to which various types of algorithm creation methods were applied. As the course went on we made
better and better performing algorithms to find the nth Fibonacci number. In another course we were told about a matrix that when multiplied successively produced Fibonacci numbers. In my linear
algebra courses I realized I could diagonalize the matrix to find a non-recursive Fibonacci function. To my surprise this worked and I
found a function.
Looking online I found that of course this same function was already well known. Mostly I was irritated that after all the
algorithms we created for faster and faster Fibonacci functions we were never told about a constant time function like this.
I recently found my paper depicting this and thought it would be a good thing to use to try out MathML, a markup language for displaying math. I went to the MathML implementations page and installed a plugin for IE to display MathML and then began writing up my paper in MathML. I wrote the MathML by hand and must say that's not how its intended to be created. The language is very verbose and it took me a long time to get the page of equations transcribed.
MathML has presentation elements and content elements that can be used separately or together. I stuck to content elements and while it looked great in IE with my extension when I tried it in FireFox which has builtin MathML support it didn't render. As it turns out FireFox doesn't support MathML content elements. I had already finished creating this page by hand and wasn't about to switch to content elements. Also, in order to get IE to render a MathML document, the document needs directives at the top for specific IE extensions which is a pain. Thankfully, the W3C has a MathML cross platform stylesheet. You just include this XSL at the top of your XHTML page and it turns content elements into appropriate presentation elements, and inserts all the known IE extension goo required for you. So now my page can look lovely and all the ickiness to get it to render is contained in the W3C's XSL.
I recently finished Braid, the Xbox Live game, and a comparison with Portal is helpful. From a screen shot Braid
looks like a normal 2D platformer, but that's like looking at a screen shot of Portal and saying its a first person shooter. While the scaffolding of the game-play may sort of fall into that
category, the games are actually about exploring the character's ability and solving puzzles. In Portal the ability is bending space and in Braid its bending time. However, whereas in Portal there
is one space bending mechanism, the portal gun, Braid's protagonist explores several different time bending techniques including, most prominently, reversing time, but also time dilation, multiple
time-lines, and other odd things.
Similar to the difference in game-play, while Portal has a strict simplicity to its visual style, Braid is much more ornate, like you're playing in an oil painting. Without seeing video of the game, or playing the demo (which is available for free on Xbox Live) its difficult to convey, but it is quite lovely and the animation adds quite a bit. Both games too are rather short leaving you just a bit hungry for more and have an interesting plot and an ending that I'd hate to spoil although Braid replaces Portal's humor with melancholy. If you enjoyed Portal and Twelve Monkeys then I'd recommend Braid.
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 | + |
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| 1 | I |
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| 2 | J |
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| L |
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| 3 | O |
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| S |
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| Z |
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| 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.
While re-reading Cryptonomicon I thought about what kind of information I'm leaking by posting links on Delicious. At work I don't post any Intranet websites for fear of revealing anything but I wondered if not posting would reveal anything. For instance, if I'm particularly busy at work might I post less indicating something about the state of the things I work on? I got an archive of my Delicious posts via the Delicious API and then ran it through a tool I made to create a couple of tables which I've graphed on Many Eyes
Sarah and I have finished playing through the games "Paper Mario", "Paper Mario: The Thousand-Year Door", and "Super Paper Mario" last week (including the various Pits of 100 Trials). We played them all on the Wii, because even though Super Paper Mario was the only one released explicitly for that platform, Wii maintains compatibility with Game Cube games such as Thousand-Year Door and Paper Mario although originally released for the Nintendo 64 is now available as a pay for download game on the Wii's Virtual Console. So, yay for Nintendo!
I think my favorite of the three is Thousand-Year Door mostly because of the RPG attack system. In Thousand-Year Door and Paper Mario when you come into contact with an enemy you go into an RPG style attack system where you take turns selecting actions. In Super Paper Mario you still have hit points and such, but you don't go into a turn based RPG style attack system, rather you do the regular Mario jumping on bad guys thing (or hitting them with a mallet etc...). Thousand-Year Door and Paper Mario are very similar in terms of game play but Thousand-Year Door looks very pretty and has made improvements to how your party-mates are handled in battle (they have HP and can fall as you would expect) and there's an audience that cheers you on during your battles.
Even if the gameplay sucked the humor throughout the series might be tempting enough. Mario's clothing and mustache are mocked throughout and standard RPG expectations are subverted. I hate to describe any of these moments for fear of ruining anything but, for instance, an optional and very difficult enemy who may only be killed after hours of work only results in one experience point, or a very intimidating enemy who you imagine you'll have to fight actually challenges you to a quiz.
Despite how I personally rank them, all the games are great and I'd recommend any of them.
It was warm and lovely out this past Saturday and Sarah I and went to a
new place for lunch, then to Kelsey Creek Park, and then out for Jane's birthday. We ate at Cafe
Pirouette which serves crepes and is done up with French decorations reminding me of my parent's house. We got in for just the end of lunch and saw the second to last customers, a gaggle of
older ladies leaving. I felt a little out of place with my "Longhorn [heart] RSS" t-shirt on. The food was good and in larger portions that I expected.
After that we went to Kelsey Creek Park and Farm. The park is hidden at the end of a quiet neighborhood, starts out with some tables and children's jungle gym
equipment, then there's a farm which includes a petting zoo, followed by many little trails going off into the forrest. There weren't too many animals out and the ones we did see didn't seem to
expect or want the sun and warm weather. We followed one of the trails for a bit and turned back before getting sun burned. You can see
my weekend photos mapped out on Live Maps.
That night we went out with some friends for Jane's birthday. Eric was just back from the RSA conference and we met Jane and Eric and others at Palace Kitchen in Seattle located immediately adjascent to the monorail's route. The weather was still good so they left the large windows open through twilight and every so often you'd see the monorail pass by.
Two weekends ago it was actually sunny and kind of warm so Sarah and I went down to Spud Fish and Chips and Juanita Beach Park. We ate fish and chips on the dock. I took a few pictures and this
time actually put some geographical information on Flickr so now I've got a map of my tiny fish and chips journey. On the map click on the floating marks to view the associated photos.
Flickr provides access to the geo data associated with your photos via GeoRSS feeds. And Google Maps displays GeoRSS feed content on their maps allowing you even to edit the data but doesn't appear to let you easily export the GeoRSS. Live Maps does the inverse, allowing you to create and export GeoRSS data but not import it. I'd like both please. Oh well.
When throwing together an HTML page at work that other people will view, I stick the following line in for style. Its IE's error page CSS and contaits a subtle gradient background that I like.
This uses the res URI scheme. You can see the other interesting IE resources using my resource list tool.
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Cadbury yawns.
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From: David Risney
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5 ratings
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| Time: 00:10 | More in Pets & Animals |
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Cadbury hears something, slowly.
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From: David Risney
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| Time: 00:15 | More in Pets & Animals |
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