Noticing that my Tetris Tiler had been mentioned in a recreational math class at Carnegie Mellon gave me sufficient motivation to dedicate some time during Spring break to pounding out some new features. The most significant is the ability to choose what set of pieces to use, with the set of available pieces being all of the polyominoes of orders two through six. This allows a number of interesting setups that weren’t possible with the fixed set of tetrominos.

One that I’ve been playing with since I first got the new features functioning is trying to tile an empty grid with a small set of unlikely pieces. Tiling empty grids was never interesting in the older version, because the program always found a boring solution quite quickly and simply. However, with the new features, it’s quite easy to find piece sets that cannot tile a fix-sized rectangular empty grid, and so an interesting problem is finding piece sets for which it’s not at all clear that any such tiling exists. This one is a good example, where each of the pieces are kind of ‘u’ shaped:

This one consists of a bunch of ’t’s:

Another feature I added allows the grid to wrap around vertically or horizontally. This can be used to create seamless repeating patterns, which could be useful, say if you need ideas for tiling your kitchen floor, or a nerdy background for your blog. For a good example, download the image below and set it as your desktop wallpaper, and specify “tiled” (or, if you’re not using Firefox, just click here to see it in a popup window).

It can also be used for this sort of nonsense:

I also added the ability to save grids/tilings, as well as download images (which is where the above images and their links came from). Future features I’m planning on include custom colors, one-sided polyominoes (i.e., distinguishing between mirror images), and an easier-to-use grid editor. You can play with it here.

I recently noticed that the phrase “we were merely freshmen” from that song by The Verve Pipe has almost entirely ’e’s for vowels (it took me a while to notice the ‘y’, so I originally thought it was exclusive). This suggests a new category of interesting phrases, that only contain one kind of vowel.

We can differentiate between phrases caught in the wild (actually published somehow), and phrases that are reasonable enough that one could imagine them being spoken or written. If we allow for unreasonable phrases (and only require correct syntax), then they could be arbitrarily and trivially long.

I’ll start it off by searching the works of Shakespeare (as found here). In the first scene of The Two Gentlemen of Verona we have the character Speed speaking the line

The shepherd seeks the sheep, and not the sheep the shepherd; but I seek my master, and my master seeks not me; therefore, I am no sheep.

The first phrase is five words long, six if you count the name “Speed” preceding the line. This ought to be beatable. Clearly Shakespeare was only an amateur.

Today’s error message is brought to you by Eclipse.

I’ve heard of mathematical crackpots before, but I wasn’t aware they were publishing books on Amazon. The following paragraph is taken directly from the supplied product description, which was presumably written by the author himself, who claims to have a B.S. in mathematics. The last two sentences are priceless:

I discovered a method of proving the Collatz Conjecture, an unsolved problem in mathematics. The Collatz Conjecture claims that any non-zero positive integer will reach 1 if the following rules are applied: If the integer is odd, multipy by 3 and add 1 (3x+1), if it is even, divide by 2 (x/2). I noticed that there are only a finite number of possible combinations for 3-digit integers when the 3x+1 and x/2 rules are followed. I also used the fact I proved that powers of 2 added to any of the positive integers cause agreement. My brother (Michael Fleming) wrote a computer program with my instructions that proved that all integers subcoll (a chosen integer subcolls if it reaches an integer less than itself), a known sole requirement for the proof of the validity of the Collatz Conjecture. He was on the team for the special effects of the movie True Lies (nominated for an academy award in Best Special Effects), and the movie Species. He also did some of the special effects for the children’s show Barney.

Today’s error message of the day:

17:54:01,994 WARN [JBossASSecurityMetadataStore] WARNING! POTENTIAL SECURITY RISK. It has been detected that the MessageSucker component which sucks messages from one node to another has not had its password changed from the installation default. Please see the JBoss Messaging user guide for instructions on how to do this.

Say what you will about technology, but there’s something wonderfully sweet about a world where the term “mathematic attacks” can be taken seriously.