My GPS was stolen last night or this morning and I'm missing it already. For instance when I drove to Novus glass repair to get my front passenger window replaced I drove down the wrong road for a while.
When I got out of my apartment this morning there was a police car sitting in my parking lot and the officer asked me: "David? ... What'd you leave in your car?". My face must have changed a lot when I had the following sequence of realizations: (a) a police officer is asking for me by name, (b) I'm not in trouble, (c) my car must have been burgled, and (d) my GPS must be stolen.
The officer was waiting outside my complex because someone had reported my car's broken window to the police in the morning. The officer was very courteous and upon taking my date of birth noted that we were born on exactly the same day. The window's safety glass was shattered and lying in tons of tiny pieces all over the passenger seat, my glove box was open and the middle armrest where I keep my CDs was open. Nothing appears to be missing other than the GPS, the GPS power cable, and the GPS dash mount. Adding insult to theft, the their scattered my CDs throughout my car and didn't take any of them, insulting my taste in music.
My car's window should be repaired now and hopefully the rain that came in through the broken window until I covered it with plastic bags (classy!) didn't do any permanent damage.
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 |
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| 2 | J |
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| L |
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| 3 | O |
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| T |
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| S |
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| Z |
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| T+ |
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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.
sequelguy posted a photo:
This dragon head sculpture actually breathes fire at night. Note the burnt brush around the head.
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