Kind of related: in the Tetris community, there iss a human player who's specialty in making Tetris pattern (using legit piece generator). He began by making the classic ">" pattern (famous amonst the bored Japanese Sega-styled (TGM) Tetris players) [1]. Then he progressively improved and he can now do some quite impressive "sculpting". Check out his space invader [2], repeated triforce [3], Luigi [4] and the rest of his youtube channel. It's mesmerizing.
The comments point out that the printer algorithm gets to choose the next piece; however, it is possible to manipulate the next piece you get through the timing of dropping the previous piece, so in theory this algorithm could produce emulator inputs for a Tetris cart that would draw similar pictures. (Albeit limited to the "resolution" of that tetris field, unlike the extra-wide field used in the video.)
That being said, it would be awesome if someone fit the algorithm onto a little microcontroller and got it to generate the control signals for a particular console (although as you already mentioned, resolution might be a limiting factor here...).
I was thinking of the original NES version, specifically. You'd need to emulate it yourself so that you could figure out when to supply inputs to manipulate the RNG and give yourself the pieces you need.
Are the timings that precise? ISTR that there were only 24 or 100 frames per second, so a micro-controller ought to be able to send the proper signals.
A microcontroller can easily send the proper signals; check out NESBot for an example. Here's a video of NESBot playing the original NES Tetris with a series of inputs that manipulates the RNG: http://tasvideos.org/1502M.html .
You just need to emulate the game when planning out the series of moves, to figure out what timing to use to manipulate the RNG and get the pieces you want.
It's a pretty good read if you're into that sort of thing, and really helps explain the mechanics of analog video (and also gives you some hints about simulating it in software). He also created his own clones of Tetris and Pong that run on the MCU as well!
It should have shown the video at first. Even for scrolling it's too much until you find out what all that really is about, that you are not willing to read it any more.
There was a precursor in 2005, a paper called "How to Construct Tetris Configurations". Their output was monochrome, but I'm sure the proof results are transferable.
That just demonstrates the algorithm and makes it clear how it works.