Michael Birken lays out, in detail, a method for teaching a computer to draw arbitrary 8-bit images by playing Tetris, strategically deploying blocks of various colors to cause exactly the picture you want to emerge. The method is (as you'd imagine), starkly terrifying in its complexity, but the video speaks for itself.
The algorithm converts pixels from a source image into squares in the Tetris playfield, one row at a time from the bottom up. To generate an individual square, the algorithm assembles a structure consisting of a rectangular region fully supported by a single square protruding from the bottom. When the rectangular region is completed, its rows are cleared, leaving behind the protruding square. Three examples of the process appear below.
The algorithm can also generate multiple squares with a single structure as shown below.
During construction of a row, all of the squares produced by this method must be supported. In the images above, the generated squares are supported by the floor of the playfield. However, if an arbitrary row contains holes, it may not provide the support necessary for the construction of the row above it. The algorithm solves this problem by constructing a flat platform on top of the row with holes. In the animation below, a platform is built above a row comprising of a single red square. The platform is a temporary structure and inserting the final piece removes it.