The New Tetris, Square mode of Tetris Worlds, and Lockjaw: The Overdose reward the player for creating 4x4 block squares out of four tetrominoes.
Building wide platforms (flat top sides) into the top of a square in progress allows more than one such square to be built at once, keeping options open for handling any tetromino.
The New Tetris was developed prior to the standardization of tetromino colors.
The diagrams below, like most other diagrams in Tetriswiki, use Tetris Worlds colors per the more recent Tetris Guideline.
Spiral J monosquare
It is best to build J and L monosquares using this spiral method so that platform width is maximised as early as possible.
L on the left and J on the right require a double slide. L on the right and J on the left require a double slide if there isn't enough support below. See below.
Spiral L monosquare
Non-spiral L and J monosquares
One side of each of the spiral monosquares depicted above requires a double slide.
These squares are built on the same side and do not require a double slide if built on top of a 3-block platform.