Sigil
Sigils, also called tetrominoes, are geometric shapes consisting of four squares; they are given as rewards for completing puzzles throughout The Talos Principle and in the tutorial of The Talos Principle 2. After collecting enough sigils, the player can unlock certain tools or areas using tetromino arrangers.
On this wiki, the Sigil template can be used to insert icons such as 
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The Talos Principle
Green
Green sigils are required for the player to leave the Land of Ruins (Building A) as well as to enter the Land of Death and the Land of Faith.
Yellow
Yellow sigils are used to unlock new puzzle elements, such as the hexahedron and connector.
The tetromino arrangers on the gates that block access to star worlds also use yellow tetrominoes, one for each star the player has collected.
Red
Red sigils are used to access floors 1 through 5 of the Tower. If the player has not yet approached the tetromino arranger for that floor, the collected red sigils are shown as a single dot in the game's interface. Once the arranger door has been visited, any sigils collected for that door are listed next to a large number for the floor.
Gray
Gray sigils are used to access floor 6 of the Tower. They are rewards for completing puzzles in the three star worlds.
Blue
The tetromino arrangers in the messenger worlds use blue tetrominoes. However, the player cannot collect blue sigils; they are not rewards connected to any puzzles.
The Talos Principle: Road to Gehenna
In the DLC for the first game, the reward for completing standard puzzles is not a sigil but rather a freed program.
There is one star world whose portal is locked behind a tetromino arranger. As in the first game, collected stars appear here as yellow tetrominoes.
The puzzles in the star world grant gray sigils as rewards. These can be used to free Admin.
The Talos Principle 2
In the sequel game, sigils appear as rewards in the Booting Process. Here, the green, yellow, and red sigils are all used to unlock gates. (In all main, lost, and gold puzzles, completion leads to a progress wheel, not a sigil.)
Very large tetrominoes—no longer referred to as "sigils"—are used to form bridges.
The Museum of the Simulation features several tetromino arrangers as standalone interactive displays. There are also 3D models of the virtual sigils in each of its three puzzle rooms. Each sigil model is initially rotating on a pole; when the player completes a puzzle, the model stops rotating and descends towards the floor while a recording of the sigil-collection sound from the first game plays over a speaker.