Solving the purple & white pillars

I have encountered two kinds of pillars in the game: I've solved the vibrating type, but I'm having trouble solving the white or purple pillars (that have floating dots in their hollowed tops).

How do I solve these pillar puzzles?

Upon completing the game, you'll unlock New Game+, which transfers your stats and adds first-person view after the intro.

Near a purple or white pillar, go into first-person view and look for a string of white tetrominos (Tetris blocks). They can be converted to buttons with the tetromino cipher.

If the white string is vertical, read it with your head tilted to the right. Then convert the tetrominos and punch them in. The sequence should be about eight units long, and unique for each game. An anticube will appear above the pillar.

Here are the codes, if you're lazy:

• Lighthouse purple pillar: ↑ LT RT ↑ LT ↑ RT ↑
• Forest white pillar (first): → RT ← LT ← ↑ ↓ A
• Forest purple pillar (second): LT A RT ↑ ↓ LT RT A
• Forest white pillar (third, near temple warp zone): ← ← ↓ ↓ → → ↑ ↑

The U-shaped tuning fork pillars work differently.