Quadrant Glitch is a major glitch allowed only in the No Logic ruleset.
When you take damage while moving over the midpoint of a large room (crossing from one quadrant of the supertile to another), it can have an effect similar to a door juke, causing later screen transitions to go to the wrong place. You might encounter this glitch by accident when taking damage on the Thieves' Town conveyor belt.
A convenient use of Quadrant Glitch is to reach the right side of Desert Palace without unlocking the door. This setup is explained further in the Desert Palace (NL) guide.
Getting zapped by a Beamos across the quadrant boundary sets up the glitch.
Eastward transitions after that go to the wrong place.