The USS Enterprise-D surrounded by two-dimensional beings
These two-dimensional beings were a species of two-dimensional entities that lived in space in the vicinity of the T'lli Beta system. Because these beings had the ability to share emotions, large numbers of this species gathered in one area could overwhelm Betazoid empathic and telepathic abilities, causing painful headaches.
In 2367, the USS Enterprise-D encountered a group of two-dimensional beings. They made their home in a cosmic string, which had a gravitational attraction like black holes or homing beacons for two-dimensional beings. Because they only existed in a single plane, starship sensors had difficulty detecting their existence, even through the use of Bayesian functions. In that instance, Data ultimately detected their presence by using two probes to scan the space around the ship. They affected the space around them through polarizing an emanating graviton field. Catching the ship in its wake, the Enterprise was carried to the cosmic string until it reflected the appearance of the string, disrupting the beings' motion long enough for them to escape. (TNG: "The Loss")