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Generally, lifeforms existed in three dimensions, but these such lifeforms were known to exist in a single plane only (and as such had either no length, no height, or no width). Some of these beings made their homes in cosmic strings, objects a single proton wide but with lengths measuring in kilometers or more. These strings 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. One such example was when they surrounded the USS Enterprise-D in 2367. In that instance, Data ultimately detected their presence by using two probes to scan the space around the ship.
Because of their strange nature, two-dimensional lifeforms could interact in strange ways with starship engines. They exerted forces similar to gravitational forces and could cause a ship's structural integrity field to begin to break down when the starship's warp drive was used to break free of their influence.
Because they could share emotions, large numbers of two-dimensional lifeforms gathered in one area could overwhelm Betazoid empathic and telepathic abilities, causing painful headaches. (TNG: "The Loss")