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Fear is an attack on the Morale of another being. It has many sources, of which the Fear Aura is the most common. The core purpose of Fear is force a rout in the enemy, greatly reducing the amount of bodies one has to cleave through in their bid for domination or survival.
Units with THIS icon in their stat sheet have a Fear Aura. Each round, a unit with an Aura has just under 24 chances to cover either the square they're on or an adjacent square (including diagonals) with its Aura. The listed value of an Aura is roughly how many times it succeeds in filling a square each round. Fear Auras only "flash" squares, however, so someone stepping into a square after it's been selected is perfectly fine.