Gun Kata is a fictional gun-fighting martial art discipline that is a significant part of the film. It is based upon the premise that, given the positions of the participants in a gun battle, the trajectories of fire are statistically predictable. By pure memorization of the positions, one can fire at the most likely location of an enemy without aiming at him in the traditional sense of pointing a gun at a specific target. By the same token, the trajectories of incoming fire are also statistically predictable, so by assuming the appropriate stance, one can keep one's body clear of the most likely way of enemy bullets.
The Gun Kata shown in Equilibrium is a hybrid mix of Kurt Wimmer's own style of Gun Kata (which he invented in his backyard) and the martial arts style of the choreographer. They disagreed on the appropriate form of Gun Kata, with Kurt Wimmer advocating a more smooth, flowing style and the choreographer supporting a more rigid style. Much of the Gun Kata seen in the movie is based on the choreographer's style (movements are rigid and rapid). Kurt Wimmer's Gun Kata is dispersed sparsely throughout the movie, most notably in the intro scene with the silhouetted man (played by Wimmer himself) practicing with dual pistols.