Stage 1 In its most basic form, the "three (3) box pattern" is use to practice and perfect the basic stances. This is done by executing a set of prearranged stances (usually 9, but can be less for beginners) in a series of continous unbroken fliud motions that move from one corner of a box to another in a series of pivots and steps. This technique teaches you how to properly utilize your footwork, as well as, your waist and shoulders action. All these things unify your upper and lower body (body, hands and feet working together (hop ga)), allowing you to generate and transfer 100% of your power and body weight into the target. However, to move along these corners require that the feet be at particular distances apart. This predetermined distance maximizes your balance, coordination and power.
In stage 2, the "three (3) box pattern" it is used to teach you how to employ various body angles and motion which carry you in and out of range of an opponent.
At stage 3, upper level footwork is taught for throws, leverages and takedown. These consist of advance pivots, as well as, triangular and circular stepping patterns, all taught in order to make your techniques more efficient. Triangular, sqaure, and circular theories of the art are also explored at this time. For example, circles form triangles in the sameway as a pie forms triangles when it is cut. Squares form triangles when the box is divided diagonally (when an "X" is placed within the box), and boxes are form when the triangle "X" is enclosed on all four sides. To see all these things in there most basic forms, simply place a square inside a circle, then superimpose an "X" over both and you will see how all three are interlinked. Everything you do in the art is based on these three, and are directly linked to the "universal pattern" .This is why so much emphasis is placed on the "3 box set" .Lastly, all three of these (sqaures, circles and triangles) are also directly related to the form, creating structure and balance in the form and in yourself.
Conclusion
The 3 box set your foundation, and without practicing the 3 box pattern set, your body will not move in a harmonious way.