Swordplay

Swordplay in both a historical and modern setting is emergent in that complex patterns of actions arise out of simple rules and maneuvers.

Footwork
Broadly defined, all actions can be broken into bladework and footwork. The common footwork maneuvers are the advance, retreat, lunge, recovery from lunge, and fleche (a type of running attack). There are other more advanced maneuvers but they only have niche usage.

Bladework
Bladework can be broken down into offensive and defensive actions. The defensive actions are parries and in the French system there are only nine of them and are determined based off of quadrant of the body and hand position (supinated or pronated). Often times a parry ends with a riposte, which is an attack following a parry.

Offensive actions include the straight attack, the beat attack (hitting the opponents blade before attacking), and the glide and opposition (where the attacker takes control of the opponents blade before the attack). There are offensive actions that don't involve the opponents blade, besides the straight attack, which include feint and disengage (where the attacker baits an action from the opponent then maneuvers their blade to a now open area) and the stop hit and point in line (extending the blade so that the opponent runs on it due to their own action).

The Tactical Wheel and Emergence
In this video it is very clearly that fencing is a complex sport, yet all of the core actions were explained in just a few paragraphs. In the science literature, emergence can only arise when interactions are present and there is a complex energy landscape. Interactions are inherent in the basic rules of the sport and a complex energy landscape is present due to the physical and mental energy input of the two fencers. Throughout the course of the match there is a gradient of exertion, sometimes the fencing is slow other times it is lightning fast.

From these interactions and energy arises the tactical wheel. The tactical wheel is the expected progression of a fencing phrase. From the simple actions above we get the following wheel (using the full language of fencing): simple attack, parry and riposte, compound attack, counter attack/attack in preparation, counter time, feint in temp, and back to simple attack.

This wheel is the optimized order that events occur in a complex set of fencing actions, the wheel is of course often broken but the first three or four steps can be reliably seen in most complex phrases. To reiterate, the wheel emerged out of the above actions and is only explained to fencers after they have the groundwork and have experienced the tactical wheel. It is a consequence of the system and not designed into it.

For a slower look at olympic fencing see this video filmed with high speed cameras.