Adding to Zakwayda's comment, designing "algorithms" for pretty curly flight paths is a mostly quantitative matter.

Assuming a physically sound dynamic model in which the missile accelerates and turns according to the wishes of the missile AI (as opposed to arbitrarily interpolating position along a path) you need to find a balance of obvious parameters and mechanisms that makes the missile chase the target, but not too well:

• maximum velocity (as an objective: the missile needs to be faster than the target to hit, excessive speed leads to overshooting dodging targets, which is probably something you want in moderation, and to increased turning radius, which might become too large for the scale of the available space)
• maximum acceleration and deceleration, which might be different
• maximum torque, which influences turning radius
• delay between launching the missile and beginning to steer it
• choosing new values of acceleration and torque at intervals instead of every frame (ensuring nice curves are executed undistorted, and that aiming degrades)