I'm creating a simple top down shooter, right now I have an enemy which simply follows the player. I'd like to change things up and have the enemies move towards the player but in a wave like motion. I have looked at some similar questions like this but they don't take into account for the Y changing. How can I simulate a wave like pattern for my enemies whilst they are homing into their target.

Edit:

Sample code

In my update method I have the following:

            Vector2 trackingPos = position - target;
            trackingPos.Normalize();
            position -= trackingPos * elaspedTime  * speed;