The perimeter fence played a big rule in the television show, it is what protected the colonists from the alien wildlife. The perimeter was setup through individual posts that would be planted in the ground and activated from a mobile device. The individual posts connected with each other and created an invisible boundary that when touched would shock you.
I wondered what a possible algorithm would be for setting up a fence system such as this, so the first problem is the actual perimeter construction. So something that came to mind was the concept of the convex hull and the gift-wrapping(jarvis walk) algorithm. The second problem that came up was I needed a way to find the left most point or fence post as the assumption is that each fence post does not really know where it is relative to the other points. So the antidote to this problem was I needed a fence post that was different from the rest so I created the Genesis Post.
When placing the Genesis Post we create a cartesian plane with the post as the origin point. When placing the other posts we can calculate their position relative to the Genesis Post and this we way we can find the leftmost point for the gift-wrapping algorithm.
Here we can the genesis point in action, it is the top most point and the lines going through it represent the x and y axis of the plane. The convex hull/perimeter that is created bu the fence posts can be seen by the lines connecting the points.
The convex hull calculation also allows us to apply some optimizations with the fence perimeter allowing us to use the minimum number of fence posts.
We placed a fence post to the right and further down, but since the older points are no longer on the convex hull we can remove them and still have a valid perimeter.
The concept for the algorithm should work, but of course their would be some hardware limitations, we might need to add some extra logic to ensure that the the posts are within some distance between them. Every post will also need to have some sort of memory and processing component as the genesis post will need to do some processing to setup the cartesian plane and be able to store information about itself. The mobile device for enabling the perimeter fence will do most of the heavy lifting and then send out the necessary information to the individual posts. There might also be some issues to ensure the distributed computation actually works. Besides that there is also the obvious issue with the invisible electrical field that shocks anything that comes close, I'm not aware that something like this exists, but maybe this could be useful one day.