Predicting the behavior of a simple system based on historical data

Question

Analytics

Good afternoon!

There is a desire to build an algorithm for predicting the future for one simple discrete system. I would like to try to predict the future based on the history of the behavior of this system in the past. I have absolutely no theory in this matter, therefore I hope for your help. Just advise where it makes sense to dig, some keywords, where to start the search.

To complete the context, I will describe my system.

There are several (12) numbered cells. Each cell can be in one of three states.
Regularly, after the same period of time, the states of the cells are simultaneously updated. In this case, the state may change, or it may remain the same.

There is a set of historical data on states. The goal of the desired algorithm is, based on this data, to try to predict the states of the cells at the next iteration.

I would be grateful for any target designation on the topic =).

Answer 1

For some reason, the phrase "regression analysis" immediately popped up in my head.
Also, maybe something like this will help.

Answer 2

Read In the Land of the Blind by Michael Flynn.

Answer 3

Some kind of AI algorithm. The same neural network: the current state is the output, N previous ones are the input.