Belt Balancer Problem (Factorio)
Answer : UTU = Universally throughput unlimited There exist UTU balancers for 3, 4, and 5 belts, and likely for any number of belts . Examples are given in this Jupyter notebook, along with a Python implementation of an iterative algorithm for computing the flow for any set of belts and splitters . I will quote some of the notebook here for those who don't wish to follow the link. I refer to splitters as junctions, since that's how they really function. Each belt is composed of unit length segments, referred to in the game as tiles. In the model, we imagine each belt flowing from left to right along coordinate direction x x x and each junction uniting two belts at the left edge of a given tile. Note that some balancers used in practice contain loops and could not be represented by our model without an infinite length belt. The state of a belt tile is represented by a density 0 ≤ ρ ≤ 1 0 \le \rho \le 1 0 ≤ ρ ≤ 1 and a velocity 0 ≤ v ≤ 1 0 \le v \le 1 0 ≤ v ≤ 1 . T...