Node Modifier

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Node Modifiers are State Connections that connect two nodes. They indicate how state changes of the source node (dS) modify the number of resources on the target node (N) as indicated by the modifier's label (M). The state changes to the target node are further processed during the subsequent time step. Thus, the new number of resources on a node that is the target of a number (n) of node modifiers is given by the following formula:

N(t+1) = N(t) + Sum(M*dS)

The figure below illustrates a node with two modifiers. By using negative node modifiers or redistributing resources from a node that has positive input node modifiers it becomes possible that the number of resources on a node becomes negative. In this case, the negative number of resources indicates a shortage. No resources can be pulled from a node that has a shortage, and resources that flow into a node with a shortage are used to compensate for the shortage first.

Node modifier can have labels that are fractions, for example '+1/3' or '-2/4'. In this case the number of resources of a target node is modified by the value indicated by the fraction's numerator every time there is a change to the number resources on the source divided by the fraction's denominator and rounded down. Thus when a source node changes from 7 to 8, the number of resources on the target is lowered by 2 if the modifier is -2/4, but if the modifier is +1/3 the number of resources on the target node does not change.

A simple, real-life example of the use of node modifiers can be found in Settlers of Catan where players gain 1 point for every village in their possession and 2 points for every city in their possession:

Node modifiers change the number of resources on other nodes. In effect, the use of node modifiers causes production or consumption of resources. These effects can also be achieved with a slightly more elaborate, but also somewhat cumbersome construction (see Node Modifier Equivalent). This construction includes other elements that are introduced later. However, as the use of node modifiers is quite common, they are useful 'syntactic sugar': simpler notations of more elaborate constructions. For this reason node modifiers are here treated as a particular type of state modifiers.