# Connections

## Formula Modifiers

A Formula on a Resource Connection determines how many Resources may move through that Connection in a given time step.

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Formula Modifiers connect an origin Node to a target Formula [F] of a Resource Connection (or that of a State Connection) and indicate how State Changes in the origin Node [S] modify the current value of the target Formula, at a current Step [F(t)] as indicated by the State Connectionâ€™s own label [M].

The new value takes effect in the next Step [F(t+1)]. The amount of the change in the origin Node is multiplied by the Formula Modifierâ€™s own Formula

`F(t + 1) = F(t) + M Ã— âˆ†S`

ðŸ”§ Let’s take the example below. Play a Step. You have a Formula Modifier (M) that reads +3 and the origin Node (Pool S) increases by 2 (the rate at which the Resource Connection transfers Resources from Source A to Pool S). The Target Formula (F) has increased by 6 in the current time step (F(t)): it added 3 to F 2 times, once for each change in the origin Node. So, in F(t+1) (play another Step), the Resource Connection corresponding to F, will transfer 7 (6+1) Resources to Pool C.

If the Formula is the Target of multiple Formula Modifiers, you will have to take the sum of all changes to find the new value: `F(t + 1) = F(t) + âˆ‘( M Ã— S )`

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The Formula of a Formula Modifier always starts with a + or – symbol.

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