# Reply To: How do spatial multipliers work?

#1850

The probability of a fire crossing a fuelbreak will depend on a number of factors inluding:

1. The configuration of the fuel break and how it relates to the surrounding cells and their probabilities for fire
2. The ultimate length of the fire perimeter that abuts against the fuel break, a longer perimeter means that there are more opportunities for crossing
3. Whether you are using direction and or slope multipliers and the relation of the fuel break to the fire source with respect to these.

In the example you give, assuming the fire is a single pixel in size and it is trying to grow by a single pixel only, that all cells surrounding that pixel are equal aside from the fuel break, and that three/eight fuel break cells are adjacent to the source cell, the probability of the fire crossing the fuel break will be:

[the sum over fuel break neighbors (relative probability/relative distance from source)]

divided by

[the sum over all neighbors﻿ (relative probability/relative distance from source)] where the relative probability for 3 fuel break cells is 0.1 and 1 for 5 other cells, relative distance is 1 for horizontal/vertical neighbors and the square root of 2 for diagonal neighbors.  In this case the probability of a fuel break cell burning is 0.05186.