Calculate Value Along Raster from Points/Polygons

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I am looking to calculate outward from a series of points in order to create buffers for points and polygons. The example below will create a raster with a point in the middle. What I am asking is how would I look from the point outward until the summed value in the all directions is ten. Once those values are foundI would like to put a polygon around them. Effectively I would like to add the cells from the point outward until a value of 10 is achieved.

This will allow for the creation of non-uniform buffers based on environmental information rather than setting an arbitrary buffer around a polygon.

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