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I will simplify my question to be better understood. Let's suppose my study area is consisted by settlements A and B. They both have the same population (1000 people each). Each settlement was converted to raster and then to point. Let's assume that each settlement has 100 points (each point corresponds to 10 people therefore a population field was added and filled up). The maximum radius of the walking distance is 3000 meters. Location 2 is accessible by many points from A and many from B (e.g. 100), location 1 is accessible by many from A and few from B (e.g. 60) and location 3 is accessible by none from A and many from B (e.g. 40). I want to show a raster output (visually similar to a density map) where each cell is assigned a value that corresponds to the number of points that can access it in a radius of 3000 meters.

In reality the shape of the settlements is complex and the population is different. The question is "accessibility" and I initially thought I wanted a "point density" output but I realized it doesn't show what I want. Are you aware of any tool that would help in this regard?

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If I understand your data corectly this might work. Assuming that you have a point shape file with each point, anywhere on your model, stands for 10 people. Than you might want to create a "grid" of polygons using the fishnet tool. Then you can create a buffer with the 3,000 meters for your grid (do not dissolve your output). At this point it would be best to use your settlment raster, if each cell can stand for population, than Zonal Statistics can sum the population value for each buffer, which stemmed from your grid (This should give a raster).

Otherwise, you can use model builder to iterate on the rows on your buffer shape file; For each row you should use select by location the points that are contained in the buffer, than summarize the selected feature, either by summing the population values, or by 10 times counr (if each point stands for 10 people). Than you can join the buffer table back to its original fishnet grid (likely with ID has the PK and FK), and rasterize the grid. Use the statistics field to give values for raster cells.

Both methods should work, the first one would be easier and faster, if you can arrange a raster data as described. Good Luck

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