# The Science (and Math) of Heat Maps

Question asked by bp_spaulding on Oct 14, 2017
Latest reply on Oct 17, 2017 by Dan_Patterson

I'm trying to model the geographic benefit of city capital investments in parks.  Different kinds of park facilities have different service areas, and so I'm trying to model benefit by type of park, which means the benefit will extend outward different distances, depending on the type of park (playground, zoo, recreation center, etc).

So I've divided investments up by park type, and dropped a point at the center of each investment.  So for my example, I want to make a heat map of the areas that benefit from a single new recreation center.  Recreation centers in our city have a service area of a half-mile.  And I know how to make a heat map that would show a benefit that would be high near the rec center, and taper down to nothing a half mile out, but I’d like to go a step further.

I would like my heat map to accurately model the approximate benefit of that public investment per acre.  More specifically, I would like my map to work such that if you added together all the investment shown in the heat map I produce, in every impacted acre around the rec center, that sum would equal the total cost of that new rec center that was the initial point of input in creating that heat map.  Or to put the same idea a different way, I’m looking for a way to incorporate three-dimensional calculus in my heat map modeling, where we can know the sum of the total area under the three-dimensional curve represented on the heat map I produce is equal to the total value of the investment in the point in the middle that was the input.

But how?  And with what tool? (And in a perfect world, also looking to do the same around a linear facility, such as a recreation trail.  But I’d be happy just to get an answer to the first part!)

Thanks in advance for any help, or similar efforts you can point me toward, as I’m coming up dry so far, but very much doubt I’m the first to do this sort of analysis!