How to calculate a heat map of distance from roads in a city?

Question

Mathematics

On the map of the city I want to make a layer of distance from the roads.
For simplicity, we can assume that the influence of a point on the road falls off as the square of the distance. And only points within a radius of N hundreds of meters affect.
Any point on the map is affected by all points of the nearest roads. You can round: break the map into squares. Take % of the area of ​​the square occupied by roads, and so get the "weight" of this square. And take the distance from the center of the square to the next point of the heat map. Not a dot, but also a square.
Am I thinking in the right direction, or is there a better approach to this problem?

Answer 1

It all depends on the accuracy you want to get.
Most likely, you need to take into account not only the distance from the roads, but also the congestion of the road, i.e. conditionally there is the Moscow Ring Road from which it is better to live 7 kilometers or a small road at the entrance to the microdistrict for which 50 m is a normal distance. Also, if powerful traffic jams periodically occur on certain sections of the road, then the influence of such a road will be much stronger than that of a simply busy highway.
In addition, in the second step, you may want to take into account the fact that if there are natural or artificial obstacles between the road and the calculated point, then the influence of the road on this point is reduced based on the type of obstacle.
I would try like this:
If you compare the road with a current conductor and compare the road congestion with the strength of the current, then you can try to use these formulas:
https://www.chem-astu.ru/chair/study/physics-part2...
You just need to select the coefficients of the formula based on from the conditions of your task.
The conditional current strength is determined from the above factors.