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====Heatmaps====
I build built '''unbuffered heatmaps using maximum R2 layers from 1995 to 2018''' for a set of "interesting" cities. I often built the same city at multiple scales. Only the zoomed-in maps are in the gallery below. I can now quite quickly build more cities if needed. It is worth noting the following:
*Because we are using unbuffered hulls, heatmap components are angular and non-diffuse.
*Agglomerations are smaller in cities with higher startup counts but are small everywhere.
File:Waltham65000MaxR2UnbufferedHeatmap.png| Waltham, MA, 1:65k
File:Boston50000MaxR2UnbufferedHeatmap.png| Boston, MA, 1:50k
</gallery>
 
I also built three buffered heatmaps of Boston as a proof of concept. I used either the average distance between the points on the edge of the hull and the centroid, or half of it, as a buffering distance. I also varied the intensity of the shading (down to 10% per layer from 20% in the 1:70000 image). Boston should have 17 agglomerations according to the maximum R2 method, so the half distance buffer might be best for picking them out.
 
<gallery widths=300 heights=300>
File:Boston70000MaxR2buffered1xHeatmap.png OK| Boston, MA, 1:70k, 1x buffer, 10% opacity
File:Boston50000MaxR2bufferedHalfxHeatmap.png OK| Boston, MA, 1:50k, 0.5x buffer, 20% opacity
File:Boston50000MaxR2buffered1xHeatmap.png OK| Boston, MA, 1:50k, 1x buffer, 20% opacity
</gallery>

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