2018.6.18 Massachusetts municipalities: degrees of separation

Big surprise, it's another map of Massachusetts! Wait, actually it's... a whole mess of maps of Massachusetts. These are explorations of degrees of separation, by adjacency of municipalities, from various starting points or edges. For these maps I've only provided small versions without municipality names shown; if you want to see the names, you can compare these with one of my other MA maps. Note that there are quite likely some mistakes in these.

Let's look at the map with Provincetown as the starting point to get the general idea:

The rules are simple. The starting town (if any) is colored white. (So are the island towns, since it's less obvious to define adjacency with them, though on further inspection I guess water boundaries actually allow it — maybe I'll revise these to include the islands at some point. Though including all water boundaries would change the mainland towns as well; for instance, Winthrop and Nahant share a water border, whereas they're 3 towns away from each other by land.) (I also generally left small partly-mainland-town islands white to save a bit of time. Need to make a template map with all the islands of coastal towns grouped together with their mainlands.) Anyway: Every town bordering the start town is colored yellow. Every town bordering those towns is colored red. This iterates through eggplant, blue, cyan, and... pistachio I guess? Then it cycles back to yellow. I find this color set provides highly visible contrast and also lets you get a pretty quick degree-of-separation number for any given town — just count up the number of pistachio bands between the start and the town to calculate the number for (inclusive of the town's own band if it's pistachio), multiply that number by 6, and then count the remaining color bands out to that town.

For example, most of the towns on the western edge of MA are 36 towns away from Provincetown, as they're in the 6th pistachio band away from it. Since P'town is way out on the end of the Cape, it provides the highest possible degree of separation from other towns.

One interesting facet of this system is that unusually-shaped towns (ones with appendages, or ones that are unusually small or large) can cause a ripple effect, as it were, in the shapes of the bands, by causing a corresponding convexity or concavity, though these tend to get smoothed out further out. For instance, in the P'town map, since Middleborough is so big and has a northwestern "ear," it gives a sharp angle to the following SE MA bands.

Here's a map starting at Mt. Washington, at the other end of the state:

Note that Provincetown is 36 towns away from Mt. Washington, matching their separation in the P'town map. Sometimes you get enclaves of more separated towns within a ring of less separated ones, such as Malden and Melrose here.

I made several more maps starting at towns, e.g. endpoint towns such as Williamstown, Salisbury, and Westport, plus Boston and Worcester, but I think more interesting to see are the maps of towns by separation from adjacent states. Going counterclockwise, we can start with New Hampshire:

Since NH and MA share a long border, there are a lot of towns relatively close to NH. But P'town is still 24 towns away. Bourne is the only connector of the Cape to the rest of the state, and e.g. Provincetown is 10 towns away from Bourne, so the Cape towns tend to have much higher separation numbers than others.

Here's the Vermont map:

P'town is 30 towns away from VT. Interesting how it keeps showing up in multiples of 6.

New York:

Connecticut:

Interesting little nucleus around Rowe & Monroe. This exists because the Quabbin towns are extra-long north–south, e.g. New Salem and Petersham, since they include land annexed from the towns drowned by the reservoir. Hence they cause a channel of reduced separation up to the northern border, which itself separates the Rowe/Monroe area from the northeastern towns of equal separation from CT.

Rhode Island:

In addition, I tried mapping degrees of separation from any adjacent state:

Similarly to the Connecticut map, the Quabbin towns form a corridor of reduced separation, causing a western nucleus of greater separation at Northampton and Hatfield.

For good measure, here's a map for number of towns away from the ocean (so coastal towns count as 1 away, analogous to the state-line towns in the state maps above):

One thing you can see here is how large in area Plymouth, Dartmouth, Westport, Ipswich etc. are compared to the small cities around Boston; and this also shows that there are no landlocked towns on the Cape. I also colored the island towns here since likewise all of them are coastal, none landlocked. Essex, Braintree, and Acushnet look potentially coastal, but each of them is separated from the ocean by a boundary between two other towns, either a land boundary or one along a narrow waterway.

Finally, I combined the all-states and ocean maps into an all-edges map:

Here there are a few separation-nuclei: the Northampton-Hatfield one again; one centered around Marlborough; and a secondary one at East and West Bridgewater. Note that every municipality is at most 5 towns away from the ocean or a different state. OK that's it!