I had been thinking about the exact same topic when I read this article, only I was using bus routes in my analogy. I created a quick program to simulate these dynamics[1].
It’s very simple, there is a grid of squares, let’s say 100 by 100, each square has some other square randomly assigned as its goal. Then I generate some paths via random walks until some fraction of squares are paths. Then I check what fraction of squares are connected to their goal via a path.
Doing this we get the following s-curve:
The y-axis shows the fraction of squares that are able to reach their goal. The x-axis is what fraction of squares were turned into path squares[2].
We can see what we probably expected, the first few paths do almost nothing but eventually each additional path has a large payoff.
The path length determines how long each random walk is. Long walks tend to create blobs of path. This is good if there are very few paths, you might get lucky and connect a couple of squares to their goals. But once there are lots of paths just turning random squares into paths is actually better.
To make the situation a bit more realistic I also simulated what happens if all generated paths are straight.
The yellow graph hasn’t changed but the longer paths are now more efficient and are never beaten by the totally random paths. These two maps show the difference, clearly the top approach would work better.
I also have to add that I find the idea that a cyclist wouldn’t cycle on a road absurd. I don’t think I know a single person who wouldn’t do this, presumably a US vs EU thing.
To be connected to its goal a square and its goal don’t have to be paths themselves just directly adjacent to a path connecting both. This is the reason the plots can go above the 45° line.
I also have to add that I find the idea that a cyclist wouldn’t cycle on a road absurd. I don’t think I know a single person who wouldn’t do this, presumably a US vs EU thing.
You mean the “No Way No How” group? If so, yeah, it feels implausible to me as well. I have a feeling that for people who were surveyed and said this, it wouldn’t match their actual behavior if they were able to experience an area with genuinely calm roads.
I had been thinking about the exact same topic when I read this article, only I was using bus routes in my analogy. I created a quick program to simulate these dynamics[1].
It’s very simple, there is a grid of squares, let’s say 100 by 100, each square has some other square randomly assigned as its goal. Then I generate some paths via random walks until some fraction of squares are paths. Then I check what fraction of squares are connected to their goal via a path.
Doing this we get the following s-curve:
The y-axis shows the fraction of squares that are able to reach their goal. The x-axis is what fraction of squares were turned into path squares[2].
We can see what we probably expected, the first few paths do almost nothing but eventually each additional path has a large payoff.
The path length determines how long each random walk is. Long walks tend to create blobs of path. This is good if there are very few paths, you might get lucky and connect a couple of squares to their goals. But once there are lots of paths just turning random squares into paths is actually better.
To make the situation a bit more realistic I also simulated what happens if all generated paths are straight.
The yellow graph hasn’t changed but the longer paths are now more efficient and are never beaten by the totally random paths. These two maps show the difference, clearly the top approach would work better.
I also have to add that I find the idea that a cyclist wouldn’t cycle on a road absurd. I don’t think I know a single person who wouldn’t do this, presumably a US vs EU thing.
Code is here.
To be connected to its goal a square and its goal don’t have to be paths themselves just directly adjacent to a path connecting both. This is the reason the plots can go above the 45° line.
Cool simulation!
You mean the “No Way No How” group? If so, yeah, it feels implausible to me as well. I have a feeling that for people who were surveyed and said this, it wouldn’t match their actual behavior if they were able to experience an area with genuinely calm roads.