## Posts Tagged 'topology'

### The Hunt for the Wumpus Goes On in My Apartment

Most of my writing is either done at a branch of the Richmond Public Library or in my office in my apartment. The apartment is fairly large as these things go: two bedrooms, a full living room and dining room, and a tiny room that’s pretty much useless for anything other than a study. It has a tiny balcony running along the front (not big enough for a chair, alas) and steps leading down to the ground floor. The picture below is a diagram of the apartment; I’ve simplified things, leaving out closets, not bothering to make the proportions exact, and so forth.

Different routes between rooms in an apartment based more or less on mine.

Note in the figure that I put a dot in each room (as well as the hallway, the balcony, and the stairs, which are proxy for the front door), along with red lines connecting pairs of dots. These lines are “direct” connections in a sense: to get from my office to the bedroom, you must pass through the landing area and the hall (and possibly also the bathroom). Alternately, you could go onto the balcony, go to the living room, dining room…but you still have to go into the hall, just at a different starting point. If we think of each room not as a room but a node in a network, we have the beginnings of another way to represent my apartment. If we don’t worry about the size and shape of each room, only about the basic path a person must take to travel around the place, we can replace the floor plan above with a graph, as shown below.

A graph of my apartment: somewhat more abstract than the picture above. The spatial relationships between the different rooms (nodes) are close to how they are on the floor plan, but the routes are drawn to connect them more directly, since the walls are gone.

The graph is useless for arranging furniture, but it’s a bit simpler than the floor plan: the arrangement of walls and doorways are gone, replaced simply with nodes. Possibly other houses and apartments might have the same graph, even if the floor plan is very different! If you think I’m heading toward topology, you’re right: as with the stretchy shapes and lack of concern about distances, our graph is unworried about how many steps between bed and toilet (as important as that may be at 2 AM). Continue reading ‘The Hunt for the Wumpus Goes On in My Apartment’