Im a plant loving guy, so when bored I think about my future fantasy garden in much the same way young girls plan out their weddings by age 7. Being a math guy, Im interested in seeing how I can make this garden as badass as possible. Life's just one giant nonlinear programming problem for maximizing awesome.
Now when I go to a garden, I try to find a path through it that covers as much of it as possible without needlessly repeating parts of the path (as eularian as possible). This helps me see as much of the garden as possible. Sometimes this isnt possible. U of Illinois's Allerton park is a arranged mostly in a line and in no fun to walk through. To see it all and get back to your car, you have to walk through the entire park twice. Dead ends are espcially annoying, my ideal garden wont have those.
Gardens that have even degree intersections are easy to find a path for. Its just a mathematical fact, so Ill use odd degree intersections. 5 paths convering to one spot seems a bit too much so ill keep it to 3 paths for all intersections. After much thought, I came up with the diagram below:
Each one of the circles is a modular unit that i can tack on as i please. This is my ideal garden. Walkng through it leasurely wont show you the entire thing, enticing you to come back later.
Its interesting to think about how travesibility might be used in the design of public spaces, both real and virtual. Shopping centers are easy to traverse and have many even degree paths, but zoos are much harder to go through in that way. I think some games would benefit by having harder to traverse levels, They make less space feel like more and would increase the amount af playability. The real key is to not tick people off, which i think ive done in my garden plans.