Lonely Planet recently published a Guide to Experimental Travel. The idea is to travel somewhere, and take a surreal approach to exploring a new place, by taking an alternative idea to route selection. In theory, this means that you might stumble across some typical touristy-type things, but you will also experience sides of the city / place / country that you wouldn't discover otherwise.
Alphatourism, for example, would be to take a street-map of the city or place you are visiting, and finding the first and last street in the index. Draw a straight line between them, and you have your route. Take a whole day to move from A to B (or A to Z, as the case is most likely to be), and take in as much of your surroundings as you can. In London, that makes for a 10-mile trek from Abbess Close south of the Thames river to Zoffany Street in the north of the street. (see the Google Map of the route here: http://kamps.org/g/?rpsg)
Alternative ways include using dice to select a series of map grid reference on your map, and travelling along the route mapped out that way, or a variant hereof, Monopoly tourism. Participants armed with the local version of a Monopoly game board explore a city at the whim of a dice roll, shuttling between elegant shopping areas and the local water plant - with the occasional visit to jail.
Another way of going about it is to buy a very old guide-book to a city (think 1970s), and see how many places you can get to, and how many of the old eateries are still available.
The most unusual invention might be erotourism, where a couple heads to the same town but travels there separately. The challenge is to find one another abroad, preferably in a country where neither one speaks the language, and where the meeting point is only vaguely set.
In short, the ultimate goal for Experimental tourism is to do the exact opposite from the "Da Vinci Code" tourism that has been surfacing recently, where you follow a tour guide around to places mentioned in the abysmal Dan Brown book.