Two alternative tube maps (more here).
“It occurred to me that it might be possible to tidy up the map by straightening the lines, evening out the distance between stations. The more I thought about it, the more I thought it was worth trying.”—Harry Beck
This grid of dots is topologically equivalent to the London Underground map. Every station is exactly 1 unit away from four other stations. By necessity, these aren’t often the stations which are actually connected to it, but I have tried to make all the interconnections as short as possible. Naturally, no interconnection passes through a false grid point on the way.
The London Underground map, rearranged so that South London gets most of the stations. The lines and river are identical to the real Tube map, but rotated so that Castelnau exchanges places with the Isle of Dogs: the axis of the river’s rotational symmetry passes roughly through the London Eye.
It has been pointed out that Kew Gardens and Silvertown stations can be found one from each end of the North (South?) London Line in both this and the real map, which is a nice coincidence.
A similar, independently conceived map was published in the Evening Standard in December 2004, but it didn’t rotate the river.
2013 update: Since this was posted, there have been a few changes. The South (North?) London and West (East) London Lines are now part of the Overground. Kew Gardens and Kew Pier stations have closed forever, but the Surrey Light Railway has been extended via West Kew Gardens and King George III to a new station at Brentford 0-1 Arsenal, where it will meet the south-western branch of Crossrail in 2029 or thereabouts.