Someone close to my heart has a marvellous system for walking round London.
She invented it herself, although I'd be interested to know if anyone else is a follower of this methodology.
Essentially, you pick a direction for your walk, then decide whether you're going to go left then right at every junction, or, alternatively, right then left.
Then you stick to it.
That would be a simple 'diagonal' through the London streets, except for the variables ...
You have to stay on your original side of the road (ie. you cannot cross the road in order to take a turning) except when you see a zebra crossing (in which case, you must cross the road, if you are waiting to turn in that particular direction). Example below:
At crossroads with traffic lights, a similar lighting rule applies - you can only effect a right or left turn if the green man allows it. If, for example, you want to go right, but the first green man showing is for straight ahead, then you carry on in a straight line.
It swiftly becomes a peculiar, semi-random trawl through London, effecting divergent walking results.
(You are allowed to reverse out of dead-ends; and, no, you don't have to walk backwards, although it might make it more interesting.)
I am almost tempted to start a Left/Right London Walking Club; there would have to be a splinter-group for Right/Left, which I don't really favour.
It would need a better name.
The Almost Random Walking Club?