Manhattan distance
Manhattan distance is a measure of the distance between two vertices used in computer go. It is determined as the number of horizontal and vertical steps one has to take to go from one stone to another.
For example, the diagram shows the path from to
. A Manhattan resident has to make 4 steps to get from one stone to another. The underlying geometry is called
taxicab geometry. (For more information read the book Taxicab Geometry by Eugene F. Krause, published by Dover in 1987. ISBN 0-486-25202-7.
Amazon)
An additional requirement can be set, demanding that the opponent's stones are never touched along the path.
(Sebastian:) But this would not be Manhattan distance anymore. Maybe Bronx distance?
Tas: Manhattan distance with traffic jams...
A "circle" is defined as the set of all points that have the same distance from a given point.
Fhayashi: Presumably, the name reflects the fact that in modern urban cities with orthogonal streets, regardless of the straight-line distance between two points, the practical distance is the number of block-sides you must transit to get to your destination...
Velobici: The concept is discussed on detail in the book Taxicab Geometry by Eugene Krause.
The Manhatten distance is between 2 stone on an empty board, but what is when the board is filled with enemy stones ?