This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# Nearest

 Nearestgives the list of to which x is nearest. Nearestgives the corresponding to the to which x is nearest. Nearestgives the same result. Nearest[{elem1, elem2, ...}->Automatic, x]takes the to be successive integers i. Nearestgives the n nearest to x. Nearest[data]generates a NearestFunction[...] which can be applied repeatedly to different x.
• If the are vectors or matrices of numbers, Nearest by default in effect uses the metric Norm[#1-#2]&.
• For strings, Nearest by default uses the edit distance metric.
• The following option can be given:
 DistanceFunction Automatic the distance metric to use
• When several elements are returned, the nearest ones are given first.
• If several elements are at the same distance, they are returned in the order they appear in data.
Find the element nearest to 20:
Find the 3 elements nearest to 20:
Find which element is nearest to in 2D:
Find "nearest" strings:
Find the element nearest to 20:
 Out[1]=
Find the 3 elements nearest to 20:
 Out[2]=

Find which element is nearest to in 2D:
 Out[1]=

Find "nearest" strings:
 Out[1]=
 Out[2]=
 Applications   (7)
Create a Voronoi diagram:
Use higher resolution:
Use a -norm ("taxicab distance"):
Highlight the 200 random points closest to the origin:
Use the "taxicab" metric:
Create a nearest function from all the words in a dictionary:
Look up words closest to a given word:
Go further:
Find the outputs from running a sequence of elementary cellular automata:
Generate a complete list of outputs from all 256 elementary cellular automata:
Find which rules give outputs nearest the specified sequences:
Use a negative distance function to find the element farthest away from the given element:
Show the returned element for all values between 1 and 5:
Find successive nearest words in a dictionary:
New in 6