BUILT-IN MATHEMATICA SYMBOL

Nearest

gives the list of

to which x is nearest.

Nearest

gives the

corresponding to the

to which x is nearest.

Nearest

gives the same result.

Nearest[{elem₁, elem₂, ...}->Automatic, x]
takes the

to be successive integers i.

Nearest

gives the n nearest

to x.

Nearest[data]
generates a NearestFunction[...] which can be applied repeatedly to different x.

MORE INFORMATION

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.

EXAMPLES

CLOSE ALL

Basic Examples (3)

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:

In[1]:=

Out[1]=

Find the 3 elements nearest to 20:

In[2]:=

Out[2]=

Find which element is nearest to

in 2D:

In[1]:=

Out[1]=

Find "nearest" strings:

In[1]:=

Out[1]=

In[2]:=

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:

Neat Examples (1)

Find successive nearest words in a dictionary: