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Nearest

Nearest[{elem₁, elem₂, ...}, x]
gives the list of elem_i to which x is nearest.

Nearest[{elem₁->v₁, elem₂->v₂, ...}, x]
gives the v_i corresponding to the elem_i to which x is nearest.

Nearest[{elem₁, elem₂, ...}->{v₁, v₂, ...}, x]
gives the same result.

Nearest[{elem₁, elem₂, ...}->Automatic, x]
takes the v_i to be successive integers i.

Nearest[data, x, n]
gives the n nearest elem_i to x.

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

MORE INFORMATION

If the elem_i 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

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Basic Examples (3)

Find the element nearest to 20:

Find the 3 elements nearest to 20:

Find which element is nearest to {2, 3} 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 {2, 3} in 2D:

In[1]:=

Out[1]=

Find "nearest" strings:

In[1]:=

Out[1]=

Applications (6)

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:

Neat Examples (1)

Find successive nearest words in a dictionary: