Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 ArrayRotations

Source Notebook

Get the rotations and reflections of an array

Contributed by: Ed Pegg Jr

ResourceFunction["ArrayRotations"][array]

returns the eight rotations and reflections of the given 2D array.

ResourceFunction["ArrayRotations"][array,False]

returns the four rotations only.

Details

Starting with a general array (for example ), rotations Rdegree and reflections Mmirror are returned in the following order:
R0Identity
R90Transpose + Reverse rows
R180Reverse both rows and columns
R270Transpose + Reverse columns
MATranspose + Reverse both (Antidiagonal mirror)
MHReverse rows (Horizonal mirror)
MDTranspose (Diagonal mirror)
MVReverse columns (Vertical mirror)

Examples

Basic Examples (3) 

The eight rotations and reflections of an array:

In[1]:=
basic = ResourceFunction[ "ArrayRotations"][{{1, 1, 0}, {0, 0, 0}, {0, 0, 0}}]
Out[1]=

Images of the returned arrays:

In[2]:=
ArrayPlot[#, PixelConstrained -> 20] & /@ basic
Out[2]=

Show only the rotations:

In[3]:=
rots = ResourceFunction[ "ArrayRotations"][{{1, 1, 0}, {0, 0, 0}, {0, 0, 0}}, False]
Out[3]=
In[4]:=
ArrayPlot[#, PixelConstrained -> 20] & /@ rots
Out[4]=

Scope (3) 

Six different arrays:

In[5]:=
sixarrays = Permutations[{{1, 1, 0}, {0, 1, 1}, {0, 1, 0}}]; ArrayPlot[#, PixelConstrained -> 20] & /@ sixarrays
Out[5]=

A canonical form of each array under symmetry:

In[6]:=
canonicalsix = First[Sort[ResourceFunction["ArrayRotations"][#]]] & /@ sixarrays; ArrayPlot[#, PixelConstrained -> 20] & /@ canonicalsix
Out[6]=

A canonical form of each array using rotations only:

In[7]:=
canonicalsixrot = First[Sort[ResourceFunction["ArrayRotations"][#, False]]] & /@ sixarrays; ArrayPlot[#, PixelConstrained -> 20] & /@ canonicalsixrot
Out[7]=

Requirements

Wolfram Language 14.0 (January 2024) or above

Version History

  • 1.1.1 – 12 March 2025
  • 1.1.0 – 21 September 2021

Related Resources

License Information