Symmetry

rotationalSymmetry

Computes the order of rotational symmetry, the number >= 1 of rotations in which a circular sequence looks exactly the same.

Example

Seq(0, 1, 2, 0, 1, 2).rotationalSymmetry // 2

symmetryIndices

Finds the indices of each element of a circular sequence close to an axis of reflectional symmetry, that is a line of symmetry that splits the sequence in two identical halves.

Example

Seq(2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2).symmetryIndices // List(1, 4, 7, 10)

symmetry

Computes the order of reflectional (mirror) symmetry, the number >= 0 of reflections in which a circular sequence looks exactly the same.

Example

Seq(2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2).symmetry // 4