Counterchange

In broad terms, a counterchange can be described as a "switchover" of motifs as read from left to right or vice versa or top to bottom or vice versa. Such a concept is more readily viewed than described, with examples shown below.

Essentially, "counterchange" can be regarded as an optional, "additional" stage of a tessellation. Upon the completion of the finished example, it is then possible to utilise this, in essence following Escher�s advice in Regalmatige Vlakverdeling (translated in Escher The Complete Graphic Work) ". . . do something, come out of there and show me what you are capable of!" Some examples of his counterchanges can be found in the above book, plates III, IV and V, between pages 170 and 175.

Now, the "intricacies" of counterchange are somewhat involved, and indeed could be the subject of a whole book. Regrettably, very little information is available on this matter, with the background to Escher�s examples being unpublished. Nonetheless, a counterchange can be applied to any tessellation, albeit some are more suited than others. For example, in a "horizontal" format (as with No.1 below), a same orientation motif is ideal, as when viewed as intended (as outlined above) the outcome is sensible, with the birds remaining in the same orientation. In contrast to this, an example whereby some of the motifs fly upside down would be out of place in an aesthetic sense. Therefore, an "appropriate" tessellation must be chosen beforehand.

(view left to right)

No.1

(view top to bottom)

No.2

(view top to bottom)

No.3