d2xyxiyi

d2xyxiyi is a notation encountered in discussions of coordinate-based string transformations, typically in puzzle design, teaching demonstrations, and light cryptography. In this context, it denotes a compact rule set for transforming data by applying a sequence of operations that are indexed by two axes and often involve a double shift. The name reflects the recurring tokens used in its examples: d2, x, y, and i, which are interpreted according to a defined local rule set.

The scheme operates on sequences drawn from a finite alphabet. A token such as d2 signals a double shift or a paired operation, while the letters x and y label two perpendicular axes along which the transformation is coordinated. The symbol i is commonly used to indicate inversion, indexing, or a reversible step within the process. A complete d2xyxiyi string is interpreted by parsing left to right and applying the corresponding operations to successive blocks of input data. Because the exact output depends on a defined rule table or key, a given d2xyxiyi string does not guarantee a unique result without that context.

In practice, d2xyxiyi is used as an educational example to illustrate how multi-step, coordinate-oriented rules can be composed to produce complex encodings from simple primitives. It serves as a teaching tool for concepts such as rule composition, reversibility, and the interaction of two-dimensional indexing with data transformations. The term is mainly encountered in informal writings and puzzle communities rather than in formal standards.

See also: encoding, cipher, puzzle notation, reversible transformations.