Transformation

 Pattern transformation is a systematic examination of how patterns might change. The results of this examination are collections of related patterns called transformational groupings.  Transformational groupings provide pattern interpretations with a broader context, and greater coherence. 

 There are only three transformations in the ADEPT LION pattern language, and the third is simply a serial application of the first two. They are called inversion, aversion and involution. 

Systematizing an examination of these transformation of channel inputs requires a few symbols.  There are three options for the "input type" of any channel:

1. no-input, symbolized as "-"
2.  self-input, symbolized as "*"
3. other-input, symbolized as "\" or "/" (for another "other")

 Inversion is a switching of an occasion’s portion and extent inputs. In the first consideration, inversion means switching the occasion inputs of the thing (portion) and use (extent) channels.
 Although “switching” is one way to understand the effect of inversion, it is more properly understood as a transformational response to the other channel’s input type.  

 Whereas inversion is driven by the input type of the other channel, aversion is a transformational response that is motivated by the input type of the examined channel itself. 

  Aversion replaces a self-input with a no-input, and replaces a no-input with a self-input.  Other-inputs are unaffected by aversion.

 Involution is a serial application of aversion and inversion. The outcome of involution is not affected by the order in which these transformations are applied. 

  The term “involution” is chosen because it is commonly understood to be a function, that when applied twice, returns the original value. This is the case with involution of patterns. Involution of a pattern two times returns to the original pattern.  It is an expression in pattern of a duality.