Followup to: Representation of structure, Phantom hierarchies of structure.
Structure waves only enter a property from instantiation point if it’s an unique match. As a result, only unambiguous properties get instantiated, and this leads to hierarchies of patterns. One property gets instantiated at multiple instantiation points, and property is usually considered to be a part of the scene, while instantiation points are embedded in the bulk of the scene. Even though such properties are represented in reduced form, the difference between explicit form of the scene and a form where all common properties get collapsed together is minor.
Structure waves don’t need to always start from the bulk of the scene, they can also start from a small property. In this case, they can only enter the scene if structure wave can unambiguously match a structural context of the scene in a context of the property. This works for rare or local properties that only apply at one point (with locality determined by the scene graph rather than spatially), or up to a certain depth for properties of big patterns in the scene (in which case a wave can exit the property and visit the whole pattern, even if it stops short of the whole scene). Also, given enough steps, structure wave could escape even patterns instantiated in multiple places.
Surprisingly, it also applies to small properties that can’t be visited from within the scene. These properties can’t be instantiated at any place in the scene, but structure waves starting from them can enter the scene. Considering such properties a part of the scene is equivalent to allowing multiple conflicting properties to be considered at one: a given interface in a scene will have multiple matching properties, so that choice between them is ambiguous, but each of the properties only matches this interface.
Following the terminology introduced for describing patterns, these ambiguous properties include instantiation points of their own that allow to instantiate the scene. Thus, implicitly, the whole scene gets instantiated multiple times, once for every alternative property.
This interpretation changes the perspective on what is represented. Where before the set of maps was supposed to only represent a single scene, restoring it with the knowledge of other scenes, now it can represent multiple alternative hypotheses about the structure of the scene. Reduced representation allows to represent not only a huge number of implicit details for a single scene, but also a huge number of implicit alternative scenes, by collapsing the repeated structures shared among alternative scenes as well as different areas of the scenes.
If alternative properties can only reach an intermediate pattern smaller than the whole scene, they specify alternative instances of that intermediate pattern. The intermediate pattern gets independently instantiated both by the scene and by the alternative properties. Context carried by structure waves can create biased versions of the intermediate pattern, specific to a certain property or instantiation point in the scene, and through these biased patterns some of the properties can find matching instantiation points in the scene, resolving ambiguity. For structure waves, there is no difference between alternative patterns that instantiate alternative structures of the same part of the scene, and different instantiation points in the scene itself.
