Information and termination

The issue of termination has recently re-emerged as a result of new approaches to design generation, which link termination to user intervention. The similarities between this approach to termination and the conventional creative artistic process suggest that the product of the generative system is amenable to analysis in terms of well-formedness. A formal measure of well-formedness could be employed as an automatic termination trigger. The paper proposes that such a measure can be derived from structural information theory. By applying the compression of structural information theory to meaningful principles of a design world we derive a consistent, universal description of the design result at any given state. This description expresses the correlation of the design with its formal constraints, as well as the general perception of the design’s patterns. The combination of the amount of structural information in the design’s code and the presence of specific (sub)patterns in the same code arguably provide the triggers for termination of a generative process. 1. Generation and termination One of the fundamental problems in computational generative systems is termination. This refers to the ability a system to determine when the generative process can conclude with a satisfactory result. The issue has been explored in the framework of formal systems such as shape grammars [1-3]. In such systems termination preferably occurs on the basis of some cues produced by the generative process itself. Consequently, termination has considered in relation to the design process (i.e. the completeness of a sequence of design actions or steps) and the design product (i.e. the fitness of the product with respect to a given framework). Recently the issue of termination is re-emerging as a result of renewed interest in automated and autonomous design generation [4, 5]. In recent generative systems termination is a matter of user intervention: the generative system concludes when the user chooses it to do so, normally of the basis of intuitive criteria relating to the state of the process (usually appreciation of the appearance or structure of the design product). What makes interactive termination interesting is that it provides a context for the formalized heuristics that characterize earlier approaches. Rather than attempt to extract and formalize incomplete cues, improvised strategies and local conditions, interactive termination reestablishes the human designer as the measure of his products and as guide of his own processes. This is essentially similar to the conventional creative artistic process, where the artist’s work may be subject to external pragmatic constraints such as medium, time or money but ultimately remains a matter of personal (aesthetic) appreciation. Acceptance of the working hypothesis that this appreciation is the cornerstone of termination means that the products of a generative system can be analysed and evaluated in terms of well-formedness. Well-formedness can be defined in terms of a number of components: 1. A formal representation for describing a class of entities 2. A given context that provides constraints for the entities and their description 3. A matching system for correlating descriptions of entities to a formal framework of constraints Well-formedness is not merely the product of the matching system. The derivation of a description is subject to formal rules that provide direct measures of consistency and coherence. An entity that is poorly described is by definition undefined and hence vague in terms of appreciation. Contextual constraints are similarly considered in terms of homogeneity and completeness. In the intuitive processes relating to the evaluation of well-formedness such evaluations relate to understanding the context of an artifact and their interrelationships. In the framework of the visual arts and design disciplines perception plays a central role in all components. Acceptance of perception as the basis of well-formedness and by extension aesthetic appreciation, we adopt an inter-subjective model of aesthetic appreciation which stresses the cognitive similarities that exist between different persons and cultures [6]. Intersubjectivity also allows us to correlate different aesthetic approaches. This is largely due to the reason for such cognitive similarities, the organization of perceptual information. Gestalt psychologists have formulated a number of principles (or ‘laws’), such as proximity, equality, closure and continuation, which underlie the derivation of a description from a percept by determining the grouping of its parts [7-9]. Probably the most important and certainly the most mysterious of the Gestalt principles of perceptual organization is Prägnanz or figural goodness which refers to subjective feelings of simplicity, regularity, stability, balance, order, harmony and homogeneity that arise when a figure is perceived. Figural goodness ultimately determines the best possible organization of image parts under the prevailing conditions. As a result, it is normally equated to preference for the simplest structure. The principle is seen as the basis for preferring one out of several possible alternative descriptions of a percept. The view of perception as information processing has led to attempts to formulate figural goodness more precisely. Given the capacity limitations of the perceptual system and the consequent necessity of minimization, it has been assumed that the less information a figure contains (i.e. the more redundant it is), the more efficiently it could be processed by the perceptual system and stored in memory [10, 11]. Palmer’s model of invariance under transformation is similarly motivated [12]. With respect to our subject such attempts promise formal structures and measures for evaluating the well-formedness of a design product throughout the design process. Such measures describe the design product by itself, as well as in relation to its context, in a similar way that an artist appreciates his work by its own merits and by fitness to its purpose or function. In the framework of generative systems this can be translated into descriptive, analytical structures that provide automatic triggers for the termination of the generative process in a transparent manner, i.e. together with an explanation of why termination is acceptable to the system and its user. 2. Structural information theory Arguably the best model in this direction is Leeuwenberg’s coding or structural information theory [13, 14]. According to Leeuwenberg a pattern is described in terms of an alphabet of atomic primitive types, such as straight-line segments and angles at which the segments meet. This description (the primitive code) carries an amount of structural information (I) that is equal to the number of elements (i.e., instances of the primitives) it contains. The structural information of the primitive code is subsequently minimized by repeatedly and progressively transforming the primitive code on the basis of a limited number of coding operations: iteration, by which the patterns a a a a a a b b b b b b (I = 12) a b a b a b a b a b a b (I = 12) become respectively 6 * [(a) (b)] (I = 3) 6 * [(a b)] (I = 3) reversal, denoted by r [. ]: a b c = r [c b a] (I= 3) Reversal allows the description of symmetrical patterns ( ): a b c c b a = a b c r [a b c] = [a b c] (I = 4) a b c b a = a b c r [ a b] = [a b (c)] (I = 4) distribution: a b a c = <(a)> <(b) (c)> (I = 3) continuation ( . ), which halts if another element or an already encoded element is encountered: a a a a a a a . a = a (I = 1) The coding process returns the end code, a code whose structural information cannot be further reduced. The structural information (I) of a pattern is that of its end code. Figure 1. Coding of square: a b a b a b a b = a b (I = 2) The structural information of a pattern is a powerful measure of its figural goodness. By equating a figure’s goodness with the parametric complexity of the code required to generate it we can both derive the different descriptions an image affords and choose the one(s) that contain the least information. Especially in situations where two or more descriptions are equally acceptable to the human perceiver, as in the Necker cube illusion, measurement of structural information clearly demonstrates that the preferred descriptions are normally equally compact. This suggest that structural information theory is particularly suited to untangling complex, overlapping or intertwined patterns, i.e. situations which are amenable to evaluations of figural goodness by e.g. invariance under geometric transformations only following an initial analysis which segments and disambiguates the image. 3. Well-formedness and structural information in visual designs The application of structural information measures to the evaluation of well-formedness in visual designs involves a number of fundamental conceptual problems: Avoidance of aesthetic bias: The compression rules employed for the derivation of the primitive and end codes may derive from universal perceptual constraints but their strong relationships to formal aesthetic systems and hence to the interpretation of a pattern pose serious questions concerning the structure, production and evaluation of a representation. For example, the ability to compress a code based on reversal and distribution relates to certain types of symmetry. These in turn may or may not be preferred in the context of a specific aesthetic system: Classicism encourages most if not all types of symmetry, while Modernism avoids bilateral symmetry but promotes translational symmetry. This does not suggest different coding systems for each aesthetic context but simply differences in the treatment of the resulting code (i.e. different matching priorities) and possibly in the order compression rules are applied. Changes in the order of application make one rule s