Programmable Self-Assembly: Constructing Global Shape using Biologically-inspire

In this thesis I present a language for instructing a sheet of identically-programmed, flexible, autonomous agents (``cells'') to assemble themselves into a predetermined global shape, using local interactions. The global shape is described as a folding construction on a continuous sheet, using a set of axioms from paper-folding (origami). I provide a means of automatically deriving the cell program, executed by all cells, from the global shape description. With this language, a wide variety of global shapes and patterns can be synthesized, using only local interactions between identically-programmed cells. Examples include flat layered shapes, all plane Euclidean constructions, and a variety of tessellation patterns. In contrast to approaches based on cellular automata or evolution, the cell program is directly derived from the global shape description and is composed from a small number of biologically-inspired primitives: gradients, neighborhood query, polarity inversion, cell-to-cell contact and flexible folding. The cell programs are robust, without relying on regular cell placement, global coordinates, or synchronous operation and can tolerate a small amount of random cell death. I show that an average cell neighborhood of 15 is sufficient to reliably self-assemble complex shapes and geometric patterns on randomly distributed cells. The language provides many insights into the relationship between local and global descriptions of behavior, such as the advantage of constructive languages, mechanisms for achieving global robustness, and mechanisms for achieving scale-independent shapes from a single cell program. The language suggests a mechanism by which many related shapes can be created by the same cell program, in the manner of D'Arcy Thompson's famous coordinate transformations. The thesis illuminates how complex morphology and pattern can emerge from local interactions, and how one can engineer robust self-assembly.

Translation Invariance in Object Recognition, and Its Relation to Other Visual Transformations

Human object recognition is generally considered to tolerate changes of the stimulus position in the visual field. A number of recent studies, however, have cast doubt on the completeness of translation invariance. In a new series of experiments we tried to investigate whether positional specificity of short-term memory is a general property of visual perception. We tested same/different discrimination of computer graphics models that were displayed at the same or at different locations of the visual field, and found complete translation invariance, regardless of the similarity of the animals and irrespective of direction and size of the displacement (Exp. 1 and 2). Decisions were strongly biased towards same decisions if stimuli appeared at a constant location, while after translation subjects displayed a tendency towards different decisions. Even if the spatial order of animal limbs was randomized ("scrambled animals"), no deteriorating effect of shifts in the field of view could be detected (Exp. 3). However, if the influence of single features was reduced (Exp. 4 and 5) small but significant effects of translation could be obtained. Under conditions that do not reveal an influence of translation, rotation in depth strongly interferes with recognition (Exp. 6). Changes of stimulus size did not reduce performance (Exp. 7). Tolerance to these object transformations seems to rely on different brain mechanisms, with translation and scale invariance being achieved in principle, while rotation invariance is not.