Related papers: Self-Assembly of Patterns in the abstract Tile Ass…
We study self-similar attractors in the space $\mathbb{R}^d$, i.e., self-similar compact sets defined by several affine operators with the same linear part. The special case of attractors when the matrix $M$ of the linear part of affine…
We present a method for the automatic assembly of apictorial jigsaw puzzles. This method relies on integral area invariants for shape matching and an optimization process to aggregate shape matches into a final puzzle assembly. Assumptions…
Within the framework of generalized combinatorial approach, the complexity is determined for infinite set of self-similar hierarchical ensembles. This complexity is shown to increase with strengthening of the hierarchy coupling to the…
Nearly thirty years after its inception, the field of DNA-programmed colloidal self-assembly has begun to realize its initial promise. In this review, we summarize recent developments in designing effective interactions and understanding…
The field of complex self-assembly is moving toward the design of multi-particle structures consisting of thousands of distinct building blocks. To exploit the potential benefits of structures with such `addressable complexity,' we need to…
We consider a model of algorithmic self-assembly of geometric shapes out of square Wang tiles studied in SODA 2010, in which there are two types of tiles (e.g., constructed out of DNA and RNA material) and one operation that destroys all…
Patterns generated by a colloidal suspension of nanospheres drying on a frictional substrate are studied by experiments and computer simulations. The obtained two-dimensional self-assembled structures are commonly used for nanosphere…
We consider the self-assembly of composite structures from a group of nanocomponents, each consisting of particles within an $N$-atom system. Self-assembly pathways and rates for nanocomposites are derived via a multiscale analysis of the…
In collective robotic systems, the automatic generation of controllers for complex tasks is still a challenging problem. Open-ended evolution of complex robot behaviors can be a possible solution whereby an intrinsic driver for pattern…
We investigate the problem of assembling general shapes and patterns in a model in which particles move based on uniform external forces until they encounter an obstacle. While previous work within this model of assembly has focused on…
Aggregating base elements into rigid objects such as furniture or sculptures is a great way for designers to convey a specific look and feel. Unfortunately, there is no existing solution to help model structurally sound aggregates. The…
Multilevel self-assembly involving small structured groups of nano-particles provides new routes to development of functional materials with a sophisticated architecture. Apart from the inter-particle forces, the geometrical shapes and…
Many forms of programmable matter have been proposed for various tasks. We use an abstract model of self-organizing particle systems for programmable matter which could be used for a variety of applications, including smart paint and…
In self-assembling systems, geometric frustration leads to complex states characterized by internal gradients of shape misfit. Frustrated assemblies have drawn recent interest due to the unique possibility that their thermodynamics can…
Biological systems exploit self-assembly to create complex structures whose arrangements are finely controlled from molecular to mesoscopic level. Herein we report an example of using fully synthetic systems that mimic two levels of…
We describe some of the important physical characteristics of the `pathways', i.e. dynamical processes, by which molecular, nanoscale and micron-scale self-assembly occurs. We highlight the fact that there exist features of self-assembly…
In this paper, we explore relationships between two models of systems which are governed by only the local interactions of large collections of simple components: cellular automata (CA) and the abstract Tile Assembly Model (aTAM). While…
The goal of inverse self-assembly is to design inter-particle interactions capable of assembling the units into a desired target structure. The effective assembly of complex structures often requires the use of multiple components, each new…
Biomolecular condensates self-assemble when proteins and nucleic acids spontaneously demix to form droplets within the crowded intracellular milieu. This simple mechanism underlies the formation of a wide variety of membraneless…
A self-affine tiling of a compact set G of positive Lebesgue measure is its partition to parallel shifts of a compact set which is affinely similar to G. We find all polyhedral sets (unions of finitely many convex polyhedra) that admit…