Universal Shape Formation for Programmable Matter

Derakhshandeh, Zahra; Gmyr, Robert; Richa, Andréa W.; Scheideler, Christian; Strothmann, Thim

doi:10.1145/2935764.2935784

Cited by 70 publications

(101 citation statements)

References 27 publications

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“…We denote a particle whose hull flag is set as a hull particle (and all others as non-hull). Then, whenever is contracted, it uses its counters to determine i ∈ [6], the next direction along the convex hull to move in. The rules for whether or not it can move in direction i are exactly as before; a successful movement can either be an expansion or a role-swap.…”

Section: Rules For Leader Computation and Movementmentioning

confidence: 99%

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Convex Hull Formation for Programmable Matter

Daymude

Gmyr

Hinnenthal

et al. 2020

Proceedings of the 21st International Conference on Distributed Computing and Networking

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We envision programmable matter as a system of nano-scale agents (called particles) with very limited computational capabilities that move and compute collectively to achieve a desired goal. We use the geometric amoebot model as our computational framework, which assumes particles move on the triangular lattice. Motivated by the problem of shape sealing whose goal is to seal an object using as little resources as possible, we investigate how a particle system can self-organize to form an object's convex hull. We give a fully distributed, local algorithm for convex hull formation and prove that it runs in O(B + H log H) asynchronous rounds, where B is the length of the object's boundary and H is the length of the object's convex hull. Our algorithm can be extended to also form the object's ortho-convex hull, which requires the same number of particles but additionally minimizes the enclosed space within the same asymptotic runtime.

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Section: Rules For Leader Computation and Movementmentioning

confidence: 99%

“…If the leader is contracted, it can always eventually move in direction i ∈ [6]. If is expanded, it can always eventually perform a handover with a follower.…”

Section: Lemma 13mentioning

confidence: 99%

Convex Hull Formation for Programmable Matter

Daymude

Gmyr

Hinnenthal

et al. 2020

Proceedings of the 21st International Conference on Distributed Computing and Networking

Self Cite

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“…In this case, we add the rules (b i , b s ) and (b i , b r ) to H. See Figure 55 for an example of the two cases we consider. Let α ∈ [1,5], let H be a rule set, let Σ be a set of bead types and let C = (P, w, H) be an H-valid configuration where w ∈ Σ * . Also, let t ∈ Σ * .…”

Section: E1 Full Description Of S δmentioning

confidence: 99%

Know When to Fold ’Em: Self-assembly of Shapes by Folding in Oritatami

Demaine

Hendricks

Olsen

et al. 2018

Lecture Notes in Computer Science

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These results serve as a foundation for the study of shape-building in this new model of self-assembly, and have the potential to provide better understanding of cotranscriptional folding in biology, as well as improved abilities of experimentalists to design artificial systems that self-assemble via this complex dynamical process.Note that in [13] in the present proceedings, the authors study a slightly different problem: they show that one can design an oritatami transcript that folds an upscaled version of a non-self-intersecting path (instead of a shape). The initial path may come from the triangular grid or from the square grid. The scale of the resulting path is somewhere in between our scales 3 and 4 according to our definition. Note that the cells are only partially covered by their scheme. Combining their result with our theorem 3, their algorithm provides an oritatami transcript partially covering the upscaled version of any shape at scale 6.

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“…The network constructors model [33] and its geometric variant studied in this paper, may be viewed as models for programmable matter operating in a dynamic environment. The Amoebot model, a programmable matter model inspired by the behavior of amoeba, was proposed in [15,18] (see also [17,19] for some more recent studies). Another very recent study considered spherical programmable matter modules that can rotate or slide relative to neighboring modules [36], trying to capture transformation mechanisms that are feasible by current technology.…”

Section: Further Related Workmentioning

confidence: 99%

Terminating distributed construction of shapes and patterns in a fair solution of automata

Michail

2017

Distrib. Comput.

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In this work, we consider a solution of automata (or nodes) that move passively in a well-mixed solution without being capable of controlling their movement. Nodes can cooperate by interacting in pairs and every such interaction may result in an update of their local states. Additionally, the nodes may also choose to connect to each other in order to start forming some required structure. Such nodes can be thought of as small programmable pieces of matter, like tiny nanorobots or programmable molecules. The model that we introduce here is a more applied version of network constructors, imposing physical (or geometric) constraints on the connections that the nodes are allowed to form. Each node can connect to other nodes only via a very limited number of local ports. Connections are always made at unit distance and are perpendicular to connections of neighboring ports, which makes the model capable of forming 2D or 3D shapes. We provide direct constructors for some basic shape construction problems, like spanning line, spanning square, and self-replication. We then develop new techniques for determining the computational and constructive capabilities of our model. One of the main novelties of our approach is that of exploiting the assumptions that the system is well-mixed and has a unique leader, in order to give terminating protocols that are correct with high probability. This allows us to develop terminating subroutines that can be sequentially composed to form larger modular protocols. One of our main results is a terminating protocol counting the size n of the system with high probability. We then use this protocol as a subroutine in order to develop our universal constructors, establishing that it is possible for the nodes to become self-organized with high probability into arbitrarily complex shapes while still detecting termination of the construction.

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Universal Shape Formation for Programmable Matter

Cited by 70 publications

References 27 publications

Convex Hull Formation for Programmable Matter

Convex Hull Formation for Programmable Matter

Know When to Fold ’Em: Self-assembly of Shapes by Folding in Oritatami

Terminating distributed construction of shapes and patterns in a fair solution of automata

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