ConspectusEarly research in nanoscience and nanotechnology focused on gaining synthetic control over the size, shape, and composition of nanostructures, as well as exploring their fundamental properties. Over the past few decades, these capabilities have become increasingly sophisticated. Today, we have well-established synthetic toolkits and methodologies that enable the design of nanostructures with tailored properties and functions, guided by sets of design rules, for use in many areas spanning biology and medicine to energy, the environment, and catalysis.To illustrate this paradigm, where synthesis and fundamental discovery drive engineering and technological innovation, we examine spherical nucleic acids (SNAs) as a case study. SNAs are nanoconstructs consisting of a nanoparticle core densely functionalized with a radially oriented oligonucleotide shell. Over the past 30 years, the evolution of SNAs has spanned their invention, the development of increasingly advanced syntheses enabling the creation of dozens of SNA classes (and related DNA-functionalized anisotropic materials, often termed programmable atom equivalents [PAEs]), the discovery of novel phenomena that have reshaped core chemical principles, and their translation into nanomedicines, biological labels, and synthons in materials science.SNAs were first developed in 1996 as gold nanoparticle-DNA conjugates. Since then, extensive study has revealed common structural features that are tied to their unique properties, defining SNAs as a distinct materials class. Most SNAs feature a core (typically a nanoparticle, though recent advances involve molecular scaffolds) that concentrate nucleic acid strands into close proximity. This architecture confers several distinctive properties: enhanced binding affinity to complementary DNA (both free and surface-bound), resistance to enzymatic degradation, reduced immune activation (unless specifically designed for immunostimulation), and efficient cellular uptake without requiring transfection agents.These synthetic and fundamental advances offer significant advantages in biomedical probe and therapeutic design. Due to their modularity, stability, biocompatibility, and ability to access intracellular compartments, SNAs have been applied as intracellular and extracellular probes, tools for gene regulation, vaccines, and gene editing platforms (especially when coupled with CRISPR/Cas9 technology). In parallel, SNAs serve as foundational elements in a new class of programmable matter: DNA-mediated colloidal crystals. Here, sequence-specific DNA interactions are used to organize SNAs into three-dimensional, periodic structures. This line of inquiry has enabled the design and synthesis of thousands of crystal variations, with different lattice symmetries, parameters, and nanoparticle compositions, unlocking the potential for novel optical and mechanical metamaterials and catalysts with exceptional properties, such as negative refractive indices, shape memory, and second harmonic generation. In sum, SNAs exemplify how synthetic mastery and fundamental discovery can catalyze innovation across disciplines, providing a framework that chemists can use in developing transformative new materials.

This review highlights a clear change in focus in the study of coacervate droplets as protocell models, moving from their role as passive microreactors that concentrate reactants to their function as chemically programmable matter capable of information processing and lifelike behaviors. We use "Input → Written State → Output" as a guiding workflow, and discuss recent advances through three operational pillars. The first is local reactivity control, where the droplet microenvironment directs reaction pathways and spatial enzyme organization, including feedback loops where reactions regulate the physical state. The second pillar is the writing of internal states, which treats droplets as stimuli-addressable chemical memory with targets of selectivity, latency, and erasability. The third pillar involves external readouts, which transduce internal states into programmed cargo release and chemical signaling within environments and across protocell communities. Finally, we outline future perspectives, discussing the transition from programming deterministic functions to directing the evolution of protocell populations that exhibit collective behaviors. By offering a cohesive conceptual toolkit, this review provides new insights beyond the simple notion of "faster reactions in droplets" and toward the engineering of higher-order, cooperative architectures with lifelike functions.

Programmable self-assembly enables the construction of complex molecular, supramolecular, and crystalline architectures from well-designed building blocks. We introduce a hypergraph-based formalism, Blocks & Bonds (B&B), which generalizes classical chemical graph theory by incorporating directed and multicolored interactions, internal symmetries, and hierarchical organization. Within this framework, we develop the Structure Code (SC), a compact and versatile language for describing self-assembled architectures. We define a Kolmogorov-style structural complexity as the total information content of SC, obtained through its tokenization and Shannon information assignment. Complementing this encoding-based measure, we introduce a much simpler quantity, the compositional complexity, which depends only on the number and cumulative usage of block and bond types in the construction set. A central result of this work is a strong empirical correlation between the token-based structural complexity and the compositional complexity across all examined systems. Owing to this agreement, the compositional complexity emerges as the most practical and broadly applicable measure: it is easy to compute, requires no explicit encoding, and yet closely tracks the actual information content of structurally diverse architectures. Applications to molecular systems (ethylene glycol and glucose), DNA-origami lattices, and crystalline assemblies show that B&B hypergraphs provide a unified, scalable, and information-efficient representation of structural organization, naturally capturing symmetry, modularity, and stereochemistry. This framework establishes a quantitative foundation for complexity-aware classification and inverse design of programmable matter.

ABSTRACT Liquid crystal elastomers (LCEs) are anisotropic polymeric smart materials with promise for soft robotic actuators, dampers, and adhesives. Realizing these applications requires precise 3D alignment of the polymer backbone, yet current manufacturing approaches struggle to produce complex spatial patterns in three dimensions. Here, we introduce a digital light processing (DLP) 3D printing strategy that enables voxel‐level control of LCE alignment domains. By integrating a rotatable magnetic array with DLP photomasking, we achieve spatially tunable structures at voxel resolutions. This approach allows freeform 180° alignment within individual voxels, generating highly nonlinear shape transformations in both 2D films and 3D architectures. Finite element modeling and inverse design guide the creation of multidomain alignment patterns that could achieve targeted nonlinear deformation behaviors. As a demonstration, multidomain LCE smart valves are fabricated that exhibit up to 70% improved flow control compared to monodomain analogues. This technique dramatically expands the design space of 3D programmable matter and establishes a pathway toward complex, application‐ready LCE systems.

Inspired by nature's reliance on antagonistic interactions to orchestrate complex dynamics, synthetic systems often replicate this by integrating multiple competing components-a strategy frequently hampered by synthetic complexity and kinetic mismatch. Here, we report a single-component spiropyran-functionalized polymer system that exhibits programmable reentrant phase transitions mediated by light-heat antagonism in reversible spiropyran isomerization. Within this system, light and heat competitively drive the interconversion of spiropyran between its ring-closed SP- and ring-opened MCH forms, allowing precise modulation of intermolecular electrostatic interactions and thereby enabling real-time control over polymer conformation and phase transitions. Following this principle, we demonstrate versatile reversible switching of a single polymer system among nonthermoresponsive, monothermoresponsive (UCST-type), and reentrant thermoresponsive states-the latter displaying LCST behavior at low temperatures and UCST behavior at high temperatures. This light-heat regulatory mechanism is further extended to hydrogels, where it enables programmable reentrant volumetric transitions and autonomous oscillatory deformation. By employing noninvasive light to flexibly tailor multimode responsiveness in a single system, our work establishes a robust and generalizable platform for dynamically programmable matter with prospects in soft robotics and biomedicine.

Biological systems can form complex three-dimensional structures through the collective behavior of identical agents -- cells that follow the same internal rules and communicate without central control. How such distributed control gives rise to precise global patterns remains a central question not only in developmental biology but also in distributed robotics, programmable matter, and multi-agent learning. Here, we introduce DiffeoMorph, an end-to-end differentiable framework for learning a morphogenesis protocol that guides a population of agents to morph into a target 3D shape. Each agent updates its position and internal state using an attention-based SE(3)-equivariant graph neural network, based on its own internal state and signals received from other agents. To train this system, we introduce a new shape-matching loss based on the 3D Zernike polynomials, which compares the predicted and target shapes as continuous spatial distributions, not as discrete point clouds, and is invariant to agent ordering, number of agents, and rigid-body transformations. To enforce full SO(3) invariance -- invariant to rotations yet sensitive to reflections, we include an alignment step that optimally rotates the predicted Zernike spectrum to match the target before computing the loss. This results in a bilevel problem, with the inner loop optimizing a unit quaternion for the best alignment and the outer loop updating the agent model. We compute gradients through the alignment step using implicit differentiation. We perform systematic benchmarking to establish the advantages of our shape-matching loss over other standard distance metrics for shape comparison tasks. We then demonstrate that DiffeoMorph can form a range of shapes -- from simple ellipsoids to complex morphologies -- using only minimal spatial cues.

Deterministic self-stabilising leader election for programmable matter with constant memory

Efficient shape formation by 3D hybrid programmable matter: An algorithm for low diameter intermediate structures

Line formation and scattering in silent programmable matter

We report on the dynamic self-assembly of TiO2-Fe photocatalytic colloidal motors into reconfigurable superstructures when subjected to UV illumination, magnetic fields, and acoustic confinement. Tuning the light intensity and magnetic field strength enables in situ control over cluster size, rotation speed, and structural compactness. Four distinct phases emerge from the interplay of dipolar repulsion, self-propulsion, and phoretic attraction. Our work presents a generalizable strategy for programmable active matter and microrobotic swarms adapting to a complex and changing environment.

Inspired by the remarkable buoyancy and collective adaptability of fire ant rafts, this study presents magnetic composite micro-floaters (MCMs) capable of stable flotation at air-water interfaces-a key advancement for magnetic microrobotic swarms in fluid environments. The system overcomes the intrinsic sinking tendency of high-density NdFeB microparticles through bioinspired surface engineering. MCMS are fabricated via a solvent-exchange phase inversion process, encapsulating NdFeB cores with hydrophobic polycaprolactone (PCL) and engineered surface roughness. This design emulates the hydrophobic cuticle and air-trapping strategies of fire ants, conferring exceptional resistance to vertical magnetic fields (up to 0.5 T) without submersion. Unlike conventional approaches, this eliminates reliance on restrictive parallel-field configurations. When subjected to programmable magnetic fields, MCM swarms exhibit dynamic self-assembly, reconfiguration into complex structures, and stable navigation through wave-disturbed environments while preserving swarm cohesion. Their multifunctional performance includes cargo transport at 70 times their weight, guided oil spill remediation via controlled aggregation, and precise manipulation of droplets (200 times their volume) for merging, stirring, and maze navigation-all achieved at the air-water interface. By synergizing fire ant-inspired flotation stability with magnetic reconfigurability, this work establishes a versatile platform for surface-based microrobotics, unlocking new opportunities in environmental remediation, microfluidics, and programmable matter.

Simulation of programmable matter systems using active tile-based self-assembly

Biological entities as diverse as birds or bacteria frequently self-assemble to display sophisticated collective dynamical behaviors. To understand and design interactions between the individual entities that originate the different flocking behaviors is one of the current most significant challenges in active matter. Here we show how a mixture of particles with perception-dependent motility and opposite misaligned visual perception spontaneously organizes into a self-propelling bean-shaped cluster. The two species initially rotate in opposite directions which, together with the steric interactions, make them segregate into two main counter-rotating domains forming a cohesive and persistently propelling single cluster. Mixtures of particles with misaligned perception and discontinuous motility are therefore a promising pathway for the design of programmable active matter.

This study reports a supramolecular gel system capable of dynamic gel-to-gel transformations and reversible inversion of optical activity between superhelical and single-helical structures without passing through a sol phase. Inspired by collagen-like adaptability, the system utilizes 4-pyridinylboronic acid and guanosine as building blocks. Hierarchical assembly is achieved through pH-responsive boronic ester formation and guanosine-mediated G-quadruplex stacking, enabling transitions between superhelices and single helices with opposite optical activity. The system employs three regulatory pathways: bidirectional pH modulation, monotonic pH increase, and monotonic pH decrease, demonstrating programmable and reversible control over chirality, morphology, and mechanical properties. In the autonomous pH regulation, we have created an out-of-equilibrium hydrogel system with controlled switching of optical activity. Unlike traditional gel-sol-gel systems, this gel maintains macroscopic stability during transformations. Our remarkable finding bridges the gap between static supramolecular assemblies and dynamic soft materials, offering a platform for designing functional, biomimetic systems. The combination of hierarchical organization, dynamic chirality control, and robust programmability positions this gel for applications in adaptive optics, responsive biomaterials, and programmable soft matter.

Noncontact actuation of small elastic structures is a challenging problem given the poor scaling of electronic actuators. Sound offers a convenient and steerable power source for actuation, but the direct conversion for actuation via primary acoustic forces is typically inefficient. We recently demonstrated that the secondary scattering forces between bubbles can be dramatically amplified by geometric patterning and used for precise actuation in a fluidic environment. Here, we build on this idea and introduce a dynamic metamaterial composed of trapped gas bubbles in a fluid. We show carefully designed structures that achieve wirelessly switchable mechanical motion via secondary acoustic radiation forces. We introduce a theoretical model of the system to describe the equilibrium configurations of the structures, and support this model with experimental results. Building on our model, we introduce design principles to achieve different actuation behaviors. Our results highlight the potential of such acousto-elastic actuators for applications in soft robotics, programmable matter, and smart materials capable of reconfigurable actuation.

Magnetic Janus particles (MJPs) with radially shifted dipoles exhibit a versatile platform for engineering responsive materials through field-directed self-assembly. Motivated by their potential in programmable soft matter, Brownian dynamics simulations are used to systematically investigate how the radial dipolar displacement s and the Langevin parameter α govern the aggregation pathways and emergent morphologies of MJPs in quasi-two-dimensional environments. We identified six distinct aggregation regimes: three arising under low magnetic fields (α ≲ 10) corresponding to the low-, intermediate-, and high-shift cases, and two emerging at intermediate (10 ≲ α ≲ 90) and high magnetic fields (α ≳ 90). These regimes exhibit a rich morphological evolution as α increases: from disordered loops (low α, low s), islands (low α, intermediate s), and worm-like clusters (low α, high s), transitioning through chiral and tangled chains (intermediate α, intermediate and high s), and culminating in fully aligned chains (intermediate α with low s, and high α for all s). A structure diagram predicted by considering a simple ratio of competing torques (RMag) effectively illustrates these transitions and specifies the conditions necessary for structural reorganization. This framework supports the rational design of adaptive colloidal architectures for applications in targeted delivery, soft microrobotics, and reconfigurable magnetic systems. Notably, the universal convergence to a growth exponent of z ≈ 0.473 under high magnetic fields (α ≳ 90) reveals a definitive kinetic signature of complete cluster alignment along the field direction, establishing a robust and tunable route to field-induced material organization.

Adaptive collective responses to local stimuli in anonymous dynamic networks

A derivation of a tight-binding model from Schrödinger formalism for various topologies of position-based semiconductor qubits is presented in the case of static and time-dependent electric fields. The simplistic tight-binding model enables the description of single-electron devices at a large integration scale. The case of two electrostatically Wannier qubits (also known as position-based qubits) in a Schrödinger model is presented with omission of spin degrees of freedom. The concept of programmable quantum matter can be implemented in the chain of coupled semiconductor quantum dots. Highly integrated and developed cryogenic CMOS nanostructures can be mapped to coupled quantum dots, the connectivity of which can be controlled by a voltage applied across the transistor gates as well as using an external magnetic field. Using the anti-correlation principle arising from the Coulomb repulsion interaction between electrons, one can implement classical and quantum inverters (Classical/Quantum Swap Gate) and many other logical gates. The anti-correlation will be weakened due to the fact that the quantumness of the physical process brings about the coexistence of correlation and anti-correlation at the same time. One of the central results presented in this work relies on the appearance of dissipation-like processes and effective potential renormalization building effective barriers in both semiconductors and in superconductors between not bended nanowire regions both in classical and in quantum regimes. The presence of non-straight wire regions is also expressed by the geometrical dissipative quantum Aharonov–Bohm effect in superconductors/semiconductors when one obtains a complex value vector potential-like field. The existence of a Coulomb interaction provides a base for the physical description of an electrostatic Q-Swap gate with any topology using open-loop nanowires, with programmable functionality. We observe strong localization of the wavepacket due to nanowire bending. Therefore, it is not always necessary to build a barrier between two nanowires to obtain two quantum dot systems. On the other hand, the results can be mapped to the problem of an electron in curved space, so they can be expressed with a programmable position-dependent metric embedded in Schrödinger’s equation. The semiconductor quantum dot system is capable of mimicking curved space, providing a bridge between fundamental and applied science in the implementation of single-electron devices.

Rubik’s cube as in-situ programmable matter and a reconfigurable mechanical metamaterial

Programmable matter represents a system of elements whose interactions can be programmed for a certain behavior to emerge (e.g., color, shape) upon suitable commands (e.g., instruction, stimuli) by altering its physical characteristics. Even though its appellation may refer to a morphable physical material, programmable matter has been represented through several approaches from different perspectives (e.g., robots, smart materials) that seek the same objective: controllable behavior such as smart shape alteration. Researchers, engineers, and artists have expressed interest in the development of smart modeling clay as a novel alternative to conventional matter and classical means of prototyping. Henceforth, users will be able to do/undo/redo forms based on computed data (CAD) or interactions (sensors), which will help them unlock more features and increase the usefulness of their products. However, with such a promising technology, many challenges need to be addressed, as programmable matter relies on energy consumption, data transmission, stimuli control, and shape formation mechanisms. Furthermore, numerous devices and technologies are created under the name of programmable matter, which may pose ambiguity to the control strategies. In this study, we determine the basic operations required to form a shape, then review different realizations using the shape shifting ability of programmable matter and their fitting classifications, and finally discuss potential challenges.