Local interactions drive emergent collective behavior, which pervades biological and social complex systems. These behaviors are scalable and robust, motivating biomimicry: engineering nature-inspired distributed systems. But uncovering the interactions that produce a desired behavior remains a core challenge. In this thesis, I present EvoSOPS, an evolutionary framework that searches landscapes of stochastic distributed algorithms for those that achieve a mathematically specified target behavior. These algorithms govern self-organizing particle systems (SOPS) comprising individuals with strictly local sensing and movement and no persistent memory. For aggregation, phototaxing, and separation behaviors, EvoSOPS discovers algorithms that achieve 4.2–15.3% higher fitness than those from the existing “stochastic approach to SOPS” based on mathematical theory from statistical physics. EvoSOPS is also flexibly applied to new behaviors such as object coating where the stochastic approach would require bespoke, extensive analysis. Across repeated runs, EvoSOPS explores distinct regions of genome space to produce genetically diverse solutions. Finally, I provide insights into the best-fitness genomes for object coating, demonstrating how EvoSOPS can bootstrap future theoretical investigations into SOPS algorithms for challenging new behaviors.

Nations censor specific information in accordance with their political, legal, and cultural standards. Each country adopts unique approaches and regulations for censorship, whether it involves moderating online content or prohibiting protests. This paper seeks to study the underlying motivations for the disparate behaviors exhibited by authorities and individuals. To achieve this, we develop a mathematical model designed to understand the dynamics between authority figures and individuals, analyzing their behaviors under various conditions. We argue that individuals essentially act in three phases - compliance, self-censoring, and defiance when faced with different situations under their own desires and the authority's parameters. We substantiate our findings by conducting different simulations on the model and visualizing the outcomes. Through these simulations, we realize why individuals exhibit behaviors falling into one of three categories, who are influenced by factors such as the level of surveillance imposed by the authority, the severity of punishments, the tolerance for dissent, or the individuals' boldness. This also helped us to understand why certain populations in a country exhibit defiance, self-censoring behavior, or compliance as they interact with each other and behave under specific conditions within a small network world.

Cancer is a disease that takes the lives of almost 10 million people every year, and due to humans’ nature as multicellular organisms, it is both inevitable and incurable. Therefore, management of the disease is of utmost importance. Due to the complexity of cancer and its development, numerous computational models have been developed that allow for precise diagnostic and management input. This experiment uses one of these said models, CancerSim, to evaluate the effect of proliferation rates on the order in which the hallmarks of cancer evolve in the simulations. To do this, the simulation is run with initial telomere length increased to simulate the effects of more living cells proliferating at every time step. The results of this experiment show no significant effect of initial telomere length on the order that hallmarks evolved, but all simulations ended with cancers that were dominant with cells that contained limitless replication and evade apoptosis hallmarks. These results may have been affected by limitations in the CancerSim model such as the inability to model metastasis and the lack of a robust angiogenesis solution. This study reveals how individual cell characteristics may not have a large effect on cancer evolution, but rather individual hallmarks can affect evolution significantly. Further studies with a revised version of CancerSim or another model could confirm the behavior demonstrated in this experiment

The world is filled with systems of entities that collaborate in motion, both natural and engineered. These cooperative distributed systems are capable of sophisticated emergent behavior arising from the comparatively simple interactions of their members. A model system for emergent collective behavior is programmable matter, a physical substance capable of autonomously changing its properties in response to user input or environmental stimuli. This dissertation studies distributed and stochastic algorithms that control the local behaviors of individual modules of programmable matter to induce complex collective behavior at the macroscale. It consists of four parts. In the first, the canonical amoebot model of programmable matter is proposed. A key goal of this model is to bring algorithmic theory closer to the physical realities of programmable matter hardware, especially with respect to concurrency and energy distribution. Two protocols are presented that together extend sequential, energy-agnostic algorithms to the more realistic concurrent, energy-constrained setting without sacrificing correctness, assuming the original algorithms satisfy certain conventions. In the second part, stateful distributed algorithms using amoebot memory and communication are presented for leader election, object coating, convex hull formation, and hexagon formation. The first three algorithms are proven to have linear runtimes when assuming a simplified sequential setting. The final algorithm for hexagon formation is instead proven to be correct under unfair asynchronous adversarial activation, the most general of all adversarial activation models. In the third part, distributed algorithms are combined with ideas from statistical physics and Markov chain design to replace algorithm reliance on memory and communication with biased random decisions, gaining inherent self-stabilizing and fault-tolerant properties. Using this stochastic approach, algorithms for compression, shortcut bridging, and separation are designed and analyzed. Finally, a two-pronged approach to "programming" physical ensembles is presented. This approach leverages the physics of local interactions to pair theoretical abstractions of self-organizing particle systems with experimental robot systems of active granular matter that intentionally lack digital computation and communication. By physically embodying the salient features of an algorithm in robot design, the algorithm's theoretical analysis can predict the robot ensemble's behavior. This approach is applied to phototaxing, aggregation, dispersion, and object transport.