Research at the Simply Complex Lab

At the Simply Complex Lab, we bring together experimental, computational, and theoretical approaches to explore one of the most fascinating frontiers of science: driven, dissipative systems.

These systems operate far from thermodynamic equilibrium, where strong nonlinearity and stochasticity give rise to rich, emergent behaviour, ranging from self-organised pattern formation to adaptation and evolution, as observed across nature.

Our core mission is to uncover the underlying principles that govern these phenomena and to emulate them in engineered systems. By doing so, we aim to create new paradigms for designing, predicting, and controlling complexity, with far-reaching implications across science, technology, and society.

Our research spans a wide range of scales and systems: from quantum to micro- and macroscales, from inanimate to living matter, from static to dynamic regimes, and from deterministic to stochastic processes. We strive to bridge fundamental physics with real-world applications through a cross-disciplinary lens.

Below, you can explore a selection of our ongoing and past research efforts, each with a brief overview of its goals, methods, and broader impact.

Emergence and Evolution of Complexity

There is no shortage of complex systems, yet most are too intricate for a full first-principles approach. Progress in understanding their behaviour requires decisive, quantitative experiments and carefully designed model systems, simple enough to be tractable, yet rich enough to exhibit the core phenomena of interest.

In our lab, we have developed such a model system: a colloidal suspension driven by ultrafast laser pulses, studied both empirically and computationally. This system is striking in its simplicity; it involves no engineered interparticle interactions, no surface functionalization, and no stimuli-responsive solvents. Yet it gives rise to an extraordinary range of emergent behaviours.

What makes this system unique is its extreme combination of strong stochasticity and large nonlinearities. The particles remain highly Brownian, meaning fluctuations are not suppressed. Nonlinearities are introduced via multiphoton absorption, which triggers simultaneous, nonlinear events such as Marangoni flows, shock wave formation, and cavitation bubbles. These events inject additional perturbations, including complex fluid flows and pressure gradients, into the system.

On top of these, many-body interactions among thousands of particles inflate the system’s nonlinear dynamics to an astronomical degree. The key to controlling this chaos lies in exploiting internal feedback mechanisms that lock stochasticity and nonlinearities into structured behaviours. We have identified and harnessed these mechanisms using only a handful of external control parameters (e.g., laser power and beam position).

This has allowed us to demonstrate, quantify, and simulate how rich structural and behavioural complexity can emerge, adapt, and evolve in a system without engineered interactions, and under conditions similar to those where complex systems emerge in nature. Work done in the past: This model system allowed us to make significant contributions to our immediate community and tangent fields by demonstrating the emergence and sustenance of rich, life-like behaviour (Nat. Commun. 2017) and an existence proof of universal scaling across systems and length scales (Nat. Phys. 2020).

In the former, we reported the first dynamic adaptive colloidal crystals of a multiplicity of patterns that emerged and were sustained far from equilibrium. These crystals were autocatalytic and exhibited a rich set of adaptive behaviours analogous to those commonly associated with living organisms: self-regulation, self-healing, self-replication, co-existence, competition, and motility. Colloidal self-assembly in previous studies relied heavily on functionalized colloids (e.g., Janus particles) and commonly employed interaction mechanisms, such as optical trapping, tweezing, and chemical or magnetic interactions, that required direct control over many degrees of freedom. Fluctuations were preferably suppressed since they bring additional degrees of freedom to be controlled. These requirements limit the system’s configurational space and do not leave much room for complexity to emerge. In contrast, we used simple, passive, identical colloidal particles with non-specific interactions. The vast majority of the degrees of freedom were nonlinearly locked by the internal feedback mechanisms, which could be controlled using only the laser power and beam position. Since the fluctuations are part of the feedback, we were free to operate under strongly stochastic conditions, which allowed the system to explore a sufficiently large portion of its phase space and exhibit a copious amount of complex pattern formation and adaptive behaviour.

The revelation that simple physical mechanisms are sufficient for the observed complexity in this unique experimental system suggested that the self-assembly mechanism should be independent of the chemical, morphological, and other specific details of the particles being assembled. To verify, we used simple, identical particles, such as ~3-nm CdTe quantum dots (in water and other chemicals) and 500-nm pure polystyrene spheres (in water), as well as complex, active, non-identical living organisms with sophisticated internal dynamics, such as ~0.7-µm soft spheres of Micrococcus luteus and ~1-µm × 2-µm rod-like, Escherichia coli bacterial cells, ~5-µm elliptical, Saccharomyces cerevisiae yeast cells, and ~15-µm MCF10A normal human mammary gland cells (all in their respective growth media). We showed that the emergence and growth of dissipative aggregates of a large variety of constituents exhibited the same scale-free autocatalytic aggregation dynamics. We also showed that the interface fluctuations of the growing aggregates obey Tracy-Widom statistics (Nat. Phys. 2020). Universal scaling of macroscopic observables was known for systems at or near thermodynamic equilibrium. However, it was unclear if far-from-equilibrium systems could exhibit such universal scaling until our work.

These results have been highlighted in popular science books, news outlets, and by journal editors, reaching a broad interdisciplinary audience.

Work to appear as preprints: Over the last few years, we followed up on these leads and showed that the system has a vast configurational space from simpler Bravais lattices to superlattices with periodic and aperiodic symmetries. We identified the dynamics leading to this structural richness and quantified the key parameters.

Current focus:

• Dr. Sayın is set out to lead our research on uncovering the dynamic behaviour and adaptive strategies leading to their competition and coexistence.
• Dr. Yavuz is planning on developing an AI-run advanced microscopy system, which will run the experiments from sample preparation to execution of the experiments at the system’s natural timescales (microseconds) to performing real-time analysis that would inform the next action. AI will control, execute, and analyse the experiments orders of magnitude faster than a human operator. This way, we hope to gain more insights into the stochastic dynamics and feedback mechanisms running this system.
• Dr. Spelthann initiated a collaboration with the Elbuken Lab of Oulu University, Finland, on using microfluidic chips to enable real-world applications of this system.