Living systems exhibit remarkable self-organization, often demonstrating anticipatory behavior. This study focuses on *Caulerpa brachypus*, a large, single-celled marine alga with differentiated organs, posing a unique challenge to understanding morphogenesis at a macroscopic scale without cellularization. The research question centers on the nature of self-organized waves of chloroplasts observed within *Caulerpa* and their relationship to internal biological clocks and external light cues. The purpose is to quantitatively characterize these waves, determine their underlying mechanisms, and explore their role in morphogenesis. Understanding these processes is crucial for advancing our knowledge of self-organization in biological systems and the role of biological oscillators in development. The alga's unique characteristics—its large size and single-celled structure—make it an ideal model to investigate the interplay between macroscopic dynamics, internal timing mechanisms, and environmental influences. The importance of this study lies in its potential to shed light on fundamental principles governing morphogenesis and the integration of internal and external signals in biological systems.

The literature review highlights the importance of anticipatory behavior in living systems, from human actions to cellular processes. It emphasizes the central role of biological oscillators and synchronization with the environment in maintaining homeostasis and enabling self-organization. Existing research on biological oscillators and their amenability to dynamical systems analysis is reviewed. Previous work on *Caulerpa*, emphasizing its unique developmental biology, is also discussed. This includes studies on cytoplasmic streaming and organ formation. The review sets the stage for this study by emphasizing the novelty of investigating macroscopic self-organized waves in a single-celled organism and the potential of dynamical systems analysis to elucidate the underlying mechanisms.

To study the self-organized green waves, a custom-built experimental setup was developed using Raspberry Pi-controlled illumination and cameras. This allowed for automated tracking of morphogenesis in tens of samples concurrently, with a temporal resolution of tens of seconds. The experimental design involved a "Cut & Regenerate" cycle, where *Caulerpa* segments were cultured and observed over weeks, providing living material for subsequent experiments. Spatiotemporal dynamics were quantitatively analyzed through coarse-graining, reducing the high-dimensional data to a macroscopic observable: the fraction of green area in a well. Time series data were subjected to power spectral analysis to quantify the temporal frequencies of the waves. Experimental perturbations included varying illumination periods (1.5h to 94h) and intensities (2^-5 to 2¹ times the reference intensity). The reference illumination intensity was measured as 4.5 μmol · s⁻¹ · m⁻². The measured illumination spectrum displayed two main modes, centered at 545nm and 440nm. Data processing involved outlier detection, replacement, and Welch's method for power spectral estimation. Dominant frequencies were determined by analyzing local maxima in the power spectra. *Caulerpa brachypus* samples were cultured in Erdschreiber’s Medium and maintained at a temperature between 22.5°C and 24.5°C. Image analysis involved setting a threshold on the blue channel of RGB images to identify green areas. The analysis includes details about sample size for each experimental condition, and further information is provided in the supplementary material and reporting summary.

The study revealed macroscopic self-organized green waves that propagate throughout *Caulerpa brachypus*, anticipating changes in illumination. Power spectral analysis showed that under driving periods between 18h and 30h, the fundamental frequency of the waves matched the driving frequency of the light cycles. This indicates a 1:1 entrainment of the biological oscillator to the external light cycle. Outside this range (e.g., 3h, 48h), power spectra revealed both the driving frequency and a distinct peak near 1/24h, indicative of an intrinsic circadian oscillator. This confirmed that the green waves are coupled to an intrinsic oscillator, entrained by the light cycles. Under constant illumination, the system transitioned into new dynamical states. The natural frequency of the oscillator increased with decreasing light intensity. At high intensities, the system exhibited intermittent oscillations and a loss of distinct harmonic peaks in the power spectrum, suggesting a transition towards temporal disorder. The study found that morphology depended on the temporal pattern of light, with samples under a 24h light-dark cycle exhibiting distinct morphological features compared to those under constant illumination. Growth rate was found to increase with light intensity, but variability also increased at higher intensities.

The findings address the research question by demonstrating that the observed macroscopic green waves are driven by a self-sustained oscillator entrained by the external light cycle. The coupling between the internal oscillator and the environmental light cue explains the anticipatory behavior of the waves. The dependence of the oscillator's frequency and the system's dynamics on light intensity highlights the complex nonlinear nature of this interaction. The observed link between light patterns and morphogenesis suggests a direct role for the green waves in developmental processes. The results contribute significantly to our understanding of self-organization and the integration of internal and external signals in biological systems. The role of photosynthesis as an energy source is highlighted as essential for the entrainment observed. The study suggests that periods of darkness are important for the typical dynamics of the alga, as constant illumination leads to increased temporal disorder, even if the average light intensity is the same as in the 12h-12h cycle.

This study provides strong evidence for self-organized macroscopic waves coupled to an intrinsic circadian oscillator in *Caulerpa brachypus*. Light is a key regulator, affecting both the frequency of oscillations and the morphology of the alga. The findings have implications for understanding self-organization, biological clocks, and morphogenesis in unicellular organisms. Future research should investigate the molecular mechanisms underlying the observed waves and their role in algal metabolism and development. Further exploration of the transition to temporal disorder under constant illumination could provide valuable insights into the system's dynamics.

The study's conclusions are based on observations from a single *Caulerpa* strain. Generalizability to other algal species or strains requires further investigation. The coarse-graining approach simplifies the complex spatiotemporal dynamics, and finer-scale analysis could provide additional insights. While the study strongly suggests a link between green waves, oscillator, and morphogenesis, direct causal relationships need further investigation. The study primarily focuses on macroscopic dynamics, leaving out detailed molecular mechanisms underlying these phenomena.