Self-organized collective coordinated behaviour is an impressive phenomenon, observed in a variety of natural and artificial systems, in which coherent global structures or dynamics emerge from local interactions between individual parts. If the degree of collective integration of a system does not depend on size, its level of robustness and adaptivity is typically increased and we refer to it as scale-invariant. In this review, we first identify three main types of self-organized scale-invariant systems: scale-invariant spatial structures, scale-invariant topologies and scale-invariant dynamics. We then provide examples of scale invariance from different domains in science, describe their origins and main features and discuss potential challenges and approaches for designing and engineering artificial systems with scale-invariant properties.

Hybrid societies are self-organizing, collective systems composed of different components, for example, natural and artificial parts (bio-hybrid) or human beings interacting with and through technical systems (socio-technical). Many different disciplines investigate methods and systems closely related to the design of hybrid societies. A~stronger collaboration between these disciplines could allow for re-use of methods and create significant synergies. We identify three main areas of challenges in the design of self-organizing hybrid societies. First, we identify the formalization challenge. There is an urgent need for a generic model that allows a description and comparison of collective hybrid societies. Second, we identify the system design challenge. Starting from the formal specification of the system, we need to develop an integrated design process. Third, we identify the challenge of interdisciplinarity. Current research on self-organizing hybrid societies stretches over many different fields and hence requires the re-use and synthesis of methods at intersections between disciplines. We then conclude by presenting our perspective for future approaches with high potential in this area.

Efficient random searches are essential to the survival of foragers searching for sparsely distributed targets. Lévy walks have been found to optimize the search over a wide range of constraints. When targets are distributed within patches, generating a spatial memory over the detected targets can be beneficial towards optimizing the search efficiency. Because foragers have limited memory, storing each target location separately is unrealistic. Instead, we propose incrementally learning a spatial distribution in favour of memorizing target locations. We demonstrate that an ensemble of Gaussian mixture models is a suitable candidate for such a spatial distribution. Using this, a hybrid foraging strategy is proposed, which interchanges random searches with informed movement. Informed movement results in displacements towards target locations, and is more likely to occur if the learned spatial distribution is correct. We show that, depending on the strength of the memory effects, foragers optimize search efficiencies by continuous revisitation of non-destructive targets. However, this negatively affects both the target and patch diversity, indicating that memory does not necessarily optimize multi-objective searches. Hence, the benefits of memory depend on the specific goals of the forager. Furthermore, through analysis of the distribution over walking distances of the forager, we show that memory changes the underlying walk characteristics. Specifically, the forager resorts to Brownian motion instead of Lévy walks, due to truncation of the long straight line displacements resulting from memory effects. This study provides a framework that opens up new avenues for investigating memory effects on foraging in sparse environments.