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We introduce a model, based on the Evolutionary Game Theory, for studying the dynamics of group formation. The latter constitutes a relevant phenomenon observed in different animal species, whose individuals tend to cluster together forming…

Many organisms exhibit branching morphologies that twist around each other and become entangled. Entanglement occurs when different objects interlock, creating complex and often irreversible configurations. This physical phenomenon is…

This paper attempts to make feasible the evolutionary emergence of novelty in a supposedly deterministic world which behavior is associated with those of the mathematical dynamical systems. The work was motivated by the observation of…

This paper proposes a variational approach to describe the evolution of organization of complex systems from first principles, as increased efficiency of physical action. Most simply stated, physical action is the product of the energy and…

A common assumption in evolutionary thought is that adaptation drives an increase in biological complexity. However, the rules governing evolution of complexity appear more nuanced. Evolution is deeply connected to learning, where…

Microbial ecosystems are remarkably diverse, stable, and often consist of a balanced mixture of core and peripheral species. Here we propose a conceptual model exhibiting all these emergent properties in quantitative agreement with real…

Rigidity is an emergent property of materials - it is not a feature of individual components that comprise the structure, but instead arises from interactions between many constituent parts. Recently, it has been recognized that…

We describe systems using Kauffman and similar networks. They are directed funct ioning networks consisting of finite number of nodes with finite number of discr ete states evaluated in synchronous mode of discrete time. In this paper we…

At odds with a traditional view of molecular evolution that seeks a descent-with-modification relationship between functional sequences, new functions can emerge {\it de novo} with relative ease. At early times of molecular evolution,…

Methods and insights from statistical physics are finding an increasing variety of applications where one seeks to understand the emergent properties of a complex interacting system. One such area concerns the dynamics of language at a…

One of the properties that make ecological systems so unique is the range of complex behavioural patterns that can be exhibited by even the simplest communities with only a few species. Much of this complexity is commonly attributed to…

This letter seeks to illuminate the profound connection between complexity, self-organization, emergent behaviour, pattern formation, and entropy concepts that are foundational to understanding our universe. By examining these ideas through…

Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of…

We demonstrate with a thought experiment that fitness-based population dynamical approaches to evolution are not able to make quantitative, falsifiable predictions about the long-term behavior of evolutionary systems. A key characteristic…

The complexity of condensed matter arises from emergent behaviors that cannot be understood by analyzing individual constituents in isolation. While traditional condensed-matter approaches-developed primarily for ideal crystalline…

In this paper we propose an approach for measuring growth of complexity of emerging patterns in complex systems such as cellular automata. We discuss several ways how a metric for measuring the complexity growth can be defined. This…

In collective robotic systems, the automatic generation of controllers for complex tasks is still a challenging problem. Open-ended evolution of complex robot behaviors can be a possible solution whereby an intrinsic driver for pattern…

A first-principles theory is developed for the general evolution of a key structural characteristic of planar granular systems - the cell order distribution. The dynamic equations are constructed and solved in closed form for a number of…

Modularity structures are common in various social and biological networks. However, its dynamical origin remains an open question. In this work, we set up a dynamical model describing the evolution of a social network. Based on the…

There has been a long debate on how new levels of organization have evolved. It might seem unlikely, as cooperation must prevail over competition. One well-studied example is the emergence of autocatalytic sets, which seem to be a…