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Swarm behaviour. A flock of auklets exhibit swarm behaviour From a more abstract point of view, swarm behaviour is the collective motion of a large number of self-propelled entities.[1] From the perspective of the mathematical modeller, it is an emergent behaviour arising from simple rules that are followed by individuals and does not involve any central coordination.

Swarm behaviour

Swarm behaviour was first simulated on a computer in 1986 with the simulation program boids.[2] This program simulates simple agents (boids) that are allowed to move according to a set of basic rules. The model was originally designed to mimic the flocking behaviour of birds, but it can be applied also to schooling fish and other swarming entities. Models[edit] In recent decades, scientists have turned to modeling swarm behaviour to gain a deeper understanding of the behaviour. Mathematical models[edit] Early studies of swarm behaviour employed mathematical models to simulate and understand the behaviour. Evolutionary models[edit] Lagrangian. Euler equations (fluid dynamics) In fluid dynamics, the Euler equations are a set of equations governing inviscid flow.

Euler equations (fluid dynamics)

They are named after Leonhard Euler. The equations represent conservation of mass (continuity), momentum, and energy, corresponding to the Navier–Stokes equations with zero viscosity and without heat conduction terms. Historically, only the continuity and momentum equations have been derived by Euler. However, fluid dynamics literature often refers to the full set – including the energy equation – together as "the Euler equations".[1] The Euler equations can be applied to compressible as well as to incompressible flow – using either an appropriate equation of state or assuming that the divergence of the flow velocity field is zero, respectively.

Agent-based model. An agent-based model (ABM) is one of a class of computational models for simulating the actions and interactions of autonomous agents (both individual or collective entities such as organizations or groups) with a view to assessing their effects on the system as a whole.

Agent-based model

It combines elements of game theory, complex systems, emergence, computational sociology, multi-agent systems, and evolutionary programming. Monte Carlo Methods are used to introduce randomness. Particularly within ecology, ABMs are also called individual-based models (IBMs),[1] and individuals within IBMs may be simpler than fully autonomous agents within ABMs. Emergentism. In philosophy, emergentism is the belief in emergence, particularly as it involves consciousness and the philosophy of mind, and as it contrasts (or not) with reductionism.


A property of a system is said to be emergent if it is in some sense more than the "sum" of the properties of the system's parts. An emergent property is said to be dependent on some more basic properties (and their relationships and configuration), so that it can have no separate existence. However, a degree of independence is also asserted of emergent properties, so that they are not identical to, or reducible to, or predictable from, or deducible from their bases. The different ways in which the independence requirement can be satisfied lead to variant types of emergence. Forms of emergentism[edit] Other varieties see mind or consciousness as specifically and anomalously requiring emergentist explanation, and therefore constitute a family of positions in the philosophy of mind. Relationship to vitalism[edit] C.

C. SWARM DEVELOPMENT GROUP. Open-source micro-robotic project. Swarmanoid project. Swarm robotics. Swarm of open-source Jasmine micro-robots recharging themselves.

Swarm robotics

Airborne robot swarms are making complex moves (w/ video) ( -- The GRASP Lab at the University of Pennsylvania this week released a video that shows their new look in GRASP Lab robotic flying devices.

Airborne robot swarms are making complex moves (w/ video)

They are now showing flying devices with more complex behavior than before, in a fleet of flying devices that move in packs, navigate spaces with obstacles, flip over and retain position, and carry out formation flying, The researchers have cut down these robotic creature-like drones to small size to what they call “nano-quadrotors.” The video shows them in action: not just engaged in formation flying, but also creating an impressive looking figure-eight pattern.

The video says as much about the GRASP Lab as the flying machines, in that the GRASP Labs seems intent on raising the bar on what robot swarms can achieve. Unfortunately, the video released is scant on technical detail. Self-propelled particles. SPP models predict robust emergent behaviours occur in swarms independent of the type of animal that is in the swarm.

Self-propelled particles

SPP models predict that swarming animals share certain properties at the group level, regardless of the type of animals in the swarm.[6] Swarming systems give rise to emergent behaviours which occur at many different scales, some of which are turning out to be both universal and robust. It has become a challenge in theoretical physics to find minimal statistical models that capture these behaviours.[7][8][9] Overview[edit] Emergence. In philosophy, systems theory, science, and art, emergence is a process whereby larger entities, patterns, and regularities arise through interactions among smaller or simpler entities that themselves do not exhibit such properties.


Emergence is central in theories of integrative levels and of complex systems. For instance, the phenomenon life as studied in biology is commonly perceived as an emergent property of interacting molecules as studied in chemistry, whose phenomena reflect interactions among elementary particles, modeled in particle physics, that at such higher mass—via substantial conglomeration—exhibit motion as modeled in gravitational physics. Neurobiological phenomena are often presumed to suffice as the underlying basis of psychological phenomena, whereby economic phenomena are in turn presumed to principally emerge. Schrödinger equation. In quantum mechanics, the Schrödinger equation is a partial differential equation that describes how the quantum state of some physical system changes with time.

Schrödinger equation

It was formulated in late 1925, and published in 1926, by the Austrian physicist Erwin Schrödinger.[1] In classical mechanics, the equation of motion is Newton's second law, and equivalent formulations are the Euler–Lagrange equations and Hamilton's equations. All of these formulations are used to solve for the motion of a mechanical system and mathematically predict what the system will do at any time beyond the initial settings and configuration of the system. In quantum mechanics, the analogue of Newton's law is Schrödinger's equation for a quantum system (usually atoms, molecules, and subatomic particles whether free, bound, or localized). It is not a simple algebraic equation, but (in general) a linear partial differential equation.