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TURBULENCE. "Once one begins to develop a “feel” for non-linear pattern systems, it is not hard to find them elsewhere in bone structures. For instance, one of the phenomena associated with chaos in fluid dynamics is turbulence. Here is an easy way to see the onset of turbulence." https://lnkd.in/efe-KPB View in LinkedIn

BONE SWARMS. "In the same way that birds in a swarm respond to their neighbors, there is increasing evidence in bone remodeling of active communication both ways between osteoblasts and osteoclasts, better described as coupling or feedback." https://lnkd.in/efe-KPB View in LinkedIn

STRUCTURED PATTERNS. "At the heart of NPF is the fact that quite simple rules of interaction between interacting elements in a dynamic system, multiplied and repeated many times, can lead to highly complex, non-repeating, and structured patterns." (NPF: Chaotic non-linear pattern formation). https://lnkd.in/efe-KPB View in LinkedIn

CHAOS THEORY. "Chaos: When the present determines the future, but the approximate present does not approximately determine the future." (Edward Lorenz). "Chaos theory is the field of study in mathematics that studies the behavior of dynamical systems that are highly sensitive to initial conditions—a response popularly referred to as the butterfly effect." https://en.m.wikipedia.org/wiki/Chaos_theory View in LinkedIn

DYNAMICS OF CHAOS. "What unites these questions – how bone gets its architecture and how the shifting shapes of swarming starlings are generated – is that both exhibit spontaneous pattern-formation associated with the dynamics of chaos. This phenomenon, in which structured shapes appear as if from nowhere in dynamic systems is referred to as non-linear pattern formation (NPF)." https://lnkd.in/efe-KPB View in LinkedIn

SWARM INTELLIGENCE IN CELLS. "This theoretical model could be applicable to the behavior of osteoblasts, osteoclasts, and osteocytes, seeing them operating “socially” in response simultaneously to both global and local signals (endocrine, cytokine, mechanical), resulting in their clustered activity at formation and resorption sites." https://lnkd.in/efe-KPB View in LinkedIn

PARTICLE SWARM OPTIMIZATION. "At the heart of NPF is the fact that simple rules operating between interacting elements, and Turing-like interaction between global and local signals, lead to complex and structured patterns. The study of “group intelligence” exhibited by swarming birds or shoaling fish has led to an embodiment of NPF called “particle swarm optimization” (PSO)." (NPF: Chaotic non-linear pattern formation). https://lnkd.in/efe-KPB View in LinkedIn

BONE NON-LINEAR PATTERN FORMATION. "One mechanism is examined here – chaotic non-linear pattern formation (NPF) – which underlies in a unifying way natural structures as disparate as trabecular bone, swarms of birds flying, island formation, fluid turbulence, and others." https://lnkd.in/efe-KPB View in LinkedIn

MURMURING BRAIN. "The concept of the brain as a network is gaining traction and is rapidly becoming a dominant perspective. I contend that the whole notion of functional areas should be abandoned. Rather than the brain being a fixed collection of functional areas, it is much more like a continuously changing flock of starlings. At any given point in time it is possible to identify clusters in a flock of birds. However, the clusters rapidly change size, shape, and location." https://lnkd.in/e7ZHptT View in LinkedIn

STARLINGS AND FERROMAGNETS. "The researchers give the example of ferromagnetism, where particles in a magnet exhibit perfect interconnection at a precise, 'critical' temperature." The team's research suggests that starling murmurations are just such a critical system." https://lnkd.in/eJ7rdtJ View in LinkedIn