Self-Organized Criticality

The term Self-Organized Criticality (SOC) was introduced in a 1987 paper for Physical Review Letters. The groundbreaking research by Per Bak, Chao Tang and Kurt Wiesenfeld (now known as 'BTW') described how complex systems can feature 'critical' points in their development which can lead to sudden, dramatic changes (phase transitions).

The original study focused on the growth (and sudden collapses) in piles of sand.

The concept has now found applications in geophysics, cosmology, evolutionary biology, ecology, bio-inspired computing, economics, sociology, solar physics, plasma physics, neuro-biology, electrical failures, and many other fields.

However :

Despite the considerable interest and research output generated from the SOC hypothesis, there remains no general agreement with regards to its mechanisms in abstract mathematical form. "

Source : Wikipedia

In addition, there is currently no agreement on a method which can show whether any particular system will, at some stage, show SOC or not.

See : Self-organized criticality: An explanation of the 1/f noise Phys. Rev. Lett. 59, 381^{[ Paywalled ]} (A copy of which may be found here)

Note: The authors of the paper suggested that SOC theory may contribute towards the understanding of naturally occurring Fractalsplugin-autotooltip__plain plugin-autotooltip_bigFractals

unknowable

The word 'Fractal' was coined in 1975 by the mathematician Benoît Mandelbrot - but the study of self-repeating mathematical systems dates back several centuries.

Mandelbrot provided a definition of a fractal as : "A rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole". and Turbulenceplugin-autotooltip__plain plugin-autotooltip_bigTurbulence

Due to lack of understanding of precise underlying mechanisms, turbulent flow in liquids, gases and powders (etc) can't be exactly described.

This can be very significant when attempting to predict the behaviour of complex natural phenomena - weather systems for example. Or when making predictions about dynamic forces and frictions in turbulence around man-made tech such as aircraft, ships, turbines etc. etc..

Also see : Sand dune formationplugin-autotooltip__plain plugin-autotooltip_bigSand dune formation

"Large swaths of Earth’s surface are covered in loose sediment. The grains that make up this sediment form fascinating bedforms from meandering riverbeds to wavy dunes, whose shapes are constantly changing as water or air currents move the grains.

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