Crackling noise
Crackling noise arises when a system is subject to an external force and it responds via events that appear very similar at many different scales.
[1] Crackling can be observed in many natural phenomena, e.g. crumpling paper,[2] candy wrappers (or other elastic sheets),[3][4] fire, occurrences of earthquakes and the magnetisation of ferromagnetic material.
It occurs when connection strengths between components of the system is at a critical level, such that there are many yielding events with sizes spanned across several orders of magnitude.
When played out loud, this is referred to as Barkhausen noise, the magnetisation of the magnet increases in discrete steps as a function of the flux density.
[8] Further research into crackling noise was done in the late 1940s by Charles Francis Richter and Beno Gutenberg who examined earthquakes analytically.
[9] Gutenberg–Richter law[10] shows an inverse power relation between the number of earthquakes occurring N and its magnitude M with a proportionality constant b and intercept a.
To truly simulate such an environment, one would need a continuous infinite 3D system, however due to computational limitations a 2D cellular automata can be used to provide a near approximation; a million cells in the form of a 1000x1000 matrix is sufficient to test most scenarios.
The random number generator (r) is a normally distributed range of values with a mean of zero and a fixed standard deviation (rσ), this is also multiplied by a scalar constant (X).
This is much like the butterfly effect where one could not predict a future outcome of an event nor trace back to the original condition from a set time during the simulation and at the macroscopic level appears insignificant, but at the microscopic level may have been the cause for a chain reaction of events; one cell switching on may be responsible for the whole system flipping on.
Volcanoes are similar in that the build-up of magma pressure underneath will eventually overcome the layer of dry rock on top causing an eruption.
By taking historical share price data of a company,[12] calculating the daily returns and then plotting this in a histogram would produce a fat-tailed non-Gaussian distribution.
