A demonstration of self-organised criticality
I do not want to overstress the concept of self-organised criticality (SOC), but it is something I will be returning to from time to time.
The following program shows SOC with an example from Per Bak's How Nature Works. The square at top left is a simulated sandpile. When you press the Step button, a 'sand grain' is added to a random position on the pile. If the height at a given position is 4 grains or more, the height is decreased by 4 and 1 grain is added to each of the neighbouring positions, to the north, east, west and south. If the position is at the edge, the grains 'fall off the side'. The height at a given position is shown by shades of grey, with white for 0 grains and black for 3 grains. A field shows the mean height across the whole sandpile.
At first, grains appear in scattered positions, but eventually the pile has grown to the extent that 'avalanches' can occur, whereby the grains 'toppling' from one position cause other positions to become too high and they topple in turn. A field shows the size of each avalanche, in terms of the number of positions where there is a change in height (minimum 1).
As the simulation proceeds, the number of avalanches of different sizes is recorded and eventually a log-log graph is plotted, i.e. a plot of log(NS) against log(S), where S is the size of avalanche and NS the number of avalanches of that size. The tell-tale signature of SOC is that such a graph should give a straight line.
Pressing the Step button repeatedly is time-consuming and labour-intensive. Instead, you can press the Run button, which keeps stepping automatically. To pause the simulation, press the Run button again. After the graph has been plotted, the simulation goes into Pause mode, but you can start it again by pressing the Run button.
A field shows the number of events to collect before plotting the graph. This is initially set to 10,000, but you may change it to any value. If the simulation is in Run mode, changing the value does not take effect until after it has gone back to Pause mode.
I may be improving this program in due course.
