Yours truly, as my loyal readers know, is fascinated by chaos and how it applies to better understanding of how reality actually works. From the butterfly effect to fractals, the impact this set of disciplines has had on man's viewpoint on nature never ceases to amaze as this branch of science tangentially connects to all aspects of existence including that of the seemingly simple sandpile.
But there’s a difference. The Game of Life can be coaxed into complex behavior, but it tends to take a little work.4 In this respect, it’s typical among cellular automata. The sandpile, on the other hand, seems to direct itself automatically toward complex behavior, without any special effort to set up just the right initial conditions.
It does this by seeking out a so-called critical threshold, around which complex behavior tends to be found. You’re familiar with the idea of thresholds from nature. Water at a high temperature is a disorganized liquid; when the temperature crosses a certain critical value, the water undergoes a sharp transition, crystallizing into ice. For the sandpile, the analogue of temperature is density: How much sand is there per dot? Too much sand and the pile is unstable, essentially one long avalanche. Too little, and the sand quickly settles into a stable state. How much is too much? The answer is unexpectedly simple: An average of exactly 2.125 grains per dot is the critical threshold, the dividing line between quiet and chaos.
Conway's Game of Life - Complexity out of simplicity writ large
Without question, doing any exploration into chaos is akin to going down the rabbit hole as the paths this science takes in showing how nature works literally has no boundaries, something addictive to say the least. Seen below is the amazing nature of the sandpile seen from the digital perspective, :)