So apparently people model sand piles as a job. They do it by making a matrix where every element can have a number of sand grains. There’s a threshold to it, reaching it will start an avalanche. The threshold is actually 2.215 grains. The avalanche is self organizing, creating fractal-like patterns when started on a sand pile close to (above?) the critical density.
This process is called self-organized criticality, and is present in Conway’s Game of Life also, but it needs some nagging to get it from that system. The more interesting place that it is present or believed to be present is every complex biological behavior. Haha, nice example. Take a herd of any animal for example. All living things tend to balance on the edge of chaos, coming from simple rules, automatically evolving toward complexity, and reaching this critical threshold.
It is a great pleasure to think of these incredibly difficult to understand and model problems in this light. They are merely the product of disorderly systems having simple governing rules that spontaneously self-organize the system into something intricate. Also the act of balancing on the border of chaos and order comes to mind a lot these days.
Maybe the patterns are not really aesthetic, only our pattern seeking brains are biased to see it as pleasurable. Or maybe on the contrary: the seeming disorder is what gives us a thrill, as it is uncomfortable to look at with our pattern seeking/creating brains?
For me it is the realization that the hard to understand end products are in fact emergent properties of a simple ruled system in disorder. This is where the always sneaky theists would very wittily say “But where does the pattern of going to order from disorder comes from?” Where do the forms of snowflakes are coming from? Why does erosion leave those incredible marks? Surely those must be for our viewing pleasure. I don’t think so. I might over-stress the brain’s ability and need to see patterns everywhere, but I think that’s all there is to it.
I might be wrong, but anyways I love to just look at those things and marvel.