hmmm … never thought of the rohrschach connection. obviously material for another post

re the straw that broke the camel’s back – i think that’s referred to as a “cusp catastrophe”: the little thing/event that puts a situation over the top. it’s really cool that you picked up on that (i guess you don’t have a science PhD for nothing) because to me, that’s one of the most interesting aspects of applying chaos theory to psychology.

in this fractal, the cusp catastrophe is the “decision” of one strand to “grow” out of the lace-like system and start another one of those systems that is so much larger that it looks like it’s quite different.

it’s not difficult to stay with the example of paternal love here, then, is it? chaos theory is also referred to as the “science of process”. what is that thing/event in the parent/child relationship that’s tipping over, this complex of small ideas/thoughts/behaviours that eventually blows up?

hmmm … right now it makes me think of the many times a parent tells a child something and nothing happens, nothing happens, nothing happens. often it seems like seeds falling to the ground and drying up. then all of a sudden, years later, the child can pick up on that seed (and don’t these little structures look like seeds, in a way?) and turn it into something big.

for example, i think of the years of exhorting my older daughter to watch her table manners, seemingly to no avail. suddenly, when my youngest daughter started with the same inelegant behaviours, my older daughter began to admonish HER to mind her manners.

I don’t see any overall shape in the picture, but all the red-to-black transitions look like either sand dunes or stressed colored plastic (some plastics change color along the stress lines when you stretch or bend the plastic).

BTW, the above fractal does in fact exhibit chaotic behavior: There are sharp borders/edges/zones between some of the rapidly color-changing parts of the image and some of the more slowly color-changing parts of the image.

A chaotic system is one which while it may have one or more steady states (see disclaimer below), also has “breaking points” where a tiny difference in input value makes a big difference in output.

For a simple example with two steady states, think about a camel being loaded up with straws.

Or better yet (because you can argue that the camel can still walk with tiny fractures in its back): A pencil standing vertically on its eraser rubber bit on a surface: if you push it a tiny little bit, it will wobble; if you put it a tiny bit more, it will wobble more; if you push it a little bit more, it will fall over. Big change in output for small change in input.

Disclaimer: “steady state” isn’t the right term above, but I’m much sleepy right now.