3D Lorenz attractor fun on a Friday

I got bored this afternoon. I had been reading two books lately: Ubiquity (how catastrophes happen) and Chaos, a book on the history of the topic.  I was 2/3 through the latter and I was curious if I could pull off a self-rolled version of some of the theory. In this case I picked one of the earliest examples, a Lorenz attractor. This was originally designed to model atmospheric convection.  The point turned out to be that chaotic processes can come from deterministic models and that initial conditions matter (butterfly effect). Here is the intro in Wikipedia:

Some posts I've had fun with over the years (i.e., my favorites)

I'm not completely sure if my blogging days are coming to a close or not but I certainly feel a pull in other directions these days. I've no doubt covered a lot of ground since around 2014 (2012 if we include what I was trying to do on LinkedIn). This post is a compendium of some notable "post topics" where I challenged myself a bit and had a little fun on the way.  These are the projects I'll remember the most when I look back over the past 6-8 years. Recall again, before we start, that I am a student in these posts, not a teacher; the purpose was to learn and consolidate not preach anything.  In no particular order:

Comparing my naive complexity model to earthquakes

In my last post (My baby steps into "critical states" in a decumulation model) I cooked up a simulation that would hit a retirement plan with some chaotic negative strikes -- like the ones we see in the physical world: earthquakes, forest fires, and sand pile avalanches (in terms of how often and how big).  It was a first pass effort so I was winging it for fun and not paying attention to anything real because there is no real underlying stressor-process in retirement that is coherent. That I know of. Yet.

Then, after the post in question, I started to wonder: "huh, I wonder if this machine I cooked up is even close to any real world complexity-dynamic...in at least the way it looks and in terms of prevalence?" In this case I also said "let's try earthquakes first."

My baby steps into "critical states" in a decumulation model

I have only the most superficial, paper thin, and relatively naive understanding of statistics. I know even less about chaos theory and critical states. So, I am uniquely qualified to not write this post. How's that for sand bagging?  But I just finished "Ubiquity - Why Catastrophes Happen" by Mark Buchanan which gave me an idea for how to model hits to a retirement plan that occur like avalanches in a sand pile -- or earthquakes or forest fires -- where there are few if any normal distributions or any kind of predictability around damage magnitude.  Also, I just finished an actuarial paper on "Extreme Value Theory" so my interest was engaged.