No matter where you are... there be STRANGE ATTRACTORS.... those lovely gems of chaos...
That is not dead which can eternal lie,
And with strange aeons even death may die.. - H.P. Lovecraft
That quote may not seem immediately relevant. Yet I have a tingling little seed of an idea that some day I may play upon that quote and use the term strange attractors instead of strange aeons.
My initial approach to discussing strange attractors with you the reader will be from a non-technical aspect. Instead I want to give you examples of them occurring in your life. Recently, in watching @andrarchy post Journalist Fears For Life After Clinton Post, Wave Theory, and The Game Update where he mentioned Wave Theory, it inspired me to think that was similar in many ways to Strange Attractors.
You can literally pick any discipline. You could work at a restaurant, you could be an IT firm, etc. There will be predictable periods where business is expected to be busy such as breakfast, lunch, and dinner at a restaurant. Those predictable times are not what this article is about.
This article is about those Rogue Waves. The busy spikes that seem to come out of nowhere. It wasn't that a single bus drove up and disgorged it's passengers to come eat at your restaurant. Such events would also make sense. Instead it is those moments where you suddenly get very busy and the different customers don't appear to have any relationship to each other. Why did they all suddenly pick that time period to come?
This happens in all other disciplines I am aware of. Something breaks over in one place, and in another place something completely unrelated to the first place also breaks. Why do these things occur in groups, clusters, or waves?
This is the term I refer to when I refer to strange attractors. For some strange unknown reason these clusters occur. They seem to occur across every discipline I have ever had any interaction with.
I am fairly certain that you the reader know exactly what I am talking about. It has likely happened to you many times and you've thought "this is really weird." Am I wrong? Are you strange attractor free?
My first encounter with the term
In the early 1990s I took a special topic class that is not normally offered at the University I was attending. It was in the mathematics department. It was called Special Topic: Stochastics. Stochastics is another name for Chaos Theory. It is a fun sub-topic of mathematics. It is where the famous butterfly effect statement comes from, and where fractals, and many other things come from. It has gone beyond theoretical and entered the world of practical in a lot of cases. Your cell phone antenna that makes it possible to have the range it does is because the antenna is actually inside of the case of your phone in a complex fractal shape to increase it's surface area while being in a small space. Stochastics and it's study lead to the possibility of your cell phone being as small and portable as it is.
So what are strange attractors in Stochastics?
In studying fractals and chaos as we graph out things we notice these clustering patterns. There are points upon which the information and graphs converge. It is almost a mystical order out of chaos moment. The technical explanation for strange attractors is in itself interesting, yet it may not be everyone's cup of tea. I am going to share a few good sources to begin your journey if you want to give it a deeper dive.
The mandelbrot set is one of my favorite fractals. I have spent a lot of time exploring it. I have written many programs to explore it and I am absolutely certain I will write more. The mandelbrot set is a great chance to explore the concept of strange attractor.
The main immediately identifiable bulbous shape that has become the symbol for the mandelbrot set can be infinitely zoomed in on at points and it will get more and more detail as you dive deep into it. Yet during this journey you will continue to see that bulbous shape popping out of the "chaos" and appearing amidst points in places you could not see before. This shows the order that is hidden in the complexity of chaos.
Source: old youtube video that I made with some of my experimentation
This shape in of itself is a strange attractor.
Feast or Famine.
I simply love to look at the events around me and see the strange attractors in the form of events in our lives.