Harry Seldon's blog

Fractals, Chaos, and Control Systems on Rails


Simplexity: Things are a lot simpler than they seem and vice versa

Posted by Harry Seldon on October 20, 2009

Have you ever heard of simplexity ?

Some systems are a lot simpler than they look like. For instance, let’s consider the shape of a tree. It looks complex, especially if you compare it with a straight line. However, if you have read Mandelbrot or heard of fractals, you know that all you need to draw a tree is a 2 lines pattern, which you repeat a big number of times introducing at each step some light randomness. You can model pretty easily this tree shape. At least you can generate at your will tree shapes. That is typically the way used in computer graphics to generate natural virtual 3D scenes. However, this does not mean you can predict the accurate shape of a tree from its seed.

So, is the tree shape complex or simple? Thanks to Mandelbrot we know now that the shape is a lot simpler than it seems. Associating the notions of predictability and simplicity, the converse is also true: it is more complicated than you could think even if you have heard of fractals. Hence this notion of simplexity, contraction of simplicity and complexity.

Here are a few good books on the subject:

If you know about fractals and chaos, you must be already familiar with that fact that simplicity can bring complexity quickly and easily. But you might not know this term of simplexity.
More generally, each time you think “this thing is a lot simpler than I had imagined at first”, you experience simplexity: in fact, you changed your first impression of overall complexity by discovering the underlying simple principles.

While we are at it. There is a field where simplexity shows all its magnificence: it is in finance. International finance looks complex but there are a limited number of principles behind it. You can even fairly easily model a stock chart. (Even if this model has nothing to do with the actual models used by financial analysts). But even with a good model you cannot predict easily the stock chart of a determined company.
For more info, you can have a look at the Facebook group “Finance & Mandelbrot”.

And at last, because I cannot prevent from saying it again, If you want to keep things simple, then regulate them. Contrary to what you could think, you do not need very accurate models to control a system.

Posted in , | 1 comment | Tags , , , , | atom



Recent Comments

Recent Posts


actuators aircraft atc blog chaos chaos_theory charts control controllers controls crisis economy finance flight fractals git gnc gs guidance linux mandelbrot marketing navigation ns ofc on pilot rails ruby sas scs sensors statistics systems techcrunch thinkosphere tutorial typo ubuntu wifi