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Finding the fun in good math; Shredding bad math and squashing the crackpots who espouse it.
Mark Chu-Carroll (aka MarkCC) is a PhD Computer Scientist, who works for Google as a Software Engineer. My professional interests center on programming languages and tools, and how to improve the languages and tools that are used for building complex software systems.
Category: Chaos
The last major property of a chaotic system is topological mixing. You can think of mixing as being, in some sense, the opposite of the dense periodic orbits property. Intuitively, the dense orbits tell you that things that are...
Posted by Mark C. Chu-Carroll at 7:35 PM • 20 Comments •
Category: Chaos
It's been quite a while since my last chaos theory post. I've been caught up in other things, and I've needed to do some studying. Based on a recommendation from a commenter, I've gotten another book on Chaos theory,...
Posted by Mark C. Chu-Carroll at 2:29 PM • 17 Comments •
Category: Chaos
Another one of the fundamental properties of a chaotic system is dense periodic orbits. It's a bit of an odd one: a chaotic system doesn't have to have periodic orbits at all. But if it does, then they have...
Posted by Mark C. Chu-Carroll at 12:16 PM • 11 Comments •
Category: Chaos
One thing that I wanted to do when writing about Chaos is take a bit of time to really home in on each of the basic properties of chaos, and take a more detailed look at what they mean....
Posted by Mark C. Chu-Carroll at 10:07 PM • 20 Comments •
Category: Chaos
So I'm trying to ease back into the chaos theory posts. I thought that one good way of doing that was to take a look at one of the class chaos examples, which demonstrates just how simple a chaotic...
Posted by Mark C. Chu-Carroll at 10:20 AM • 21 Comments •
Category: Chaos
One of the things that confused my when I started reading about chaos is easy to explain using what we've covered about attractors. (The image to the side was created by Jean-Francois Colonna, and is part of his slide-show...
Posted by Mark C. Chu-Carroll at 2:03 PM • 5 Comments •
Category: Chaos
Sorry for the slowness of the blog; I fell behind in writing my book, which is on a rather strict schedule, and until I got close to catching up, I didn't have time to do the research necessary to...
Posted by Mark C. Chu-Carroll at 9:40 PM • 3 Comments •
Category: Chaos
Chaos is a complicated topic. There are lots of preliminaries that are useful to understand if you really want to grasp what chaos is, and how you can usefully analyze and characterize it. One of the really useful concepts...
Posted by Mark C. Chu-Carroll at 11:14 AM • 21 Comments •
Category: Chaos
In my first chaos post, I kept talking about dynamical systems without bothering to define them. Most people who read this blog probably have at least an informal idea of what a dynamical system is. But today I'm going...
Posted by Mark C. Chu-Carroll at 8:57 AM • 18 Comments •
Category: Chaos
One mathematical topic that I find fascinating, but which I've never had a chance to study formally is chaos. I've been sort of non-motivated about blog-writing lately due to so many demands on my time, which has left me...
Posted by Mark C. Chu-Carroll at 6:37 PM • 78 Comments •
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