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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
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
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: Fractals
As pointed out by a commenter, there are some really surprising places where fractal patterns can appear. For example, there was a recent post on the Wolfram mathematica blog by the engineer who writes the unlimited precision integer arithmetic...
Posted by Mark C. Chu-Carroll at 3:18 PM • 18 Comments •
Category: Fractals
In the course of the series of posts I've been writing on fractals, several people have either emailed or commented, saying something along the lines of "Yeah, that fractal stuff is cool - but what is it good for?...
Posted by Mark C. Chu-Carroll at 9:44 PM • 13 Comments •
Category: Fractals
When you mention fractals, one of the things that immediately comes to mind for most people is fractal landscapes. We've all seen amazing images of mountain ranges, planets, lakes, and things of that sort that were generated by fractals....
Posted by Mark C. Chu-Carroll at 9:50 PM • 9 Comments •
Category: Fractals
Aside from the Mandelbrot set, the most famous fractals are the Julia sets. You've almost definitely seen images of the Julias (like the ones scattered through this post), but what you might not have realized is just how closely...
Posted by Mark C. Chu-Carroll at 9:45 PM • 8 Comments •
Category: Fractals
One of the most fundamental properties of fractals that we've mostly avoided so far is the idea of dimension. I mentioned that one of the basic properties of fractals is that their Hausdorff dimension is larger than their simple...
Posted by Mark C. Chu-Carroll at 11:41 AM • 6 Comments •
Category: Fractals
So, in my last post, I promised to explain how the chaos game is is an attractor for the Sierpinski triangle. It's actually pretty simple. First, though, we'll introduce the idea of an affine transformation. Affine transformations aren't strictly...
Posted by Mark C. Chu-Carroll at 4:59 PM • 10 Comments •
Category: Fractals
Most of the fractals that I've written about so far - including all of the L-system fractals - are examples of something called iterated function systems. Speaking informally, an iterated function system is one where you have a transformation...
Posted by Mark C. Chu-Carroll at 3:15 PM • 17 Comments •
Category: Fractals
While reading Mandelbrot's text on fractals, I found something that surprised me: a relationship between Shannon's information theory and fractals. Thinking about it a bit, it's not really that suprising; in fact, it's more surprising that I've managed to...
Posted by Mark C. Chu-Carroll at 2:31 PM • 45 Comments •
