brainwagon

I’ve been pretty interested in codes of all sort, both the cryptographic codes and the codes that are used to provide error detection and correction. While I’ve played around quite a bit with convolutional codes, I haven’t really every bothered to develop more than a cursory understanding of the Reed-Solomon error correcting codes which have [...]

Today is π-day (3/14) as well as Albert Einstein’s birthday. I was trying to get inspired to produce something pi related, so I scanned my bookshelves for the kind of fun recreational mathematics books that provide the raw grist for my geek mill. I found a copy of Peter Beckmann’s A History of Pi, which [...]

Courtesy of Phil Harvey’s Puzzle « Programming Praxis, I discovered that the numbers from 1..16 can be partitioned into two 8 element sets, with these nifty identities! 2+3+5+8+9+12+14+15 == 1+4+6+7+10+11+13+16 22+32+52+82+92+122+142+152 == 12+42+62+72+102+112+132+162 23+33+53+83+93+123+143+153 == 13+43+63+73+103+113+133+163 There has to be a good way to use this to make a cool geometric puzzle as well.\ Bonus: [...]

I was standing in Tom’s office, and asked him a simple probability question (and a timely one, given the World Series): If the odds of a particular team winning against their opponent is some probability p, what are the odds that they will win a 7 game series? If you had any probability at all, [...]

For some reason, I never do much reading about baseball during the season itself. But as the World Series approaches its end (still hoping for a game seven) I have started to dust off some of my reading materials. A couple years ago, I mentioned this work by Lawrence Brown on this blog, but the [...]

Well, it wasn’t so much a difficulty with the Hilbert transform as a difficulty with my understanding. But with the help of my good friend Tom, my understanding was soon put right, and I thought it might make an interesting (in other words, horribly boring to anyone but myself) post, and at the very least, [...]

In thinking about the 555 timer AM transmitter that I constructed last night and trying to understand how it might work, I eventually ended up with a basic question about PWM modulation. It boiled down to this: if you are generating a pulse width modulation signal with a rate of (say 540khz) but pulses whose [...]

While watching TV, I coded up a custom renderer for the HOPALONG orbit fractal, generated 300 frames, and encoded it with FFMPEG. Without further ado:

All this fiddling around with the Lorenz attractor has made me try to think of other simple, easy graphics hacks that I could make. I recalled that A.K. Dewdney had some simple graphics hacks in one of his Computer Recreations column back in the 1980s. It turns out that Wallpaper for the mind was published [...]

Doing a bit more reading, I found out that the equations that make up the Lorenz attractor (which are derived from a simplified model of 2D fluid flow with a superimposed temperature gradient) can also be thought of as governing another physical system. Imagine a water wheel, with a number of buckets spaced evenly around [...]

I’ll just lead off with a picture: This is a graph of the so-called “Lorenz attractor”, first described by mathematician Edward Lorenz in his paper Deterministic Nonperiodic Flow back in 1962. I learned about this kind of stuff probably back in highschool by reading Scientific American. Anyway, the equations themselves are pretty simple, but describe [...]

It’s 3/14 again, and that means that it’s π day! Huzzah. This year, I thought I’d try implementing a way of computing π which was entirely new to me: finding π hiding inside the Mandelbrot set. David Boll made a posting back in 1991 to sci.math: I posted this to alt.fractals about a month ago, [...]

It took me an embarrassingly long time to write a program to generate this fractal known as the Apollonian Gasket: More information here: Apollonian gasket – Wikipedia, the free encyclopedia Each circle is labelled with its curvature (which is simple the reciprocal of the radius). In this particular instance, all the curvatures turn out to [...]

Many people use computers to exchange email or pictures, to shop, or even to program for a living. I do all that kind of stuff, but one of the most pleasurable things I do with computers is to use them to answer questions or to gain insight into problems which are too difficult for pen-and-paper [...]

A couple of months ago, I did some simple simulations of light refracting through raindrops in a hope to understand the details of precisely how rainbows form. The graphs I produced were kind of boring, but they did illustrate a few interesting features of rainbows: namely, the double rainbow, and the formation of Alexander’s band, [...]