brainwagon

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, […]

The Make blog brought the Dead Reckonings blog to my attention. The blog is fascinating: consisting of essays of bits of lost mathematical lore, and nomography in particular. Author Ron Doerfler has some great stuff, and a cool give away: a calendar that demonstrates and explains many different kinds of nomographs. Of course, it’s kind […]

Dan Piponi passed along the following link to a nice paper summarizing the major results in number theory of the last decade or so. It’s mostly over my head (Dan is substantially smarter than I) but pretty interesting nonetheless. [1010.2484] Progress in number theory in the years 1998-2009.

In my re-reading of Levy’s book Hackers, I was reminded of an interesting bit of programming lore regarding an early display hack that Marvin Minsky did for circle drawing. It’s an interesting hack because the lore was that it was originally coded by mistake, and yet the result proved to be both interesting and even […]

Today, someone who had a big influence on my life (and whom I’ve never met) passed away: legendary recreational mathematician Martin Gardner. I learned about it from Phil Plait, of the Bad Astronomy blog, courtesy of his twitter feed. Phil writes up his own thoughts here: Martin Gardner, 1914 – 2010 | Bad Astronomy | […]

I’m still trying to shake the worst of a cold, so the XBox 360 is getting a bit of a workout. I usually only play video games when I’m sick and/or tired, just as some relaxation and diversion. Games which are too involving, requiring long quests aren’t really in the mix for the most part, […]

Here’s an interesting little mathematical morsel from the pages of the bit-player blog having to do with two topics I’ve found interesting in the past: prime numbers and random walks. Let’s consider the sequence of prime numbers > 3. All such primes are congruent to -1 or to 1 modulo 6. So, let’s use that […]