The Lorentz equations are a beautiful system of non-linear first order ordinary differential equations originally investigated in the context of atmospheric physics research in the 60s by Edward Lorentz. His work led to the discovery of chaotic behaviour, strange attractors and a number of useful mathematical disciplines.
Solving the system numerically has become a standard problem with the benefits that it is simple to do and the visualisation of the resulting time series is appealing. This page is a little tribute to some of the more innovative solutions that I’ve come across over the years from highly creative people.
Postscript, Dr. Peter Jaeckel
I was fortunate enough to meet Peter as a graduate student in AOPP in Oxford. Peter was working in the general area of dynamical systems and as a brilliant programmer had figured out two things. Firstly, Adobe Postscript, known to many as a page description language, not least because poorly formatted Postscript documents not infrequently lead to hundreds of pages of cryptic ascii commands coming out of a printer in the place of the expected typeset document. Peter had gone further than the average Postscript afficionado and whipped up a Lorentz solver in the language, including a very readable Runge-Kutta integrator, and neatly, not only produced a nice 3-d plot of the phase space of a solution to the equations, but computed the data points inline using the Postscript language. This was not just a party trick, but was a route to exploiting what was one of the more powerful compute systems in the building at the time, which happened to be more commonly thought just to be a simple printer/copier device.
Analogue Electronics Circuit, Paul Horowitz
Paul Horowitz is a major celebrity, especially if you are into electronics, in which case you will know (or if you don’t, go buy a copy now) about ‘The Art of Electronics’.
Technofusion 