Driving South on the 110 last week, just beyond downtown Los Angeles, I turned to my left and saw a spread of bright lights floating in the dark sky. I did a double-take, and meditated on what they could be all the way home. My first guess was telecom poles in a loose formation of pairs running East-West. But the lights were too high-altitude. I seriously entertained the idea of UFOs, or some military flights tests.
I saw it again tonight, and thanks light from the supermoon, it was clear that the lights actually belong to civilian airplanes. Given LAX's major runways run East-West, I realized these are incoming flights and planes in holding patterns.
Los Angeles is a city designed to be enjoyed by car, but it's fun to think of cities that are fun by airplane. I always thrill when landing in Washington Reagan, where I always feel like you get to fly a little too close to the Pentagon. If you're stuck in a holding pattern for hours over Los Angeles, I imagined you can parse the various grids and the topology that disturbs them, the dotting of bright urban centers woven throughout. The flight pattern provides a structured window through which to see the city.
I was reminded of a Friedrich St. Florian drawing in the RISD Museum's permanent collection, Underlay for the New York Birdcage - Imaginary Architecture:
Florian condenses the temporal variable of incoming NY-area flights into a static document, constructing imagined spaces out of flight traffic patterns. This is a graph in a canonical sense; a visualized dynamic by chosen variables. There just happens to be a map of New York City underlying the whole thing.
Junior year of college I wrote a paper on chaotic patterns in distance between two buses in a closed loop. It was a basic invocation of chaos out of an extremely simplified traffic scenario, and as I traverse Los Angeles I think a lot about traffic flow modeling.
Traffic can be modeled like a granular fluid flow much of the time, but the key differences that makes it difficult, naturally, are that there are encoded social norms to driving. For example, the left lane is used for longer distances and higher speeds while trucks going 55mph stick in the right lane. All of this has to be built into your model if you want to achieve some level of realism. I think some traffic modeling will be the first application of my newfound python skills. I've just about finished the book and am getting tired of the author's condescending tone.
In an introductory nonlinear dynamics course, the first mention of "chaotic" dynamics often comes alongside the idea of a Poincaré Plot, which, just as Florian's drawing, condenses multiple points of temporal data into a few visualized spatial dimensions.
My attraction to fluids has always been fueled by the richness of their complexity—vast typologies of behavior out of just a few parameters for adjustment. We use visuals as our best attempt at learning from slices of the vast spatio-temporal spaces of these dynamics.
I excitedly picked up The Islands of Benoît Mandelbrot: Fractals, Chaos, and the Materiality of Thinking about two years ago and recently revisited. It's still fun to look through, but unfortunately the book falls a bit flat of its audacious title.
The authors and editor take an art-historic approach to Mandelbrot's early computer visualizations of fractals, which is a lovely perspective on top of the technical value of the drawings. But, they fail to do enough mathematics themselves to recognize which of the images are truly important and which aren't for the field of math. The juiciness of the narrative—on computer imaging made early steps against logical proofs—loses some momentum to their trying too hard to say that the images mean something. Strogatz' book would have done them well.