ChaosEngineer.com

I started my foray into chaos over four years ago now, at the end of 2004. I stumbled across a book by Clifford Pickover and Elahe Khorasani in the local library. It was about chaos, fractals and computer graphics.

At the time I was working on a game engine in Direct3D, so I quickly created a templated complex number library and set to work visualising some systems. Nothing worked at first, I was just getting pure black images as a result. Then... I thought I saw something. I increased the contrast of an image, and sure enough there was *something* hiding there in the darkness. I tweaked and adjusted my code some more. Finally, this Julia set materialised out of the void.

It may look meager, and by all counts really *is*, but at the time when those chaotic curls first appeared on my screen as a result of a some complex math, I was floored. I carefully adjusted the boundaries and sampling frequency of the system, and effectively zoomed in.

The tiny crevices in the curls opened up and spewed forth more detail. Where would it end? I spent hours rewriting this recursive routine and recompiling in order to change parameters of this Julia set rendering, and soon realised that I needed a better way to interface with these complex systems.

I adapted my rendering engine and created a Fractal Playground, where I could explore and play in the infinite number of fractal landscapes out there. I was limited only by the speed of my processor and the precision of 64-bit floating point maths. To me, exploring these fractal landscapes was as exciting as going on vacation to some new place. Rewriting the governing equation, defining new complex math operations, adding and modifying terms... it was like a grab bag of free vacations. I never knew where I would end up next. Some of these places were drab and repetitive, while others astounded me as soon as I stepped off the tarmac. The ones that I really remember are the ones that were drab on the outside, but with a little digging revealed themselves as fractal geodes... containing an unrivalled inner beauty encased within a plain shroud.

This image which is aptly named 'Buried Treasure' I found about 10E30 deep into a fractal landscape that seemed totally composed of white noise. I followed just a hint of a crevice in the noise down to this treasure. There were no real discernible features until this image appeared. Quite beautiful as well... it looks like the fancy sort of wood carving you would see on antique furniture.

I moved on from the typical convergence digrams where the color of a sample was defined by the number of iterations required to push it's magnitude past a threshold value. It was possible as well to track the actual orbit of a sample in complex space as you iterated it. Instead of just looking at the magnitude of a sample as it was iterated, I started plotting the values on the complex plane.

I referred to these as vector diagrams. The first time I plotted the orbits, as with many things, it didn't seem to work or make sense. There was far too much going on to understand the nuances. I needed a reference, and to start with a limited set of points. I first drew a convergence map, and then plotted the orbit of each sample on every 16th row or something. The results were intriguing. I soon found that plotting orbits in an aesthetically pleasing and efficient manner was quite difficult. Many wild and very strange images resulted from my experiments with this temperamental routine.

There was much more to be done however. This playground was fine for exploring, and giving brief reports on these landscapes, but it vastly lacked "production" features. The images I saved were limited in size to my screen resolution. The playground had a fullscreen mode, and I resorted to using the windows PrntScrn functionality to copy the full screen images to the clipboard and saving them off that way. I knew it was possible to create fractal images of arbitrary resolution... sometimes I hard coded a routine to dump a huge image of a system. It was a clunky way of accomplishing things, and many times while exploring I wished for the ability to do this dynamically. I also needed a better way to interface with the complex systems. Bringing up a dialog box and tabbing through controls, or even clicking on menu items was an annoyance while exploring. Fullscreen mode and modifying parameters (besides the zoom and pan) were mutually exclusive.

I was a bit daunted at first at the notion of entirely reworking the playground. My main code module (the one that contained the Windows entry point) had like a hundred global variables and was just under ten thousand lines long. In my state of fractal fervor, every new feature on the playground, every little test and modification was implemented as a kludge. I only cared about immediate results, and had cast maintainability to the wind. I built an empire out of bubblegum and bailing twine.

I rewrote the core routines, and this time built them out of brick instead of sticks and mud. I encapsulated everything, and made the multitude of non-exclusive boolean options for the system into a bitfield. There was now a single "state" variable where each individual bit represented a switch I could flip for a given option. One of the biggest and most effective changes was implementing a physically-based camera that existed in complex space. Physically-based, meaning the camera had momentum and friction, and moving it was all based on applying forces. When zooming/panning the weight of the camera would carry it for a bit even after releasing the controls. Note that this pre-dated the weighted interface of the iPhone by quite some time, and this idea was purely my own.

Now with the interface exclusive from the OS, I had a platform for fractal exploration that I never needed to bring out of fullscreen mode. With input and update routines built much like a game engine, I could define esoteric keypresses to my heart's desire, and the only change would be in the class's UpdateInput method. As I thought of new options, I defined a new bit in the bitfield and added accessors. It was simple to add routines for dumping the current scene to a huge detailed image, or saving each frame to make videos from. Now THIS was the kind of vehicle I needed for traversing the world of complex geometry.

Around this time I was an active member of the electronica scene in my area. I talked with some of the people setting up shows and got myself an invite to be a VJ for an upcoming event. I secured myself a projector and hauled my behemoth number cruncher (thanks, Stu!) to the venue. I had myself a little electroluminescent keyboard that worked perfect for manipulating the system in the darkness of the drum & bass arena. People were definitely impressed. One dude recognized the Mandelbrot set and was amazed to see it in such a dynamic light. That was probably the biggest compliment of the night. Everyone thought the convolving text routine where I feed text into a vector diagram and let the system swirl it around was mighty badass. All in all, it was quite a success.

Bolstered by the positive feedback from my first VJ gig, I was determined to expand the capabilities of this new application. Around this time I started experimenting with strange attractors. I used vector vector maps in the original fractal playground to build a "hit map" where computed locations of sample orbits were added to two-dimensional array that far exceeded the depth of a typical image. After subsampling the complex field and running thousands of iterations, I ran some statistical routines to get an idea of the spread of this data. I managed to clamp this data into a range acceptable by images, and interpolated the data into this clamped region to get some visual output. The results reminded me of images of strange attractors I had seen before. I didn't really know what a strange attractor was, but I figured they must be scads easier to work with than these complex vector diagrams.

I created a new application (again using parts from my game engine) for visualizing and manipulating strange attractors. These strange attractors proved to be quite varied and appealing. I especially enjoyed the way they moved when modulating the parameters over time. I produced hundreds of high resolution images and a few videos of these systems, all which were received well. I needed to get this new form of chaos integrated into my VJ software so I could switch between the systems on the fly. It was around this time that I migrated out of Windows and into linux, so this application would be the first to be resurrected in OpenGL.