Baker Space

I studied briefly a startlingly simple system that exhibits chaotic behavior. I wrote about these experiments in a writing system I had just built by combining my Hot Draw Clone with the native paragraph editor to make a mixed text and graphic authoring system.


A chaotic system need not be big to be unknowable in a way that is distinctly different from big systems that are just confusing. While reading on the subject I had learned of several very simple systems that brought the necessary conditions for chaos to the fore. One was the called the Baker Space. See Wikipedia .

Two processes combine to make for chaos' delicious unknowability: repetition and decision.

A feedback loop with enough gain will oscillate, a kind of repetition. The orbit of a planet or the swing of a pendulum are oscillations too: all repetitions that are periodic, not yet chaotic.

A decision depends on force of some kind to drive a small choice into a larger consequence. A coin teeters on edge until gravity forces it to heads or tails.

Two bodies orbit periodically because there is no choice. Three bodies orbit chaotically because each body finds itself tugged between the gravity of the other two and sometimes must "decide" to go with one or the other.

The Baker Space is a square that is divided down the middle with the two halves squished and stacked to make a new square. When repeated over the space becomes chaotic in that the path of any point from square to square becomes unpredictable.

Even a small decision will lead to chaos when its modest consequences are fed back into similar decisions, over and over, through repetition.


I programmed the slicing and squishing of computer images. I found that with each iteration the image became less recognizable.

I tested my writing system by capturing this progression as snapshots and commenting on my appreciation of the two drivers of chaos laid bare.

I found that due to the discrete nature of my cutting and squishing a jumbled picture would eventually return to whole. I wrote about that too.

My writing environment managed a collection of images, each with discussion. I understood that producing a printed page required more page layout than my system provided. I was suspicious that page layout was an artificial problem imposed by the non-interactivity of paper.

My writing environment served me well since it managed the collection and review of the images I had produced and then allowed me to reflect on the process that created them and comment as insight came to me.