This is a piece I made recently titled In Transit.

It depicts paths, which each transition from random motion to a regular spiral motion as the letters along the path grow.

It is a generative piece, meaning it comes from the execution of a computer program I wrote. You can play with that program here to create similar images. Drag to pan, scroll to zoom.

I recommend playing with the “iterations” slider to see how the path evolves over time.

This piece has several meanings. It is first of all a model of capitalism: MCM’ (meaning, money, commodities, money) represents the basic logic of capitalism. Start with some money, use it to buy commodities, increase their value and sell them for more money, rinse and repeat.

Each spiral corresponds to one capital (think, a firm) following this logic.

This logic, perfectly followed, implies exponential growth of money (and commodities). It is the god of the capitalists, and what they constantly refer to in their sermons (i.e., power point presentations). An exponential spiral unfolding over time.

But this logic can never be followed perfectly. The whims of a small business owner, a product that doesn’t sell, mere random chance, can block a sum of money from experiencing this beautiful exponential growth when it is small enough.

On the other hand, once a capital gets big, it puts into place all manner of stabilizing mechanisms to ensure this perfect exponential is followed as closely as possible: diversifying across industries to offset a loss here with a gain there, forcing the state to bail it out if there’s a complete failure, corporate boards that squeeze out any room for human whims that may cut against the imperative to maximize profit.

The more general meaning, which subsumes this one, is this: there is an inverse relationship between reality (i.e., effectiveness, power to transform the world, robustness, efficiency, scale) and potential (flexibility, freedom). Of course occasionally this trade-off can be masked by sacrificing something else (e.g., as in the case of cars sacrificing the biosphere.)

Think airplanes/trains vs walking. To reproduce a behavior at scale, or at speed, or at a certain level of robustness, that behavior must be physically inscribed in the world, which tends to mean it is fixed, rigid.

Process for creating this work

This is a generative work. There is a small number of parameters which taken together produce the work. Therefore, the creation of the work involves essentially two steps:

1. Defining the procedure, which given a set of parameters, produces an image.
2. Selecting parameters which give an aesthetically pleasing result.

The art is in both parts of this process, and they are not independent. In exploring the space of parameters, I often tweak the logic of the procedure to get a more beautiful result.

The procedure

I wanted the work to represent a development over time, in which the logic of evolution is somehow random when the magnitude of a capital is small, and essentially deterministic (following the perfect spiral motion) when a capital is large. And, to interpolate continuously between the two extreme behaviors of randomness and perfect spiral motion in intermediate sizes.

The state of a capital will basically be:

• its size $s$ (represented as the text size, corresponding to the value)
• its $(x, y)$ position
• its angle $\theta$ (represented by the rotation of the text)

Its representation as an M or a C will simply be alternated in subsequent steps.

What this set-up suggests is to define a differential equation that describes how the state of a capital should evolve over time. Then, we can evolve the state for a fixed amount of time to get from one position to the next in the sequence.

A differential equation in our setting will be a function that given the current time and state produces a vector in the tangent space of $(x, y, \theta, s)$ or in this case, simply a 4-dimensional real vector.

In our case, we want $(x, y)$ at time $T$ be the integral $\int_0^T s(t) \cdot (\cos \theta(t), \sin \theta(t)) dt$. I.e., the position is obtained by stepping the $\theta$ direction with length scaled by the size $s$.

Therefore, $\frac{dx}{dt}$ and $\frac{dy}{dt}$ are already determined ($s \cos \theta$ and $s \sin \theta$ respectively).

So, what we need to write down is a function $G_t(x \colon \mathbb{R}, y \colon \mathbb{R}, \theta \colon \mathbb{R}, s \colon \mathbb{R}) \colon \mathbb{R}^2$ where the two outputs are $\frac{d\theta}{dt}$ and $\frac{ds}{dt}$. I.e., how the angle and size change with time.

If we can find the differential equation $S_t \colon \mathbb{R}^4 \to \mathbb{R}^2$ describing perfect spiral motion and define a differential equation $R_t$ for random motion, then given a “fader” function $f$ which monotonically maps the size into the interval $[0, 1]$, we can define the interpolated equation by $G_t := f(t) S_t + (1 - f(t)) R_t$, so when $f(t)$ is close to 0, it acts more like random motion, and when $f$ is close to 1, it acts more like spiral motion.

For the perfect spiral motion, we have $\frac{d \theta}{dt} = c$ for some constant $c$, constantly turning in one direction. Exponential growth means $\frac{d s}{d t} = e^{c_s t} c_s$.

For the pure random motion, I essentially let the change in the angle $\frac{d \theta}{dt}$ and the change in size $\frac{d s}{dt}$ both be independent Simplex noise – the graphics programmer’s best friend – fed with time as the input, and scaled.

This insures that the angle and size change smoothly over time in the random regime.

Selecting parameters

I built a web interface (as seen at the top of this page) for playing with the parameters to find some nice ones, and then layered 3 different trajectories in pink, teal, and black. Building custom mini-editors is a great (almost necessary) technique for making art with the computer.