Waiting for Malevich (previously known as Random Walker), comprises an infinite number of digital drawings. Produced by an algorithm, drawings are traces of simple two-dimensional random walk, obeying Brownian motion, wandering on the screen until the current end of the path hits the edge of the frame buffer, the halting condition of the algorithm. The resulting drawing is printed, and the screen buffer is emptied, making space for the new drawing. What started as the most basic algorithmic generative process without any “intelligent” design, a ground zero as it were, embodies both the fractal dimension of difference and Lucretius’ ontology of motion. Each drawing is not a representational copy of some original Platonic form but a material expression of the stochastic process of random walk. A figure, emerging from the movement of pixels, is nothing else than figura, “a form produced through the motion of a trace, line, or a sketch.” It is a trace of a corporeal flow, a pedetic morphogenesis.

Since the pixel values in this algorithm take only values of zero and one (zero indicating that the random walk did not cross that particular pixel and one that it did), the drawn path is not simply a line, but both line and surface, due to the black blocks of pixels indicating areas that random walk crossed multiple times. This area resides in the fractal dimension, topologically between one and two dimensions. Fractal in nature, keeping their structural integrity on every level of magnification, these originals are not fragments that would form a whole or totalising image when assembled since they produce and reproduce endlessly. While all the drawings look visually different, each carries the same statistical properties --- like circumference or area covered, constituting infinite originals.

The project’s original name was Random Walker, which described what works does practically. Through the theoretical investigation, it became evident that the work does more than walk randomly. One of the statistical properties of a two-dimensional random walk is recurrence, which states that there is a probability of 1 that the random walk will eventually return to its starting point. This property is valid only for random walks in one-dimensional and two-dimensional space. In any higher dimensional space, there is no guarantee that the random walk will return to its starting point. Given enough time (up to infinity), the random walk would eventually colour every pixel black and produce an entirely black piece of paper resembling Malevich’s Black Square. In the case of Waiting for Malevich this will never occur due to the halting condition, which stops the random walk when it touches the screen boundary and does not allow for enough time for the recurrence to happen --- hence the change of the name of the work.

An alternative scenario could be one where it bounces off in the opposite direction, continues on the opposite side of the screen, or wanders freely. In such a scenario, the halting condition could be triggered only when every single pixel has been set to 1. Under those conditions and after some (very long) time, a drawing will emerge where the random path fills the entire screen surface, and the drawing emerges, resembling and being recognised as a black rectangle, to end the wait for Malevich. Another long wait would produce another completely black drawing. The two stand in a similar relationship to The Fountain or Brillo Boxes and raise the question of how they differ. Instead of pondering the visual difference that two identical black drawings produce, the work reveals how ana-material difference produces two identical objects through different random paths or, in the sense of Nail’s interpretation of Lucretius, “the ‘shape’ made by matter in weaving motion and not some idealist essence”.

Producing a single drawing of a random walk would not be an artwork but an illustration for the book or a web page concerning statistics. Only through numerous drawings, the aesthetics, the meaning, and the sense of Waiting for Malevich start to emerge. The work ran from the start until the end of the research and became a zeitgeber, giving the research a peculiar stochastic rhythm. First installed in the studio and then later in the live/work space of the artist, Waiting for Malevich was a constant reminder for the artist (and his random visitors) of difference at work. As time progressed, the artist could estimate the extent of the drawing’s coverage based on the duration since the last edge hit --- a play between stochastic number generator and human sense of time.

In the interview for the Art21 video series, McCollum recounts a mishap where one of the assistants produced 48 identical objects, which infuriated McCollum because the whole point of the project was that all the works were unique. One of his friends suggested that those duplicates are more valuable since they are unique in their duplicity. In the case of Waiting for Malevich a duplicate would be priceless since the probability of any specific path occurring twice is on the order of 10^-348 and, for all practical purposes, equals zero. The screen size used for the generation of drawings was 1024x768 pixels which yield the shortest path to the edge of the screen in the length of 348 pixels --- the half of the shorter side. With eight possible directions --- including diagonal movements --- the probability of such a drawing emerging twice is (1/8)^-348. While it is necessary to add the probabilities for all longer paths to arrive at the total probability of any two same paths happening, they are all several orders of magnitude smaller, with the limit value of the sum still being at 10^-348. For context, there are estimated to be around 10^80 atoms in the observable universe, so even if we considered every atom as a unique event, the probability of any specific sequence of such events would still be vastly higher than 10^-348.