The grain of randomness: what decides a repetition

The starting point is a conversation with a model, published as it stands, asking in turn for a generative drawing in the spirit of five artists. The answer takes the same shape every time: three or four geometric primitives, and a single slider called chaos, disorder, intensity, accumulation or obliteration depending on the artist. That slider always sets the same thing, a quantity of chance.

A quantity of chance says almost nothing about what will be seen. The same dose produces unrelated fields depending on where it is injected: on each element’s place, on the interval between two of them, on whether an element is there at all, or on its weight. That level has no name in the code produced, and it is what decides. Call it the grain.

A generator written in one go mixes the four levels without distinguishing them. A single line draws a number and applies it to position, size and opacity at once, so the slider pushes all four together. The result is adjustable and unreadable: when disorder is raised, which of the four decisions produces the visible effect is unknown.

The generator below separates them. The four grains draw on the same stream of numbers and consume as much of it as each other: at equal quantity, only the destination changes.

The move to make is simple: leave the quantity where it is and change the grain. Nothing else moves, and the field becomes unrecognisable. Then put the quantity at zero: the four grains return the same field, position for position, whatever the seed. That is the baseline that makes the rest measurable. The third slider, the hand, is the subject of section five.

The measured departure is the distance between where the rule puts an element and where it ends up. At sixty per cent quantity, on the rows family, two hundred draws give this.

Two grains move nothing at all and are still legible on the field, one by removing seventy-seven elements, the other by touching weight alone. Between the two that do move, the largest departure varies by a factor of three. The quantity did not change from one row to the next.

The two grains that move differ on one point only: the first draws a departure for each element, the second adds that departure to the previous one. The addition changes the nature of the object. Measured over four hundred draws, the departure of the position grain stays flat, around zero point eight of a pixel, whatever the element’s rank in the row. The drift grain’s departure grows, and grows exactly as the square root of the rank: the ratio between departure and that root holds at zero point three five from the second element to the forty-sixth, to within a hundredth.

That is the signature of a random walk, and it has a practical consequence. No single step is large: each element sits about where it should relative to the one before. But the error is never corrected, and by the end of the row the departure from the model is close to three times that of the independent grain, at identical quantity. That is how a rule can come apart with no visible breach anywhere.

The distinction is the one that separates a hand from a machine. A hand laying marks side by side does not fit each mark to an invisible grid, it places it relative to the previous one. Its irregularity therefore accumulates, and a drawn line drifts off its axis while no interval is at fault. A generator drawing independently will never produce that effect, whatever the dose.

A field whose randomness all bears on a single channel reads as a diagram: the marks are perfect rectangles, all of the same ink and the same weight. What is missing is not disorder, there is plenty of that already, but matter. The third slider adds some: rotation, weight, opacity. It never touches position or presence, and that separation can be checked.

The hand pushed to its maximum leaves the mean departure at zero on the grains that move nothing, and leaves it unchanged on those that do: at the drift grain set to twenty per cent, the departure is zero point six five of a pixel whether the hand is at zero or at a hundred. The two controls are therefore orthogonal, and that is the result that justifies separating them. A sheet can be covered in tremor without the rule moving by a pixel, and a small dose of the right grain is enough to undo it.

The four families carry the same set of grains on four different repetition devices, each after a manner an artist made their own. They are not equally telling. The grid is where the position grain reads best, because a square lattice gives the eye a reference; drift there becomes hard to tell from a rotation. The rows are the opposite: the only family where drift is seen for what it is, since a single line carries the accumulation.

The dots are the family of the presence grain, because a field of dots is judged not on where each one sits but on how much ground is left between them. The discs are the case apart, for a reason that has nothing to do with grain: the device rests not on where the elements sit but on what their overlap produces. The clusters are placed on the golden angle, with no row and no column, and the filled circles mix at the intersection instead of masking each other. Six neighbouring reds are enough: simultaneous contrast is a fact about colours side by side, not about distant ones.

The field opens full screen, with the same controls as the instrument built for the reversed drawings: left and right arrows change family, up and down change surface, the space bar draws again, escape closes. On a touch screen, a horizontal and a vertical drag do the same, the dominant axis deciding which of the two applies.

One thing was lost on the way. On a scanned historical sheet, reversing the image requires a filter: a matrix computes a negative, tints the luminance and puts the red back so vermilion stays vermilion. That filter exists because the paper is information that has to be decided about. Here there is no paper. A generated field is a list of shapes each carrying which of three inks it uses, and the switch reassigns three properties without computing anything. It is simpler, and it is a loss: there the instrument revealed something because it worked on matter that existed before it. Here, everything shown was decided by the sliders.

Four grains are not the four possible grains. Chance can also bear on the order of elements, on the number of rows, on the length of a line, or operate at two levels at once with different quantities, which is probably the commonest case in a real drawing. The generator offers one at a time, because mixing them makes the demonstration impossible and that was the defect to correct.

The piece says nothing about the quality of what comes out. A field drawn at random is rarely good, the sorting remains entirely to be done, and that sorting is work the sliders do not do. It says nothing either about what matters most in the works evoked: scale, material, and the fact that a sheet covered in ink marks is looked at from close up. Three hundred pixels across have nothing to say about that.