Hayter begins his complex trail through labyrinths of experimental drawing - partially explored, partly still beckonning - encouraged by music, mathematics, physical sciences and the unconscious - but mostly led by his own fine intuition in talking about the means of such exploration.

"In principle work at the Atelier 17 is directed toward means of expression rather than motivation, inspiration, functions of the artifact or other metaphysical considerations. The pursuit of these is of real service to the many associated who still teach us as much as we teach them, it might be to reveal an enormously wider field of possible activity than we have hitherto foreseen."*
Drawing is understood as the simplest available means of projecting thought in the form of a concrete external object, but it is an instrument of research rather than a means of describing external objects; in view of our general principle of avoiding precept, command, direction and the expresssion of approval or disapproval to influence action, it might appear that everything is left to the personal initiative of the members. This is not true: operations are undertaken from unconscious doodles to precise mechanical structures, leading to unforeseen results. These experiments are based upon open-ended situations or processes that have arisen in our experience, suggested by unfinished researches, equivocal situations, unresolved puzzles. These are not teaching tricks; no answers exist, or they are unknown to us.

"Both beginners and seniors provide themselves with a variety of instruments such as rulers, compasses, squares, protractors, ship curves, pens, pencils, brushes, wax crayons, felt pens, knives, scissors, stencils, and so on. Furthermore, paper, boards, graph paper, tracing paper, carbon paper, white, black, or coloured may be needed. Each individual pursues a different operation, but comparisons between results and collective drawings are made on a large scale. At each session new operations are invented; as in all group activity, far more images are exposed than any one individual could produce alone. It is a sort of collective game of consequences, not all of them rational. Those members who have previous experience of interest in mathematics, such as analytic geometry, vector analysis, topology, or Fibonacci series, might be invited to carry out such operations that the associate likes; the next step is the attempt one he or she detests." *

Space does not permit a detailed description of all of these experiments, but the different categories are listed below. Each can produce many variants. Fields, from the simplest to the most dizzily curved, can all be represented by repeated lines covering the whole paper (or extension) which create the impression of numerous types of space. Thus while keeping what is present on the surface of paper - for example the lines - no mysterious distances disappearing into the depths - one can produce from the uninterrupted lines or interrupted lines or curved lines, rigorous but homogeneous fields, or pulsating fields or by the combination of several, three-dimensional volumes or even the vertiginous oscillations involving the ambiguities in the reader's eye. Hayter, as mentioned in the introduction, while being acutely aware of pattern in two dimensions, went beyond this to create labile regions by the interposition and interference of many dimensional fields or of the colours which could either agree with or contradict the arising shape. Through such spatial oscillations even the stomach-jerking sensations of a ride on a roller-coaster might arise. Look out!

But what is the line itself? One can offer numerous examples of this line: it can be an outline - a margin of a solid or an area; it can designate latitude, longitude and depth; it can be applied to the outer area of a sphere or to the inner area; it can be a plumb line, which is subject to gravitational pull or force; it can symbolize something external to itself (as in Figurative Drawing), in which it might symbolize something conventionally (as in English or French) or whith an intrinsic relation as with Chinese; it might even refer to the melodic line as used in music. What do all of these have in common? They all involve a path, a record of actual or possible displacements.

In the course of this book all of these will be considered and demonstrated but in this section, one concentrates on line as covering a sheet of paper - as two-dimensional pattern or of several of these fields interpenetrating to create volume or even a fourth-dimensional pattern oscillating in and out which draws one into vertigo.

*'New ways of Gravure', S.W. Hayter, New-York, 1981, Watson-Guptill Publications, 'Les Méthodes d'Enseignement à l'Atelier 17'.

Straight-line systems (superimpose, cut, fold)

Straight-line diverging and converging axes

Straight-line and curved-line systems (sigmoid and helical axes)

Straight-line systems, curved axes and helicoid curves

Curved coordinates

Two continuous traces