Image and Process:

i. Visual (conceptual) Space:

The artist and Bauhaus teacher Paul Klee developed, in his "The Thinking Eye - A Pedagogical Sketchbook", the foundations of a visual language on the basis of a single point. As the point "moves" (or is moved by the artist) it creates the lines, shapes and planes which underlie Klee's imaginative images. From a number of basic movements (creating lines, curves, spirals, squares, etc.) Klee was able to build a repertoire of elements which he could use to develop his personal language further.

As a young student, I was impressed with the "shamanistic" nature of his work -which gave me the impression that important questions could be resolved through this ceative divination process involving the artist and his medium. Perhaps, if one knew how the universe worked -then one could shape it (and oneself) into a harmonius and pleasurable whole. Logically, the universe which one would understand best would be the one which oneself had built. Maybe, building a universe of visual signs could help one to understand how the universe one lived in also worked.

In Klee's system,  the "movement" is implied  by the use of images that would (or could) have been produced if the point really had moved. The images  -although created by the movement of the artist's hand -are themselves static. It is the mind (and hand) of the artist that has created the movement -as indeed it is  the artist's conceptual system that has determined how and when the point is supposed to move. -It is also the viewer's perceptual and cognitive systems that are responsible for "interpreting" the image.

ii. Computational (dynamic) Space:

In computational Space "movement" and "change" are not implied or suggested. They are the practical  and conceptual fundament of the computational process itself. Indeed, at the basis of the "computational Process) can always be found  the questions of deciding (or computing) what, when, how and why something is to be changed.

In Klee's system, we start with a hypothetical physical entity (the point) -even though Klee admits that it has no size, no shape, or colour. We then have to decide how this hypothetical object is to manifest itself in concrete (visual) space -as an expression of the artist's system of (imagined) movement and change.

In computational space, we start with the (hypothetical) concept of "change" -and then decide in which (conceptual or concrete system) this "change" is to be manifest (visibly or invisibly) within a sensory or procedural domain. The conceptual basis for this approach was formulated by the British mathematician Allan Turing as part of his research into code breaking during WWII. See "Turing Machine".

iii. The Intersection of Visual and computational Spaces:

Images are generally reflections of the underlying (ordering) system that created them -either through natural (organic) processes or by the action of a machine or the combination of human brain, hand and eye.

Therefore in computational space -does the image create the system or does the system create the image? Or do they perhaps each create the other?....  Underlying the concept of Computational Space lie the problems of Ontology, Epistemology and Taxonomy: The relationship between the conceptual categories we use to describe our universe of experience -and how these definitions affect the perceived behaviour of the systems being described.

Presumably, such complex interactions will become somewhat easier to study, if the systems we are studying have been created by ourselves. For this reason, Computational Space can be a fascinating and effective laboratory.