The work phase
space.color is based on
the 6-dimensional hypercube.
This geometrically defined structure has 32 diagonals. The two
endpoints of each diagonal lie diametrically opposite in the
structure. A "diagonal-path" is the connection of two such
diametric points through the network of edges of this complex
structure. In a 6-dimensional hypercube, each of these 32 diagonals
have 720 different "diagonal-paths".
For each work a random selection of four "diagonal-paths" from this
repertoire of 23040 (32x720) possible paths is made and shown in
its 2-D projection.
A 6-dimensional "diagonal-path" is built therefore from six
consecutive connected vectors, each having a different but distinct
direction. Each direction represents one of the six mathematical
dimensions.
In space.color the
four chosen "diagonal-paths" (thick lines) are ordered from 1 to 4
and the corresponding vectors are connected with thin lines. Thus
vector pairs are created and together with the thin lines they form
planar quadrilaterals, or color fields. (see illustration below)
The two outer "diagonal-paths" (1 and 4) are connected in
the same way but without thin lines, wrapping the image around the
outside of the bounding rectangle.
The hypercube is rotated in 6-dimensional space and then projected
into 2-dimensional space.The resulting image overlays the color
fields from front to back. Together with the "diagonal-paths", the
resulting image creates unimaginable constellations.
Schematic construction of the image | |
diagonal-path 1 diagonal-path 2 diagonal-path 3 diagonal-path 4 |