Philip Van Loocke
"Hypercubes grown by trees"
Photographic print, 16.5" x 23.5", 2006
The first submission illustrates some solutions found for the unconstrained
MDS-error function. It illustrates how the present method integrates
non-linear elements. The linear elements are the side-lines of the
In most of the illustrations, the edges were partially filled. As is the
for ordinary MDS, they are not necessarily plane surfaces. But most of the
non-linearity in the representations is due to the trees. Three examples
non-linear trees were included in the illustration. At the bottom, two
shown of a hypercube based house that was made with different software,
the user can choose within bounds the location of the edges.
"Constrained hypercubes grown by symmetry breaking in curved trees"
Photographic paper, 16.5" x 23.5"
The second submission illustrates some solutions obtained for the
MDS-error function. The hypercube visualizations are such that they have
horizontal ground floor. The origin of the tree is in the same plane.
were permitted to partially grow branches below this plane. Constraining MDS
gives a different error surface, again with a large wealth of local
correspond to aesthetically pleasing solutions. The red 'blossoms' in
picture correspond to four branches of very high curvature. Some forms
rotations of each other.
"The tree that evolved into a bird"
11.7" x 16.5" , 2006
This submission illustrates the type of trees used, but for ternary
and for eight branching levels. The tree was initialized linearly, with
endpoints coinciding with points on the Sierpinski triangle. Branches were
provided of fractally defined weights. These defined curvature for all
at all levels. In the main figure, only branches of the five highest
Philip Van Loocke is a
Mathematician and Professor of Philosophy at the
University of Ghent (Belgium), Dept of Philosophy, Art and Consciousness
Statement about my art:
"The artwork combines two lines of research. First, three dimensional fractal
trees were provided with angular parameters which define the way in
curl. Second, a multi-dimensional scaling (MDS) approach was used to obtain
visualizations of high-dimensional objects. In the combination of both
the vertices of hypercube visualizations were located at the endpoints
trees. The trees were bent by a stochastic algorithm until the MDS-error
function reached a local minimum. The error function defines a landscape
high-dimensional parameter space, with much more local minima than in
ordinary MDS. From the artist point of view, this is an advantage, since
local minima correspond to configurations of aesthetic quality. The
initialized in a symmetric way, so that the search algorithm corresponds
partial symmetry breaking process. In view of possible design relevance,
situations in which constraints were added to the MDS-error function were
studied. For instance, also solutions for runs in which particular
constrained to be located in the same plane are illustrated."