Starting Point - drawing from Baur & Martin's research:

OCTAGON - 8 sided polygons

Starting Point - HEXAGON - 6 sided polygons

Fig. 1 Primary research for paper in algebra on polygon tilings (Baur, K. Martin, P.) see:

http://imsc.uni-graz.at/baur/Articles/Subdivisions.pdf


Link to final paper:

The Fibres of the Scott Map on Polygon Tilings are the Flip Equivalence Classes (Baur, K. Martin, P. 2016, p.2)

https://arxiv.org/pdf/1601.05080v1.pdf

The agility of perspective nearness

understanding confluence

Acknowledgements:
This research is gratefully funded by the Unconventional Grant:

The Collaborative Mind - Arts & Mathematics, Karl Franzens University, Graz

Plabic tracings:

We "Copernicans", of modern times say: Earth is not the "whole nature", it is one of the stars in infinite space. The earth is a spherical body, though not the only one, and on one level perceptible in its totality, but as a primordial sythesis as a unity it is a one off. But yet, it is still a body!

see interactive maps with further examples of Plabic tilings (Author: Pavel Galashin)

 

Circles and their relationships to each other:

Wir Kopernikaner, wir Menschen der Neuzeit sagen: Die Erde ist nicht die <ganze Natur>, sie ist einer der Sterne im unendlichen Weltraum.  Die Erde ist ein kugelförmiger Körper, freilich nicht auf einmal und von Einem wahrnehmbar in seiner Gänze, aber in einer primordialen Synthese als Einheit aneinandergeknüpfter Einzelerfeahrungen. Doch ein Körper!
(Husserl, 2006 p. 153)

The Duo:

The Duo separates:

you’re just a young butterfly,
don’t be afraid,
it takes many years to find the way home
once you’ve left this cocoon,

you will get used to the idea that leaving is always a journey of stillness.

there is no motion where your wings
have begun to move on the winds of love

you hardly need to breathe,
as every flutter holds a breath
that propels you forward to the everlasting light.

Did you know that your youth is like this?
an everlasting dream on the wings of freedom?

 

 

a butterfly breath, 2016

The Duo replicates itself, revealing "frozen" perspectives simultaenously:

 

"frame" a view

 

what can you intuit from a frame?

a facade?

an architecture?

In changing perspectives, one must only leap into another's shoes to see and hear what the other sees and hears.
If I leap into a position where I see a multitude of perspectives before me, of the same object, is this source suddenly multifaceted, or is it only now that I can perceive its unity?

The agility of perspective:

TO COMPOSITIONAL MODEL

The agility of perspective nearness:

Confluence is a flowing together of two streams, or the like, which melts into itself, a body which becomes one. As this is an easily visible phenomenon, like when two rivers merge into one, I chose to explore this topic through the aid of visual form, in the 3-d modeling program called Rhinoceros [See www.rhino3d.com/]. Spatiality and temporality are key terms to understand how the development of this research evolved.

I also draw from Husserl’s embracing of transcendental “Lebenswelt” to place the intentionality of how to understand the pursuit of “architectural form” in this model.

According to Husserl, there are two dimensions from which every system derives its meaning: 1) the formal, or syntactic, dimension, which corresponds to the structure of the system itself, that is, to the relations among its elements; and 2) the transcendental, or semantic, dimension, that is, the reference of each element to the reality of the Lebenswelt, including its historic constitution. (Pérez-Gómez, 1983, pp. 467-8)

In using a form which has a skin, but no architectural “use”, I am quickly forcing the audience to contend with a utopian plane of sculptural essence. Historically, these are in some ways new objects for our eyes, but it is the way that we can look at them, through 3d interface and graphical image that takes us to build new intuitive expressions about them.

Naum Gabo’s explorations with one-face objects swept the plane into a new geometric beauty. These objects are taken as sculptural precedents for this research.

Antoine Pevsner,

developable column (1942), oxidized tin on brass, 20"

Friebel, T. 2008 Homage á Gabo

lines of intersection

The Sounds of Intersection by Tamara Friebel on Sketchfab

Statement on "The Agility of Perspective Nearness"

If we understand confluence to be a flowing together of two streams, or the like, this artistic research tries to uncover the intricacy of an “agility of perspective nearness". I draw from current research in algebra, in collaborative thought with Karin Baur. After decorating tiling with strands, induced plabic graphs of an octagon are used to produce a full set of Non-Uniform Rational B-splines (NURBS) circles of an irregular nature.  Five of these circles are selected according to their graphical fluency to create 2 self-intersecting surfaces, which share some alignments in common. These one-face skins express self-similarity, but remain unique and can be separated, along a perceived line of perspective nearness. This agility of closeness and/or separateness is fascinating, and helps to understand confluence, where 2 bodies merge to a whole. These graphical discoveries lead to multiple derivatives in artistic output, with intuitive resemblance to the research on confluence as a whole.