Vasarely [Quami], 1950
Stella [Irregular polygon], 1965
All the artworks can be classified into one system according to the geometrc structures of the work.
The upper three works are polygonal mosaics.
I introduce a new model called proto-shape: a polygon made of definite number of line segment with free angle and free size.
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Both look like overlapped polygons. ( This is a seeing of iconic level.)But on perceptional level, the two shapes can be seen as two polygons to share sides.
The left is made of a triangle and a six- sided polygon and
the right is made of a triangle and a eight- sided polygon.
A concave polygon can easily be identified by paying attention to the concave.
Concave polygons can be classified.
A triangle does not have enough sides to make a concave.
A quadrilateral can make only one concave.
Polygons with more sides can be made by paying attention to the concaves and the convexes.
I used to buy many art magazines and Auctioner's catalogues in Strand for this type of Vasarely's works.
Now I find more digital works than my collection .
Without extending the polygonal table I made the nine- sided polygon by cutting off two concaves on a five- sided polygon.
mechanical compositional method
Vasarely seems to have used some algorithmic method.
The below illustration shows such imginary process.
1) Draw five six- sided polygons surrounding a five- sided polygon.
2) Add concaves on the polygons.
3) Move some shape parallel.
Stella and Vazarely used polygons as motif.
The polygon distribution diagram below shows that Klee used the same method.
There are several many-sided polygons: three eight-sided polygons(vermillion) and three seven-sided polygons(brown).
None of them have remarkable feature as main role.
They look like the back ground of the surrounding convex polygons .
So I draw auxiliary lines to show the likely hidden parts of the polygons.
In this way I can eliminate all the concave polygons.
The convex polygons which are made with cardboard can be overlapped to make the design.
There are one hexagon and the rest are pentagons, quadrilaterals and triangles.
This basic design was constructed firstly
and the secondary surface structure was made by extending and overlapping the surrounding polygons.
The structural model below confirms my asumption.
The overlapping shapes make three dimensional illusion.
For example the two polygonal corners are lined on a vertical line near the center, which look like steeples
and the parts on the lower right look like eaves structure.
Finally I make two models for harmony and balance: scale model and line extension model.
The extended lines intersect at many points, which makes the structure balanced.
The diagram of modern art movement by Alfred Barr shows that all the movements until 1935 converged to two types: non-geometric abstract art and geometric abstract art.
Most followers took this diagram as a model to fablicate more movements for extending the network of the diagram.
The importance in this diagram is that the final stage is formal: artwork became geometrically analyzable.
Without any analysis we can recognize that these three works belong to the same genre.
It seems that they were made without any direct influence though the makers had the notion of making abstract art.
The world of internet overflows with art-images which themselves are new medium of art.
But geometrical patterns can easily be classified on the level of seeing shape.
The same type of works can be collected to study the difference of syntax.
Creating new artwork means inventing new syntactic device.
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