Arp and Mondrian have common structure

Any visible thing becomes two dimensional design as retinal image.
The lines of every design can be traced with string.
Any network of string has geometrical features.

①There are certain Arp drawings which look like broken networks.

②Imagining that the network is stretchable, fix it on grid.
A string is the smallest element of shape and a  loop is the closed string.
And the smallest network has a point D (3):
D (3) means a dot from which three lines coming out.
On the grid there are only two different types of dot: D (3) and D (4).
Mondrian composition is the typical structure of this type and some Arp belong to this group.

③The model being free proportion, any number of squares and lines can be located anywhere.
So the squares and lines can be put aside in order to check the network.

④Link structure appears,expressing joint parts as different unit.
Every network has its own link structure.
Usually Arp is associated with Surrealism but formally he was the follower of Cubism.
Almost all the modern art originated from Cubism.
These Arp works have the same type of link structure as Mondrian: link structure with D (3) and D(4).
Grammatically both belong to the same type on the basic level.


" Others have seen what is and asked why. I have seen what could be and asked why not."         (Picasso)
Abstract art indeed started from Cubism.
As Picasso was a draft man by nature; everything had to be drawn,
Cubism started as linear composition with clear outline.

                                         (Picasso, Mondrian, Halley, Stella and Tuttle)

Picasso was so much interested in every type of shapes that he could almost foresee the pre-existent grammar.

" I like all painting. I always look at the paintings- good or bad- in barbershops, furniture stores, provincial hotels. I am like a drinker who needs wine. As long as it is wine, it does not matter which wine." ( Picasso)

Ancient Chinese characters passed similar abstract process as Picasso's abstraction.
But Picasso had to rediscover abstract art because the European art world was mainly concerned with painting only.

 In digital art world the viewer can take initiative.
Most of the interesting images appear as digital image nowadays,
so we should call them digital art work.
Definition of formalism is, according to Wikipedia,
"The context for the work, including the reason for its creation, the historical background, and the life of the artist, not considered to be significant."
Without knowledge of the history, the medium, the size, and whereabouts of the original of digital images online, I enjoy seeing them.
Art is not art because the authorities said so but because the the viewers enjoy the image.
Herbert Read defined 'visual art as anything which being seen giving pleasure'.
So I define pleasing digital images online are art.

I found online a group of images which shows the abstract process of the character 'horse'.
I took the liberty of adding the string structure models underneath.

The original of the four on the left are very small incised images on bronze vessels and the right  two are of calligraphy.

We reached the smallest structure which I call 'link structure'.
The grammar is not only for literature but for all writings.
Likewise the visual grammar is for all shapes.
Inventive artists always used intuitively the pre-existing grammar to make variation.

After sufficient visual experiences, we notice that a loop is a connected string and that a string is a broken loop.
Then we acquire ability to connect a string and disconnect a loop, which can be called syntactical ability.
There are Arp works with real string, one of which I picked below.

Real string may be easier to make variation because most of the geometrical characteristics are not fixed.
There are two ways to make a loop from the simplest network.

 To connect 2 D(3), there are several ways.

Now we have four 2 D(3).

Adding one string to the possible locations of each 2 D(3), 3 D(3) can be made.

Likewise 4 D(3) can be made.

Ancient Greek failed to establish aesthetics because they thought that painting and sculpture were the major, pure art and neglected much simpler, purer art like Ancient Greek icon.

Sciences always  started after finding  the smallest elements.
In biology the notion that every living thing was made of cells was important starting point.
With sufficient digital art works, we can easily arrange them from the simple shapes to the more complicated ones according to the countable characteristics, which is the beginning of art science.
Universal and timeless formal grammar is the basis of aesthetics.
Formally there is no difference between representative art and abstract art: every image is two dimensionally geometrical.
There are certain quantifiable geometrical characteristics common to all shapes.
The difference is the quantity of the characteristics.
Representational shape which is due to utilitarian purpose may have larger number in the countable characteristics.
The characteristic which distinguish Arp from Mondrian is concavity: Mondrian shape has no concave.
I will write about concavity next time.