Art-making is logical(Mondrian puzzle)

Anything we see becomes the image on retina, which is two-dimensional shape.
On this level we can build up art theory of everything we see.
Though the retinal image is the whole view which the two eyes see, shape-seeing is selective: we pick up what is interesting, neglecting the surrounding image.
We see images and read articles disregarding the surrounding ads on PC screen.
And when we see a sculpture we do not see the background.

The eyes follow the outline of a mountain range.
The contour of a nude can be the motive of a picture.
The outline of a nose has various expressions: Roman nose; aquiline.
Sports car's sleek silhouette is commonly appreciated.
These examples show that we daily see lines selectively from the whole view.
The fovea can pay attention on a line, moving along it, whilst the retina sees the whole simultaneously.

The smallest element of shapes including art work is a string.
We can trace any shape with string.
When a string is attached to the side of another string, we see three strings coming out from the touching point, dot.
In general a shape is a network of strings; the atom of design is a string and the molecule of design is a branch.
String shape appears as essential element of the images of art and nature.
Shape seeing is seeing strings.

Digital image has given us new habit .
I used to print new found digital images as reproduction collection but soon realised that seeing them on PC screen is more convenient..
Internet became part of visible world to find interesting images.
When all the pictures we want to see are stocked online we do not need picture books; we can pick only images we like.
Then we realise that we do not need the authorities' selection any more, as it has happened in the musical world.
We have entered the digital art age.
Redefining that art is very pleasing shape, the new art theory can be built up based on huge amount of digital images available without historical reference.
The digital images are increasing constantly.
And comparing the images became easier; making the images smaller on the same plane.
Being able to enjoy seeing digital images is the necessary condition to be artist.
The task of artist is to invent the method of making new pleasing shapes.
I have been writing these logs using digital images online solely though I developed my idea on reproduction.

The artists' interest is a line within the frame.
So the model for these images can be like this:

I searched and found easily online the illustration in the book"Tristram Shandy" which I saw more than forty years ago.

The models of each lines can be expressed like this:

The model is stretchable like rubber string and bendable like lead wire.
A string alone can make art: one stroke drawing.
Picasso made some such drawings.

I remember seeing young Klee's drawing of a pig drawn blindfolded though I failed to find it online.
He started from a muzzle, passing the back to the tail then coming back to the starting point.
This method works because the hand moves tracing the imagined pig drawing.

Easy way to remember this image above is to imagine tracing the line from the top to the bottom end.
Instead of tracing it with the index finger, moving the eyes along the line works.
Then closing eyes and imagine to move eyes works as well.
It seems the eyeballs are actually moving under eyelid.
It is not easy to imagine the whole image.
Imagining tracing the line is easy way to conceive the image, which suggests that seeing a line is moving the eyes along it.
Seeing a line is primitive: tactile.

We Japanese can read hundreds of Chinese characters but be able to write less than fifty percent of them.
We remember those as sign but to know how to write, the structures must be remembered.
Obviously seeing art work is not sign seeing but shape seeing.
The reason why so many people fail to enjoy abstract art is that people lose the childhood habit of sense-seeing.
Sign-seeing is seeing the whole image at once and art-seeing is moving eye tracing the lines.

A string can be expressed on grid, gaining proportion and angle.
The simplest  network has a touching point of three strings, which I call D(3), D meaning dot.
When a string is on the grid, only three or four strings can be attached on grid point, dot.
Now it is ready to explain a Mondrian puzzle.

① I chose a Mondrian with simple grid line from Google image.
② Disregarding the proportion, express the design on grid.
③ Make the grid except the frame line with match sticks( 7 by 7 horizontal sticks and 8 by 6    vertical sticks)
④ Make a new pattern by removing a stick. The number of the new patterns are the same as the number of the sticks.
⑤ Remove one again from each of the new patterns.
Repeat the same procedures.
The Mondrian pattern has 28 horizontal sticks and 36 vertical sticks.
So the pattern can be found in the group of ( 49+48) -(28+36) removal.

Let me take smaller structure as example to save the space.

The match structure of these is a branch of D(4)+D(4).

There is a way to make proportional variations automatically.

The smaller the grid is, the closer the design becomes to the original,


String model D(3) below can represent the letters T, Y, E, F.

And a dot can hold infinite strings although only eight on grid.

These string grid model except 7 are used for Chinese characters: 丁；十；大；木；米.

More complicated patterns can be made by attaching more than two string model patterns.


Let me introduce another match stick puzzle.
Make two branch model D(3), then connect them.

The shapes can be transformed each other, turning a branch 90 degrees around the dot.

Chinese character 工、上、下、and alphabet H are made, which suggests they have the same basis, the grammar.
The turned images and the mirrored images are considered to be the same as the rule.

Think of adding a new string on the model of H.
There are three possible points to add it.

Turning a branch around the joint 90 degrees, the shapes can be transformed.

All turned out to be the same.

To make 4 D(3) there are 6 possible points to attach a string.

These three become the same branch pattern.

There are many possible patterns  made like these:

" For Baumgarten aesthetics is the science of sense experience, a younger sister of logic, and most perfect kind of knowledge that sense experience can have."(Aesthetics from Wikipedia)

To make variation is intuitively logical process, which can be further progressed to logic.
Creativity is the ability to use a kind of logical process.