squares 1~5

squares 1~5

Thursday, May 23, 2019

Mondrian did not use golden ratio but integer ratio for proportion

I picked up this illustration from the previous blog "How to make Mondrian."
This suggests that I could express all the Mondrian in the big eyed grid.
I have read about Mondrian's use of Golden Ratio very often.
I searched in (Golden Ratio. Mondrian).
It seems that his use of Golden Ratio is accepted with no doubt.
I found one suitable blog to point the problem: [Katari-e no Sekai].

....[Your painting is made of squares only.]
Mondrian answered that I see no squares.
There are only Golden Squares.

There are two accompanied illustrations
The left illustration is recognized as Golden Rectangle as it is divided to squares.
I do not see Golden Rectangles in the right picture.
I see all the rectangles are different as Mondrian said.

I used soft "paint" to extract the rectangle.
Then I changed the size to find suitable one for grid.

The rectangle 8/5 is near perfect match:
  8/5=1.8 ( Golden Ratio is 1.618)

The  Mondrian on the right is expressed on grid.

Mondrian started Chinese Lattice-like work with four different rectangles.

The next type does not have regular units but looks like installed shelf;
 rectangles with same width piling up
and rectangles with same height lining on horizontal line.

 A  large almost-square appears near center.

Cabinet likeness disappears: all the rectangles are attached to the frame.

I picked works of high resolution for checking.

10/8
9/9






15/12
32/16
31/20
23/21
25/21
31/31
37/36

75/76
This suggests that all his works can be designed on regular grid when the good digital images are available.

Relatively small number of grid eyes is enough to design Mondrian composition, which is why the proportion clearly recognizable.

There is great consequence in the use of simple grid.

A) Historical art is applied art.
Pure art does not depend on the current art history.
It can be created on the innate sense ability.

B) golden ratio was used as temporal fashion.

On the other hand the visual grammar is innate ability of all human.
Recognition of natural number is not mathematical but pre-mathematical perception.
The grammar is the base of all intellectual activity including mathematics.
Mondrian re-discovered the visual grammar after following Cubism.

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