Uploaded to www.rart.com/Gallery/Monds20112go, 
in May, 2011

First uploaded August 18, 2003

The Monds Universes

In the Spring of 2003, I had finally time to realize a dream. I wanted to pay tribute to and use the paintings of Piet Mondrian in Rart. Mondrian, a Dutch painter, was born in the Netherlands in 1872 and died in New York City 1944. From the 1920es on he used a deceptively simple form language based on simple elements which has had a profound influence on art and decoration since.

There are two sets of universes in the series. One set consists of typical Rart universes where the observer can interact with the universe which unfolds forever and occasionally produces views of lasting beauty. They use the elements of the form language of Mondrian. The lines go vertically and horizontally, top to bottom, side to side, or hang on to other lines as children. There are also the colored squares that form random patterns with a very restricted number of colors. The squares elements may be explored in the universe Monds_ColorSqs. As with all Rart universes running as applets, you get access to the parameter dialog to change operating parameters through a long mouse click.

In the other series, I have actually tried to reproduce works by Mondrian and given them life in different form. The works of Mondrian are often described in terms of balance and movement and so I have tried to introduce animation as a means of illustrating something about the original. A delightful booklet that I bought at the Museum of Modern Art in New York, consists of two essays about Mondrian by Meyer Shapiro. They are titled "On the Humanity of Abstract Painting" and "Mondrian: Order and Randomness in Abstract Painting". (On the Humanity of Abstract Art, published 1995 in the United States by George Braziller, Inc.).


We modified in 2011 a continuously running demo, where the universes, both the ones that explore the visual language and the renditions of actual paintings, are interspersed with comments commenting on the next universe. The Demo has its own HTML introduction which may be seen at Monds_Intro.


Inspired by Piet Mondrian: Painting I (Composition in White and Black), 1926 now at the Museum of Modern Art, New York. Also by a very similar painting, Composition 1, 1930 now at the Guggenheim museum in New York. For the latter we also have the dimensions 29 5/8 x 29 5/8 inches; vertical axis 41 3/8 inches

Shapiro describes several paintings in great detail. He writes about Painting I in part as follows: ". . . what seems at first glance a square set within a diamond square - a banal motif of decorators and doodlers - becomes to the probing eye a complex design with a subtly balanced asymmetry of unequal lines. . . . The intercepting edge advances and the intercepted square recedes as if passing underneath the edge."

In the Mondrian world of the time in question, the most assertive compositional elements are the lines, mostly black that crisscross the paintings horizontally and vertically. In the Rart universes, I introduced movements of the lines. Through the parameter "Moving Mode" the observer can select a number of modes. The lines move between preset limits, which may be the edge of the universe. For example in the mode "Right to Left, Upward", the vertical lines move right to left to the right limit and when a line reaches the left limit, it will disappear and immediately reappear at the right limit. In the same way lines go from bottom to the upper limit and reappear at the lower limit. For Composition I, I decided to select the "All Outward" mode as the default. In this mode, all lines move from the canter of the universe outward until they reach the outer limit, when they reappear in the middle again. You can in this universe select another moving mode including one, "No Move" when the lines just stop until another mode is selected. You can also select the speed of the moving lines and, through the parameter "Line Width", their thickness.

The 'Cycle' of 'Moving Mode' is the default of the Demo. The cycle goes through the two originals in still renderings followed with the four lines moving outward.

In this case, I give the observer the opportunity to select still renderings of the two paintings that inspired this universe. They are selected through the parameter "Moving Mode".



Inspired by Piet Mondrian, Composition with Blue and Yellow, 1932, now at the Beyeler Collection, Switzerland.

The reproduction I found on the web ( see it at The Beyeler Collection web site) looks OK, but, as we shall see with Monds_3 and Monds_4, there may be considerable differences between different reproductions on the web and therefore probably also differences between originals and their web representations.

This composition is very simple, yet incredibly dramatic and balanced. It is the first universe where I use the child lines and the first where I use the colored squares delimited by lines and the edge of the painting. There are two lines in the painting boldly dividing the canvas into four quadrants. The upper left is all yellow-mustard colored. In the lower right is one child line pointing down and one child line between the center vertical and the child line. I the Rart world, I denoted a child line that goes from a parent to the edge of the painting ChildLine, Type 1, and a child line between two parallel parents ChildLine, Type 2. There is a blue colored square between the down pointing child line and the edge of canvas delimited by a third child line going from the down pointing child line to the right.

Of course, an observer may select whatever mode of movement that pleases him or her. I decided that I should arrange for an oscillation around the ideal as originally painted by Mondrian. I set the limits so that the main features of the painting remain intact. If you select another moving mode, the limits become even more obvious as the lines jump from the one limit to the other.

We were, because of our desire to move slowly, forced to rethink the idea of speed of a line. Normally a universe, as in the case of the Monds universes, repaints the screen every 50 millisecond or with a frequency of 20 screens per second. Often enough to offer a smooth animation most of the time. However, a moving line can move no less than one pixel at a time and it would be reasonable to have the slowest speed be one pixel per cycle. Unfortunately, this was not slow enough for Monds_2. Instead we had to program the movement such that the line moves every four cycles, that is to say with a speed of a quarter pixel per cycle. It could perhaps be made even slower, but then you loose the smoothness and the movement starts looking jumpy.

The 'Cycle' of 'Moving Mode' is the default of the Demo. The cycle follows the original in still renderings with the lines oscillating around the mean.

In Monds_2, you may also take a look at a representation of the original painting by selecting "See Original" from the "Moving Mode" parameter.



Inspired by Piet Mondrian, Composition with Red, Yellow, and Blue , 1935-1942.
Oil on canvas, 39 3/4" x 20 1/8". At the Museum of Modern Art, San Francisco.

SF MoMA considers this painting an important acquisition and describes the work in some detail with a reproduction. See Composition with Red, Yellow, and Blue. It is of interest that the painting was exhibited in 1936, but, according to the SF MoMA notes "dramatically repainted" in 1942 when Mondrian moved to New York and was inspired to add " . . . the blue vertical at the bottom left and two small, unbound red squares floating in the area above it. New "rungs" off the vertical lines have been added to reinforce a more horizontal rhythm to the work.". If I understood the thing about what vertical rungs were added I could have rendered the painting before and after. Instead I contemplated randomness and order.

Before I talk about the animation,however, I should say something about color. I found two versions of the painting on the Internet, the one at the SF MoMA web site linked to above and another one at the Harvard University Art Museums. See the Harvard version of Composition with Red, Yellow, and Blue. As you can see they have widely different colors. In particular the base color is almost yellow in the SF MoMA version, while it is white/blue in the Harvard version. I chose to work with the Harvard version since I like it better and the bluish white also appear as a base color in other reproductions (e.g. Composition with Blue and Yellow, seen above as Monds_2).

In Monds_3, I wanted to contrast the carefully crafted order of the Mondrian work with the randomness that is represented by reality. And so I designed a cycle where the work disintegrates but keeps recognizable versions of the original elements. Disintegration, randomization, disorder progresses to a point when the picture is frozen again for a few seconds in a state of "maximum disorder". It then slowly reforms itself in phases and ends up at the original state. We can safely assume that the maximum disorder states always are different. There is a profound truth in the observation that there are many more disordered states than ordered states and that time in general is irreversible because entropy is irreversible. Well, here you have a situation where (if I may say so myself) clever programming lets you witness the breakup and reform of a work of art. I wish I could have shown it to Mondrian.

The 'Cycle' of 'Moving Mode' is the default of the Demo. The cycle starts with a still rendering and goes through a series of transformations which end with the lines attempting to recover their original positions as described above.

You may play with the universe and modify the way the lines move through the parameter "Moving Mode"..



Inspired by Piet Mondrian, Place de la Concorde , 1938-1943.
Oil on canvas, 37 x 37 1/4 in. (94 x 94.3 cm). At the Dallas Museum of Art, Texas

This important work also exists in two versions on the web. One is at the web site of the Dallas Museum of Art (See Place de la Concorde) and another at the Harvard University Art Museums web site (See the other version of Place de la Concorde). While these reproductions also differ, there are lesser differences than for Composition with Red, Yellow, and Blue, Monds_3, Again I choose to work with the Harvard version.

Monds_4 is similar to Monds_3. The elements are the same. But what happens is that Concorde, on the one hand is more complex because it has more elements on the other hand simpler because of a greater symmetry vertically and horizontally. When contemplating what I should do with this as a universe, I finally decided that it was similar enough to Monds_3 that I should do the same cycling from original work through randomization to a place of high disorder and then continue the cycle to restoration of the original. However, I also felt that I would offer the opportunity for the observer to play with the universe keeping all the elements including the number of lines and child lines and only letting the observer vary the Moving Mode.

The 'Cycle' of 'Moving Mode' is the default of the Demo.



Inspired by Piet Mondrian, Broadway Boogie Woogie. 1942-43.
Oil on canvas, 50 x 50"(127 x 127 cm). At the Museum of Modern Art, New York.

This work represents the culmination of the artistry of Piet Mondrian. MoMa has a reproduction with a description. See Broadway Boogie Woogie at MoMa. The following statement tells us something of what Mondrian wanted with his painting and with his replacement of black lines with bars with sequences of colored squares: "Mondrian's love of boogie-woogie must have come partly because he saw its goals as analogous to his own: "destruction of melody" which is the destruction of natural appearance; and construction through the continuous opposition of pure means—dynamic rhythm."

As the description points out, Mondrian broke with his tradition of black bars. This was a challenge to reproduce in Rart but the following Rart universes show the way: Monds_ColorLines, and Monds_CLChildren. Parameters offer the same move alternatives as for the black lines.

Monds_ColorLines is like the Monds_Lines universe, but with the lines colored with colored squares. The colors are in this universe chosen randomly from a palette of colors. The default palette is from the four colors used in Broadway Boogie Woogie. A parameter, Color Line Mode, lets you select how the squares move along the lines: "No Move", "Move Slower", "Move Faster", "Move Back and Forth", "Step Softly", and "Step Harder" with "No Move" as the default. It took some time to have this work smoothly since the colors once selected remain the same even if the squares move along the bars and come back at the beginning as they move off the end.. I decided after a number of tries to have the line length adjusted to an even number of squares.

Monds_CLChildren (Monds Color Lines Children) is like Monds_ChildLines but with multicolored squares. The colors are selected just as in Monds_ColorLines. A parameter is used to set the total number of child lines, with a fixed proportion of child lines with one parent, to child lines with two parents. Incidentally, in this universe, we have bumped to the upper limit of allowed uParameters in the present Rart environment. It is not very difficult to add to the number of parameters, but I think it would look too complicated for the average user.

Next, we shall contemplate the final challenge: Broadway Boogie Woogie.

Monds_5 is recently completed, Spring 2011. I have developed a way to set the exact colors in sequence as on the original, but it is a long and time consuming process. Instead I decided to let the squares be colored randomly for most of the lines . However, the most exciting thing about the rendering, is the movement along the lines of the squares. This must surely have been the idea of this painting to show the hustle and bustle of the big city with its square grid of streets and avenues. The movements along the lines surely represent traffic and so the alternatives of move make sense. I also had the problem of creating a cycle of randomness and order to this great painting. In the end I decided to introduce a night and day cycle where I actually changed the dominant white of the day to black of the night. I hope Mondrian would have approved.


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