Equilibrium and rhythm in Piet Mondrian’s Neo-Plastic compositions

An important modern artistic movement of the twentieth century is Piet Mondrian’s Neo-Plastic art and theory. From 1917 to 1944 and concurrent with the creation of his Neo-Plastic paintings, he explained his esthetic principles of NeoPlasticism in writings, though posteriori to the act of painting. Although a majority of scholars acknowledges a parallel evolution between his paintings and writings, Mondrian’s art is usually analyzed based on his sources of inspiration such as Theosophy, Hegelism, Platonism, and De Stijl. Hence, this paper aims to use Mondrian’s writings, as a stand-alone lens of scrutiny, to examine his esthetic evolution between two groups of paintings in theory and practice. The first group is early Neo-Plastic paintings created between 1919 and 1921, while the second group ismature works painted between 1935 and 1937. This article demonstrates the esthetic development in Mondrian’s thought by showing the degrees of conformity of his art with the fourth and the fifth principles of Neo-Plasticism (written by Mondrian in 1926) in regard to the expression of “equilibrium” and “rhythm” as universal and dynamic. Overall, this article will further the previous discussion on the parallel evolution of Mondrian’s writings and his paintings. This article shows that when it comes to the expression of equilibrium and rhythm, there are more similarities between the fourth and the fifth principles with his early Neo-Plastic


PUBLIC INTEREST STATEMENT
Despite the importance of Piet Mondrian (1872Mondrian ( -1944 in the history of modern art, he has not received as much scholarly attention as other artists. When they do study him, scholars often approach his works from historical or philosophical standpoints. Yet, when it comes to Mondrian, we have an important source of information: his writings. Indeed, Mondrian is an interesting artist, who was not only painting, but also writing about his art and his esthetic philosophies. Particularly important are his six principles of Neo-Plasticism, which he wrote in the 1920s. In this paper, I am examining the degrees of similarities and deviations between his writings and two groups of paintings he created between 1919-1921 and 1935-1937, focusing mainly on his expression of balance and rhythm in relation to his fourth and fifth principles of Neo-Plasticism.

Introduction
Neo-Plasticism was an important modern movement of the early twentieth century, yet it is mostly a "one man" movement, that of Piet Mondrian (1872Mondrian ( -1944. His exploration of abstraction is an interesting one, as he was first influenced by many sources such as Theosophy, Hegelism, Cubism, and De Stijl. Like many modern artists, he started his artistic career as a representational artist. Indeed, prior to 1911, he painted with a naturalist paintbrush. Starting around 1914 however, he started to explore abstraction, and his paintings became more and more drastic as years past. In a quick succession of influences and experimentations, Mondrian worked with different styles and approaches, to finally create his own artistic vocabulary and theory: Neo-Plasticism. For Mondrian, Neo-Plasticism was more than an art form, but was also a philosophical approach to life through art. Throughout his writings, he discussed how his art, including paintings and theories, could be used by people to live utopian lives based on moral values. As will be discussed in more detail in this article, for Mondrian, Neo-Plasticism had six fundamental or core principles which he wrote in his 1926 essay entitled Principes généraux du Néo-Plasticisme or General Principles of  This article focuses on the concepts of equilibrium and rhythm as universal which are discussed in his fourth and fifth principles. In this article, we ask and investigate how Mondrian's artistic visions, more specifically the concepts of equilibrium and rhythm, changed from one period to another. To do so, we will compare artworks and texts from two different periods. The first group of paintings (Mondrian, 1919(Mondrian, -1920 is from the beginning of his Neo-Plastic exploration to his membership to the De Stijl group, whereas the second group of paintings was painted between 1935 and 1937. Paintings from these two time periods (early and late Neo-Plasticism) will be compared to Mondrian's fourth and the fifth principles of Neo-Plasticism, where he discussed equilibrium and rhythm. As mentioned, Mondrian wrote his six principles in 1926. Although he did not edit or change, at least in writing, the six principles, we see an esthetic and visual shift in his use of element of lines for the expression of equilibrium and rhythm as universal, both in his paintings and in his writings. This new approach to Mondrian's artistic vision, that is to look specifically at his writings and paintings in relation to each other rather than trying to explain his paintings through contextualization, is an important and innovative approach to this modern painter. Although this approach may also be used when analyzing other modern artists who experimented with their canvases, such as Kandinsky, we also believe that focusing on the artistic process rather than specific paintings as finished products can be useful for research-based practices which seems to be growing among practitioners.
Indeed, much like research by practice as studies in artistic processes, we contend that to understand the development of Mondrian's artistic ideas on equilibrium and rhythm, his paintings should be analyzed in relation to the theoretical texts he concurrently wrote. Similarly, Threlfall explicitly referred to such analogy between Mondrian's paintings and his writings: It cannot be said that Mondrian's writings achieved the stature of his paintings, especially his New York series, but what can be said is that the writings evolved through a process that is analogous to the manner in which the paintings evolved. (Threlfall, 1978, p. 62) In fact, his paintings and his esthetic theories have been in constant evolution during his life. Furthermore, as Reynolds indicated, Mondrian, like other fellow modern artists such as Kandinsky, wrote his theories as a result of his intuitive experimentation on the canvas. "As with Kandinsky, Mondrian's theories are in fact intimately related to his pictorial innovations" (Reynolds, 1995, p. 155). That is to say his theories, as Mondrian himself stated, came after the creation of his artworks. Hence, in this article, except for his six principles written in 1926, only writings written concurrently to, or only slightly after, the creation of the paintings under analysis were used. Therefore, although we acknowledge that the writings were written slightly after his experimentation on canvas, paintings and texts of the same time period are used here, together, as a representation of his esthetic vision for these specific time periods.
At this point, we need to explain the logics behind using the content of the fourth and the fifth principles of Neo-Plasticism written in 1926 as a point of departure for the analysis of and comparison with from Mondrian's pre-1926 Neo-Plastic compositions and essays (Mondrian, 1919(Mondrian, -1920. It is noteworthy that Mondrian wrote six principles of Neo-Plasticism in 1926 in response to a questionnaire distributed by Del Marle to the De Stijl circle of artists (including Mondrian) to explain the esthetic rules of Neo-Plasticism and Elementarism (Holtzman & James, 1986, p. 213). Although these principles were written in 1926, the elements of such principles were part of Mondrian's experimentation in the late 1910s and early 1920s. According to Seuphor, one of Mondrian's intimate friends and one of the editors of his writing in Paris, Mondrian had already mentioned those principles as early as 1920 in a pamphlet. Regarding this, Seuphor said that "[t]he little essay he wrote with my help in 1926 for the magazine Vouloir (which did not publish it) is definitely an advance over the pamphlet of 1920. I think it is the best formulation of his fundamental ideas about Neo-Plasticism. It also has the merit of being brief" (Seuphor, 1956, p. 166). Although his six principles of Neo-Plasticism do not seem to have changed over time, it would be wrong to suggest that his esthetic theories remained constant throughout his Neo-Plastic exploration. In other words, although he crystalized the principles in 1926, he continued to experiment, adjust, and work with the concepts of equilibrium and rhythm after he wrote his six principles. In our later analytical sections, we are investigating how these concepts-equilibrium and rhythmevolved in Mondrian's artistic visions using paintings and texts from two different periods of his artistic career.

Analysis of the fourth and fifth principles of Neo-Plasticism
We now turn to the concept of equilibrium and rhythm discussed by Mondrian in his fourth and fifth principles of Neo-Plasticism. As mentioned before, he first wrote his six principles in 1926 in an article he wrote in French. 2 In the fourth principle, Mondrian stated: "[t]he constant equilibrium is achieved by the relationship of position, and is expressed by the straight line (limit of the means of imaging) in its principal opposition (rectangular)". For the fifth principle, Mondrian stated "The equilibrium, that neutralizes and annihilates the means of imaging, is possible by the relationships of proportion in which they are placed and which create the living rhythm" Mondrian (as cited in Veen, 2017b, p. 6). In the fourth principle, Mondrian, similarly to his other essays, emphasized on the primary and essential role of lines at right angleopposition principale in French and "principal opposition" in English-to express equilibrium. He also affirmed the role of lines to delimit means of imaging as mentioned earlier. By "plastic means", means of imaging, Mondrian here means color and non-color planes. Moreover, with the term "constant equilibrium", Mondrian emphasized on the dynamic nature of equilibrium. In the fifth principle, while he complemented what he said in the fourth principle in respect to the method of expression of equilibrium, he also provided us with method to express rhythm. As he stated, the equilibrium also is the outcome of relationships of proportion-rapport de proportion in French-between line and planes. Furthermore, from the fifth principle, it is inferred that what Mondrian called "living rhythm"-rythme vivant in French-is the outcome of relationships of proportion between planes and lines-in variety of length and widths. Overall, if we interpret two principles as one, it means that the so-called "living rhythm" is the offspring of equilibrium which is achieved through relationships of position and proportion between planes and lines.
3. Equilibrium and the fourth principle of Neo-Plastic compositions (Mondrian, 1919(Mondrian, -1920 To investigate how he envisaged equilibrium and rhythm, we will analyze Neo-Plastic compositions created between 1919 and 1921 while also using specific essays of Mondrian written between 1919 and 1923 which specifically talked about equilibrium and rhythm. Essays dated all the way to 1923 were selected due to the fact that, as mentioned earlier, Mondrian usually wrote after he experimented on canvas. Veen's (2011) exhaustive scrutiny on Mondrian's original writings shows that Mondrian wrote 13 short and long pieces of writings between 1919 and 1923. However, mostly long essays for De Stijl magazine he wrote between 1919 and 1923 were used for the analysis of this section. As such, four essays were chosen in which Mondrian informed the reader about his esthetic principles of Neo-Plasticism: Dialogue on the New Plastic-Dialoog over de Nieuwe Beelding (1919), Natural Reality and Abstract Reality: A Trialogue-Natuurlijke en abstracte realiteit (1919)(1920), and No Axiom but the Plastic Principle-Geen axioma maar beeldend principe (1923). In his essays of this period, Mondrian mainly introduced the foundation of Neo-Plastic art and theory in opposition to traditional forms of representation. As such, he even explained his new esthetic vision by discussing his earlier naturalistic paintings as a trialogue between a non-artist, a representational artist, and a pure abstract artist (Mondrian himself).
These paintings of Mondrian are not his first attempt at pure abstractions, yet the paintings executed between 1919 and 1921 are referred to as his early Neo-Plastic compositions. Similar to the other early Neo-Plastic compositions of the time, the four examples chosen here show planes of primary colors, as well as non-colors (mainly light gray and black), a use of single and even lines of similar thickness which are not extended to the edges of the canvas. This last visual detail is one of the main characteristics setting this time period apart from his previous and later periods. Furthermore, compared to earlier paintings, Mondrian, for the first time, abstained from depicting the lines as grid lines. He also asymmetrically sliced the composition into unequal-sized planes of color and non-color. Now that we looked at the overall characteristics of early Neo-Plastic compositions, we now turn to equilibrium and how Mondrian explored and portrayed it. In these early Neo-Plastic paintings, we contend that he achieved equilibrium by focusing on the relationship between vertical and horizontal lines, as well as between the dimensions of colors and non-colors.
In 1926, Mondrian indicated that equilibrium is achieved through the relationship between perpendicular lines. However, as mentioned before, looking at his earlier texts, it is obvious that Mondrian was already interested in the concept of equilibrium. Already in 1921, he talked about the relationships of position-verhouding van stand in Dutch-of lines have a key role in delimiting the dimension and proportion of planes. Mondrian believed that the "determinate expression of relationships" (Mondrian, 1921, p. 150) between dual opposing of plastic means results in universal equilibrium. Therefore, at the time, based in his early experimentations, lines at right angle "determine" the immutable and mutable relationships in Neo-Plastic esthetics. The term "determinate"-bepaalde in Dutch-for Mondrian meant the most objective, exact, pure, and universal expression of relationships, which differs from indeterminate-onbepaalde in Dutch-that is a subjective expression of relationships between elements of painting in representational art. Throughout the evolution of Neo-Plastic esthetics, for Mondrian, the oppositions of vertical and horizontal lines express the most determinate relationships or in Dutch verhouding in bepaaldheid (Veen, 2017a, p. 623). Therefore, Mondrian saw the relationship between perpendicular lines as "immutable" in Neo-Plastic esthetics. Whereas the relationships of dimension, color to non-color, and proportion of planes in respect to each other are considered secondary and so therefore "mutable". Indeed, without the existence of lines, there would be no exact or clear relationships between planes. In the absence of lines, the viewer is faced with a vague and subjective perception of dimension and proportion of color planes in respect to each other. As such, Mondrian envisioned that in realistic representations the relationships between line, color, and form are veiled and expressed indeterminately. In this respect, in his essay Dialogue on the New Plastic-Dialoog over de Nieuwe Beelding (1919) written as a dialogue when character A (a singer) asks Mondrian (character B: painter) about his point of view on the use of "natural appearance" to express relationships in painting, Mondrian answered: A. Do you find, then, that natural appearance interferes with the plastic expression of relationships? B. One cannot express both natural appearance as we see it and plastic relationships with the same determinateness. In naturalistic form, in naturalistic color, and in naturalistic line, plastic relationships are veiled. To be expressed plastically in a determinate way, relationships must be represented only through color and line. (Mondrian, 1919, p. 75) Considering the important role of lines in determining the color and non-color planes in theory of Neo-Plasticism, by looking at compositions dated between 1919 and 1921, one realizes a certain degree of inconsistency in the role of lines as it is stated in the fourth principle of Neo-Plasticism. In these paintings-see Figures 1-4-the incomplete extension of lines to the fringes of the composition resulted in the decline in determinateness of relationships between dimensions-verhouding van afmeting in Dutch-and proportions of peripheral planes in relation to the central enclosed planes. Thus, in these early compositions, the paintings are not yet entirely true to the fourth principle of Neo-Plasticism of 1926. According to what Mondrian stated in the fourth principle, the equilibrium is the outcome of relationships between lines and planes as their boundaries-lines acting as limits of planes. However, in these early compositions, such boundary, limit, limité in French, was not portrayed clearly in the peripheral planes of color and non-color. Indeed, Mondrian in early Neo-Plastic compositions was more or less following De Stijl principles and so he left the lines curtailed to the edges of the canvas. According to De Stijl principles, the incomplete extension of lines to the sides of the canvas results in illusion of growth or expansion of colors beyond the boundary of line (Elder, 2006, p. 13). By reducing the intersections of lines in his compositions dated 1920-1921, he managed to portray a more dynamic interplay between abstracted forms (color and non-color planes), intensified lines (straight lines at right angle), and space. The reduction in the number of lines, asymmetrical positioning of lines, and minimal use of element of color in compositions of 1920 and 1921 also resulted in a sense of instability and illusion of movement of lines and open-ended color planes in the periphery of the canvas. This vivid visual effect of balance is what Mondrian called "constant equilibrium", L'équilibre constant in French, between plastic means. In fact, those compositions of this period which are painted with fewer thick lines and with color planes situated on the fringes of composition show a more robust relationships between perpendicular lines. Overall, Mondrian's adherence to the De Stijl principles-that is the incomplete extension of lines to the edges of the canvas-explains these inconsistencies between the premises of the fourth principle with these early Neo-Plastic compositions.   (Mondrian, 1920). Composition with red yellow, blue, and black. Oil on canvas, 59.5 × 59.5 cm. Reproduced with the permission of Gemeentemuseum, The Hague. motifs used in his previous paintings (Holtzman & James, 1986, p. 82). In the first scene of the trialogue, three characters X (a layman), Y (a naturalistic painter), and Z (an abstract-real painter -Mondrian himself) are involved in a conversation about one of Mondrian's naturalistic paintings that is a landscape with a wide horizon in the late evening with the moon on the sky. In the first scene of trialogue, two characters, X and Z (Mondrian), debate on the use of naturalistic forms to express harmony and balance. Mondrian (Z) tries to convince X to the necessity to use lines as two opposing contraries (vertical versus horizontal) to determinately express relationships in painting. When X asks Z for various kinds of relationships necessary for determinate and universal expression of harmony in painting, Z indicated to three different relationships of position, dimension, and color to non-color. However, Z further emphasized that relationships of position of lines are primary and substantial for expression of other two kinds of relationships: "Both the relationships of color and the relationships of dimension are sustained by the relationship of position" (Mondrian, 1919(Mondrian, -1920. In his compositions executed after 1922, Mondrian managed to find an appropriate method to express equilibrium through the opposition of prominent lines at right angle. Thanks to the use of the lines delimiting the planes, Mondrian further succeeded in depicting equilibrium between the planar and linear structures of his compositions. As such, the "constant equilibrium", mentioned both in his early texts and in the 1926 fourth principle of Neo-Plasticism, is expressed in his early Neo-Plastic paintings through the tendency of lines to retain and delimit the planes within the canvas on one hand and reverse the tendency of the planar scheme (in particular those open-ended planes in the periphery) to expand beyond the edge of the composition, on the other.
Mondrian, in the seventh scene of the trialogue, explained that mutual interactions of lines and planes in space bring what he calls "constant equilibrium". Based on his interest in interpreting everything based on a dual system of oppositions, he envisaged form and space as two contraries of "limitation"-beperking in Dutch, and "expansion"-uitbreiding in Dutch. For Mondrian, the term 'limitation' refers to naturalistic forms and their subjective and indeterminate expression in representational painting. Whereas the term 'expansion' denotes the depiction of naturalistic forms on a flat plane, the canvas, by use of intensified, purified elements of painting as an abstract translation of spatiality in painting. That is to say expansion simply means the portrayal of form into space which, according to Mondrian, was portrayed vaguely and subjective through the use of conventional rules such as perspective and foreshortening in representational painting. Mondrian postulated that such "expansion" was expressed indeterminately, vaguely, in representational painting. Thereby, he believed the limitation of form should be abstracted or what he called "interiorization". Moreover, the expansion (spatial expression) is expressed as concrete and determinate through "exteriorization" of illusionistic and atmospheric space. What brings these two oppositions of limitation and expansion into unity and equilibrium are straight lines at right angle. Indeed, in the seventh scene of the trialogue mentioned earlier, he stated that "[t]his expression consists of the straight and the planar: only the straight can express expansion and limitation equivalently. These two opposites appear plastically through the most extreme difference of position: the perpendicular" (Mondrian, 1919(Mondrian, -1920 4. Rhythm and the fifth principle in Neo-Plastic compositions (1919-1921 Moving from the analysis of early compositions based on the concept of equilibrium, we now come to Mondrian's interest in the expression of "rhythm". As a consequence of the incomplete extension of lines to the edges of the canvas in the painting of the early period, the rhythm also cannot be expressed determinately enough since there is no active involvement of proportionate ratios of marginal planes with other enclosed planes. This matter is discernible in all paintings of this period, particularly in Composition with Red Yellow, Blue and Black (1920) It is worth mentioning that "constant equilibrium" as mentioned above is also expressed as a result of the relationships of proportion between color and non-color planes. Indeed, as Mondrian stated in the fifth principle, equilibrium is also the outcome of the relationship of planes' proportion in respect to each other. In the 1921-1924 paintings, it is through the perpetual interaction of immutable and mutable relationships between dissimilar sized color and non-color planes upon each other that the duality of plastic oppositions (vertical versus horizontal, color versus non-color) and their relationships (i.e. line-plane, line-line, line-color, and so on) turn into a neutral but constant state of rhythm and so equilibrium. Hence, the equilibrium of the composition is attained through the perpetual rhythm of proportion of planes-as mutable-and relationship of position of lines-as immutable-in respect to each other. We contend that this rhythm, which emerges from the constant relationship between dimension and proportion of planes in these early (1921)(1922)(1923)(1924) paintings, is an early representation of what Mondrian will call rhythm vivant or living rhythm (Veen, 2017b) in his 1926 fifth principle.
To further understand the evolution of immutable and mutable relationships in Neo-Plastic theory, it is necessary to study Mondrian's idea toward two extremes: relative and absolute. Mondrian in his article entitled No Axiom but the Plastic Principle-Geen axioma maar beeldend principe emphasized on "immutable" (absolute) over "mutable" (relative). This short article which was written in 1923 but published in August 1924 (Veen, 2011, p. 163) is among the last contributions of Mondrian to the De Stijl journal. According to Holtzman and James (1986), Mondrian's emphasis on the term "immutable" (absolute) in this article is partly related to the Dadaists vision, in particular Georges Ribemont-Dessaignes who negated the need for esthetic principles and beauty as truth in painting of De Stijl artists (p. 178). As Mondrian stated in the opening of the article, the people should break away with all previous traditions in art and life as fixed axioms. He stated that there is no such absoluteness in principles and opinion of people as doctrines. Instead, everything should be seen and perceived as relative. However, Mondrian stated that by accepting relativity in everything, we feel the need for "absolute" as something unattainable and unreachable: "by understanding the relativity of everything, we gain an intuitive sense of the absolute. Moreover, the relativity, the mutability of things creates in us a desire for the absolute, the immutable" (Mondrian, 1923, p. 178). Mondrian further connected the relative (mutable) with the depiction of naturalistic form in representational painting that results in a 'lyrical' and 'descriptive' expression in painting. For Mondrian, such relative vision veiled the true manifestation of absolute in art. Moreover, he indicated that modernization in life and society and the necessity for "clarity and purity in everything" (Mondrian, 1923, p. 178) direct one to move from relative to absolute. As such, people no longer want the two sides of extremes as relative and absolute. Instead, we seek equilibrium between absolute and relative. At this point, Mondrian claimed that such equivalence between immutable (absolute) and mutable (relative) was already achieved in art and in particular in his Neo-Plastic art through the antagonization of dual oppositions-that of the opposing means of imaging or plastic means. Furthermore, such realization of immutable and mutable in unity and equivalence is only attainable through two primary dual oppositions of vertical and horizontal lines: Neo-Plasticism constructed its universal plastic means, the rectangular color plane. Through the duality of position of the straight it expresses equilibrium (equivalence) of relative and absolute. It opposes the color plane to the noncolor plane (white, gray, and black), so that through this duality the opposites can annihilate one another in the multiplicity of the composition. The perpendicular position expresses the constant; the rhythm of the composition expresses the relative. (Mondrian, 1923, p. 179) In Figures 1-4, the more Mondrian reduced the quantity of lines and colors, the more degree of equivalence is palpable as outcome of such immutable and mutable relationships between position and proportion of color and non-color planes (i.e. rhythm). Thus, one realizes a more objective, determinate, expression of rhythm, and so equilibrium, in the compositions of 1920 and 1921 (see Figures 3 and 4) compared to those created prior to 1920 (see Figures 1 and 2). The thin gray lines and relatively similar sized planes in his compositions of 1919 (see Figure 1) resulted in a static relationships of proportion of color planes and non-colors planes. This means that when it comes to the evolution of rhythm in Mondrian's artistic process, these early paintings only partially portray "vital rhythm" as Mondrian explained in his fifth principle (1926). In his compositions of 1920 and 1921, thanks to the use of fewer, yet thicker lines and intersections, as well as more variety in color planes' dimensions, there is a more vivid tension in the relationships of proportion of planes in respect to each other and to the whole composition. Because the rhythm in these early Neo-Plastic compositions is heavily dependent on the immutable relationships of perpendicular lines, the equilibrium, which is the outcome of the immutable relationships between lines at right angles, is not yet expressed as a liberal and dynamic factor. Overall, we found more similarities for the determinate expression of rhythm as a universal between the content of the fifth principle and what Mondrian depicted in his 1920 and 1921 compositions, in contrast to those paintings created prior to 1920. Neo-Plastic compositions (1935-1937 To assess equilibrium in his later artistic vision, we chose four paintings that were painted between 1935 and 1937, as well as three texts written concurrent or slightly after the creation of these paintings. The chosen three essays are: Plastic Art and Pure Plastic Art (1936), Neo-Plastic (1938), and The Necessity for a New Teaching in Art, Architecture, and Industry (1938). In 1936, Mondrian was asked to write Plastic Art and Pure Plastic Art as an article for an English journal Circle: An International Survey of Constructive Art published in 1937 in Paris. This 1936 issue was published to promote the core ideas of the British Constructivist groups Axis and Circle (Holtzman & James, 1986, p. 288;Veen, 2011;p. 278). The second piece of writing for this article is Neo-Plastic written originally in French, then translated in German, and published in August 1938 as a short article in the Swiss magazine Wrek (Veen, 2011, p. 294). Mondrian wrote this short piece of writing as a response to Peter Meyer, the editor of the journal, who considered the non-representational expression in art as a "negation" of the very goal of art making (Holtzman & James, 1986, p. 305). This essay is important because in it, Mondrian discussed his earlier (1926) first, fourth, and fifth principles, but in a more refined and mature way, with textual clarifications which we see as outcomes of his later artistic experiments on canvas (1935)(1936)(1937). The third piece of writing is The Necessity for a New Teaching in Art, Architecture, and Industry which was published in 1938 as a long essay originally written partly in Dutch and partly in English. The Dutch title of the essay is Een plan voor een werkelijk modern esthetsiche school (Veen, 2011, p. 299) which means "A plan for a truly modern aesthetic school", a slightly different translation than Mondrian's English title. This essay is of great importance, since in it, Mondrian elaborated on his plan to establish a modern art school based on his Neo-Plastic esthetic vision. Mondrian, after 1921, continued with his artistic experimentations trying to reach equilibrium and rhythm in his paintings. The visual characteristics of the works created between 1924 and 1932 are similar to his earlier works. These works share common characteristics such as asymmetric positionings, a minimal use of perpendicular lines, the use of small color planes in the peripheral sides of the composition, and the adoption of non-colors, 3 especially white. In contrast to his earlier works however, after 1924, he innovatively stretched the lines to the fringes of the canvas. This change was concurrent with Mondrian's move away from the De Stijl group, most particularly his break away with fellow artist and architect Theo van Doesburg. Such change in the characteristics of the lines resulted in a purer articulation of rhythm and equilibrium due to the more active involvement between the peripheral and central planes, which now had a mutable relationship of proportion and dimension. Moreover, he intensified the level of dynamism in rhythm and equilibrium not only between dissimilar sized color planes and open-ended non-color planes, but also through abrupt changes in the thickness of the lines. Such sudden change in the thickness of lines is most distinct in his lozenge and upright compositions of 1930and 1931. In his 1924-1932 compositions, Mondrian used the core values he wrote his 1926 fourth and the fifth principles to achieve equilibrium and rhythm by relational opposition of lines as well as variant relationships of size, color to non-color, and proportion of planes.

Equilibrium and his
However, after 1932, Mondrian gradually took a different path to achieve a purer expression of rhythm and equilibrium. He steadily changed the previous constructive role of lines, planes, and colors into a destructive one (Bois, 1994, p. 315). Such destruction for Mondrian was not a one-way act of abolition or annihilation of means of imaging. Instead, as he explained in his texts, it was a reconstruction of a "deepened" or interiorized form. The first thing he amended was the rectangularity of color and non-color planes that were previously a consequence of intersecting vertical and horizontal lines. That is to say, Mondrian altered the previous role of lines delimiting planes as rectangular shapes. This means that lines were no longer used to create planes. Such change in the role of lines was initiated by the adoption of double lines in 1932, which was soon changed into tripled and quadrupled and then to a meshed network of lines after 1935. This repetition of lines resulted in the abolition of planes as planes (Bois, 1994, p. 315). It also led to the abolishment of the flatness of the surface of the composition. Looking at compositions created between 1932 and 1933, one realizes an increasing closeness between double or tripled lines. After 1935, he started to widen the space between lines (Figures 5-8), which resulted in the expression the rhythm, and so equilibrium, independently from the mutable relationships of proportion and dimension of color and non-color planes.
Equilibrium, in these later compositions (1935)(1936)(1937), is no longer merely reliant on the invariant relationships of position of the perpendicular lines as perimeter of planes or what Mondrian stated in the fourth principle as "limit of the means of imaging"-limite du moyen plastique-Mondrian (as cited in Veen, 2017b, p. 6;2017a, p. 283). This is because, as stated before, there is no constructive role for the lines to create sets of planes with tangible dimension and proportion. Moreover, the lines appear segmented in shorter fragments due to the existence of constant white flickering effects at their intersections. Such portrayal of lines as disjointed shorter lines is evident in Figures 6 and 8. In his texts written after 1934, Mondrian started to use the term "dynamic equilibrium" or Équilibre dynamique in French, instead of the term "constant equilibrium" of his earlier essays. We contend that in his 1935-1937 paintings, as we just described, the visual balance he achieved through his novel rendering of rhythm is this dynamic equilibrium he wrote about in his texts at the time. In fact, due to the changes in the pictorial role of lines, the very essence of immutable relationships of position of lines has changed. The equilibrium, henceforth, is expressed through perpetual interplay between plurality of lines and their white intervals, which seem to be in constant visual movement with each other. Indeed, the immutable relationships of lines are no longer exhibited in limited flat surfaces on the canvas, but experienced within an infinite space encompassing the inner and outer space of the composition. For Mondrian, this boundless space is vital for the articulation of pure relationships since it is through the mutual interaction between these "relationships" that the spectator experiences equilibrium and rhythm as universal concepts. Indeed, in his works of this period, Mondrian has refined the pictorial characteristics of lines and planes into purified means of expression. In these texts, Mondrian explained that these purified elements of painting are the most concrete and objective articulations of form in respect to the space. In his article Plastic Art and Pure Plastic Art (1936), he distinguishes the differences between  figurative and non-figurative art. He called the purified elements in non-figurative art (best exemplified in his post-1935 Neo-Plastic compositions) "neutral form": "the latter [non-figurative art] uses simple and neutral forms, or, ultimately, the free line and the pure colour" (Mondrian, 1936, p. 290). We relate the term "free line" in the given quote, repeated several times in this essay, to his more liberal and destructive use of lines in his post-1932 compositions.
In the compositions of this period, lines are no longer constructive entities standing for themselves or as themselves. This was an esthetic revelation for Mondrian, who then, in his post-1938 essays, started to refer to the neutralized forms as "limited space":  The plastic is expressed not only through the picture or the object itself, but also by what surrounds it: space. The picture, the object, and the space create relationships. The object itself has its own relationships, but space is empty and without relationships. The object is a limited space with relationships. (Mondrian, 1938b, p. 312) Indeed, Mondrian now expressed dynamic equilibrium through the relationships of neutral forms in space. In The Necessity for a New Teaching in Art, Architecture, and Industry (Mondrian, 1938), while Mondrian explained the essence of "plastic" and "means of imaging", he also discussed the mutual relationship between purified, neutral, forms as "limited space" and the "empty space" of the composition. Such terms as limited space and empty space are reminiscent of his use of the terms "limitation" and "expansion" mainly used in his early writings published in De Stijl magazine.
In fact, the immutable relationships of position of lines in the compositions of this period (see Figures 5-8) were articulated through the empty and infinite space. The vivid relationships of the rhythm of lines resulted in the expression of dynamic equilibrium. It is worth mentioning that although he used the term "rhythm" in his previous writings, he adopted the term "dynamic equilibrium" after 1934, a term not used in his 1926 principles of Neo-Plasticism. Mondrian explained "dynamic equilibrium" as the reciprocal connection between parts and the whole. The interaction and nullification of parts (here opposing plastic means) to the whole results in unity, as a "complete whole" (holistic experience of unity or equilibrium). In other words, the concept of equilibrium, a concept which, as we have seen, has been important for him since his early Neoplastic paintings, and which is identified as a principle of Neo-Plasticism in his 1926 six principles, has now evolved, in both his paintings and writings, into "dynamic equilibrium". Indeed, such dynamic nature of equilibrium is what Mondrian envisaged as one of the main esthetic elements of his Neo-Plastic art. In his article Plastic Art and Pure Plastic Art which is based on "constructivist" ideas, Mondrian mainly emphasized on the distinctive characteristics and differences between figurative art and non-figurative art (Neo-Plastic art in particular). In this article, Mondrian explained the nature of non-figurative art based on mutual acts of "destruction" of static equilibrium in particular form and "construction" of a dynamic equilibrium. As such, he explained the nature of "dynamic equilibrium" as an outcome of such reciprocal relationships between the actions of destruction and construction: It is of the greatest importance to note the destructive-constructive quality of dynamic equilibrium. Then we shall understand that the equilibrium of which we speak in nonfigurative art is not without movement of action but is on the contrary a continual movement. (Mondrian, 1936, p. 294) It is noteworthy that in his early compositions (Mondrian, 1919(Mondrian, -1920, the relation between parts -each plastic mean (line, color)-to the whole was more or less static, or what Mondrian called in his early essays published in the De Stijl magazine, "repose". Such "repose" was mainly depicted through the immutable relationships of position of lines in the compositions mentioned in this article. Nonetheless, in compositions of this period (1935)(1936)(1937) due to the plurality of lines and constant white glittering effect at the intersections of lines, the equilibrium is no longer expressed using fixed positions of lines at straight angle. Instead, the balance is the outcome of a pulsing rhythm (see Figures 7 and 8) exhibited through the relationship between limited (i.e. purified plastic means) and empty space, which we relate to what he called "dynamic equilibrium" in his essays of the time. Still in his text, to explain the term "dynamic equilibrium", he used as an example the relation between elements of a building (as parts) and a city. In his essay The Necessity for a New Teaching in Art, Architecture, and Industry (Mondrian, 1938), he discussed the fundamental rules governing on characteristics and use of means of imaging, in his esthetic vision for future art students: To the extent that this opposition is harmonious, the object is equilibrated. But this equilibrium still creates a "thing." The "thing" must be annihilated by multiplicity in order to be destroyed as something separate. A building is not a totality. A city is more of a wholeeverything is relative. In a building there are rooms: the rooms form the building. This resolution into a complete whole is dynamic equilibrium. It annihilates the static equilibrium of the "thing" alone. Dynamic equilibrium arises through relationships. The nature of this equilibrium is determined by the forms and colors. Their rhythm creates dynamic equilibrium. (Mondrian, 1938b, p. 312) In this later text, Mondrian sees dynamic equilibrium is the offspring of the relationships between "parts" and a "complete whole". In the above quote, Mondrian also mentioned the annihilation of the relation between line and plane, something he achieved by multiplying the lines. As such, the static equilibrium attained through neutralization of duality of means of imaging was recreated as a dynamic equilibrium through the repetition of lines in compositions of this period. In his 1935-1937 compositions, Mondrian, in his quest for a purer expression of rhythm and equilibrium as dynamic, prioritized "relationships" over his earlier constructive pictorial role of plastic means. So, in the compositions of this period (1935)(1936)(1937), he turned the attention of the viewer from the visual characteristics of lines, planes, and colors to the relationships between the plastic means-as limited space-and empty space.
6. Rhythm and the fifth principles in his late Neo-Plastic compositions (1935-1937 By looking at the compositions of this period, we also find deviations from the fifth principle of Neo-Plasticism written earlier (1926) when it comes to the expression of rhythm. For some of the artworks, rhythm as dynamic equilibrium is not expressed through mutable relationships of proportion of planes in respect to each other. Instead, the rhythm is articulated through frequent immutable relationships between lines-stretched throughout the width and length of the canvas -and their white intervals, forming a dynamic whole. Due to the intense white flickering effect at the intersections of the lines-in particular visible in Figures 7 and 8-there is no concrete dimension and proportion for planes in respect to the space of the composition. Instead, the rhythm is expressed through plurality of lines in various thickness, intervals, and asymmetry. The diversity in length and thickness of lines resulted in the creation of networks of lines.
Besides the variety in length and thickness of lines, one should not neglect the presence of tiny cells of color animating the rhythm, and so equilibrium, in the above compositions. The blue cells on the lower right side in Figures 5 and 7, the red cell on the left side in Figure 6, and the tiny cells of yellow and red on the lower right side in Figure 8 are all visually involved in expression of dynamic rhythm. Similarly, the uneven spacing amidst the dense thin lines on the right side of the composition in Figure 7 and the narrow intervals of lines on the left side in Figure 8 also intensify the degree of vitality in rhythm as dynamic equilibrium. Vitality of rhythm was already emphasized in the 1926 fifth principle of Neo-Plasticism, and we see it as one of the distinct characteristics of Neo-Plastic art as a non-figurative art. In other words, although the concept was already important for Mondrian in 1926, he continued to visually experiment with the concept throughout the years. He also put more emphasis and elaborated on the topic in his later texts. In his article Plastic Art and Pure Plastic Art where Mondrian most explicitly distinguished figurative art from nonfigurative art, favoring the non-figurative esthetic ideas of Constructivist painters, Mondrian considered "dynamic rhythm" as one of the key esthetic components of non-figurative art. He also defined such "living" or "vital" rhythm as outcomes of reciprocated relations between pure means of imaging. Such dynamic rhythm is what Mondrian shown in compositions of this period (1935)(1936)(1937) through mutual relationships between lines in multiplicity and their white intervals.
Non-figurative art is created by establishing a dynamic rhythm of determinate mutual relations which excludes the formation of any particular form. [. . .] The dynamic rhythm which is essential in all art is also the essential element of a non-figurative work. In figurative art this rhythm is veiled. (Mondrian, 1936, p. 295) Overall, in this time period, the rhythm as dynamic equilibrium was primarily attained through the perpetual relationships between the position of lines-Mondrian called them free lines as limited space in writings of this period-and the empty space of the composition. Mondrian in his short article Neo-Plastic written for the Swiss journal Wrek, while re-emphasizing his principles of Neo-Plasticism, focused on the importance of elements of rhythm as dynamic in his theory of Neo-Plasticism. As we have seen in compositions of this period, Mondrian enhanced the level of vitality of his art by using a multiplicity of lines of varied thickness. In other words, we believe that in the artworks of this period, Mondrian expressed more thoroughly "living rhythm" as stated in his 1926 fifth principles of Neo-Plasticism.
All plastic art reveals that its essential content moves us aesthetically through the expression of vital equilibrium. All plastic art achieves this by establishing a dynamic rhythm of forms, lines, colors, and relationships. These forms, lines, and colors are only the "means" for establishing rhythm. These means determine its character, but it is their mutual relationships that create its dynamic expression. (Mondrian, 1938a, p. 305)

Conclusion
In this article, we have shown although Mondrian was interested in the concept of rhythm and equilibrium, as attested by his 1926 six principles, throughout his Neo-Plastic experimentations, he visually achieved them differently in different time periods.
Interestingly, we also see stronger similarities between fourth principle of Neo-Plasticismpertinent to the expression of equilibrium-with the visual elements used in the early 1919-1921 compositions than with his later (1935)(1936)(1937) works. In this respect, in early compositions, equilibrium was the outcome of the constant immutable relationships of position of the vertical and horizontal lines as boundary of plastic means, something which was still true for him when he wrote his fourth principle in 1926. Due to the more or less indeterminate relationship between the peripheral planes and the centrally enclosed ones, these early compositions resulted in a certain degree of inconsistency when it comes to equilibrium. In these early paintings, "constant equilibrium" was attained through the interaction between immutable relationships between lines and variable relationships between dimensions of color and non-color planes.
In contrast, in his later compositions of 1935-1937, due to the different use of visual elements -in particular elements of line-equilibrium was expressed as rhythm and dynamic interactions of lines and the infinite space. Due to frequent intersections of lines and an intense white flickering effect at the junctions of these lines, there was no identifiable plane with concrete dimension in the compositions. As such, elements of line are now given a destructive role rather than the constructive one they held in the creation of planes as rectangular shapes. In his later artworks, the space was bisected into small cells of white no longer representative of planes. In the Neo-Plastic compositions of this period, equilibrium is experienced as an outcome of perpetual rhythm between frequent intersecting lines, variety in thickness or intervals between lines, and tiny cells of color.
Something similar is also visible with the concept of rhythm. In other words, his earlier experimentations with rhythm were still valid when he wrote in 1926 principles of Neo-Plasticism, while his later experimentations do not conform as easily with his 1926 descriptions. In the early Neo-Plastic compositions, the rhythm was the outcome of variant relationships of proportion of color and non-color planes. Moreover, the rhythm in these compositions was static (repose) due to the dominance of the immutable relationships of position of lines in respect to the two-dimensional surface of the composition. More importantly, the rhythm and equilibrium were two separate but correlated elements in these compositions. As such, the rhythm in these works was an outcome of mutable relationships of proportion, color to non-color, and dimension of planes in the periphery and center of the composition.