1921  1944 oNEOPLASTICISM o Part 2 o1933  1940 o osee Part 1o1921  1933 ooosee Part 3 o1940  1944
1 
2 
3 
4 
Observation of the four works 1, 2, 3, 4 in sequential order reveals a gradual increase in the number of lines, which divide the space of the canvas into a growing number of parts. The tendency observed during the 1920s toward a space of evergreater rarefaction and synthesis gradually gave way to the opposite tendency, whereby an increasing level of articulation and complexity was progressively reintroduced into the Neoplastic canvases as from 1933.
With a view to outlining the most significant developments of this period, I shall now present an initial explanation, based solely on these four paintings for the moment, before going on to consider the other works painted by Mondrian between 1932 and 1943 in detail.
Composition B with Double Line, Yellow and Gray (1) is the first Neoplastic composition with two horizontal lines running very close to one another in place of the single horizontal to be seen in all the previous works. The thickness of the two horizontal lines is half that of the vertical. It is almost as though the two thin black horizontals served to mark out a white line opposing the black no longer solely at the level of form (horizontal or vertical) but also in terms of color (black or white). Like other compositions based on the N. III layout, 1 presents an area of square form closed on four sides in the lower right section. The square field expresses a moment of equilibrium between the opposing directions, which elsewhere give birth to variable proportions and then expand in a univocal and absolute way (in exclusively horizontal or vertical terms) toward an incommensurable space. The large yellow field in the upper left section and the gray one lower down to the right help to keep the square in a state of unstable equilibrium. 

1  Composition B with Double Line, Yellow and Gray, 1932, Oil on Canvas, cm. 50 x 50 
Diagram A 
Diagram B 
Diagram C 

2  Composition in Black and White with Double Lines, 1934, Oil on Canvas, cm. 59,4 x 60,3 
The place of the closed square form seen in 1 is taken here by a more complex structure made up of two juxtaposed rectangles (Diagrams A and B) that interact to generate a square form (diagram C). This is a pattern already seen in a composition of 1925. The square form, i.e. an equivalence of opposites, appears to be challenged by two opposing forms of predominance, which lends greater dynamism to the square form of the typical N. III layout.
Running through the central area are two horizontal lines that seem to be those of Composition B with Double Line, Yellow and Gray (1) undergoing expansion.
The interaction between verticals and horizontals generates a small square (Diagram C). A relationship is established between a small square of sharply defined and definite size appearing in the center and a larger indefinite square placed in the lower section, which could almost be seen as the smaller one an instant after the lines have passed. The dynamic movement of these lines drags along the small central square, which opens up while remaining in unstable equilibrium between vertical (A) and horizontal (B) predominance.
Different parts of a Neoplastic composition are to be seen as successive moments of one and the same space undergoing transformation.
The two horizontal lines running through the central area of Composition in Black and White with Double Lines (2) become four in this composition which is again based on the N. III layout. In this case, however, the field inside the square form is no longer white but yellow and presents a vertical segment echoed by an external horizontal segment in the lower section. The square form appears in a state of unstable equilibrium between an internal vertical and an external horizontal. I recall Mondrian identifying the vertical with the spiritual whereas the horizontal was a plastic symbol of the natural. Unity (the square form) is in a state of unstable equilibrium between inner and outer worlds. This is the first canvas based on the N. III layout in which the white field of the square accommodates a linear segment, which is another sign of the need to open up the unitary synthesis to manifold space. This linear segment seems designed to indicate the beginning of a process of interpenetration between square and lines. 

3  Composition with Yellow, 1936, Oil on Canvas, cm. 66 x 74 
4  Composition 12 with Blue, 193742, Oil on Canvas, cm. 60,5 x 62 
Diagram 4a 
Diagram 4b 
Diagram 4c 
We see here thirteen perpendicular black lines forming a large number of relations that generate white planes of various shapes and sizes. Areas of greater or lesser horizontal and vertical extension can be seen. Vertical and horizontal attain equivalence in some points for an instant to form smaller or larger squares.
Consider diagram 4a and the pair of vertical lines (A) that intersect with the six horizontals to generate five planes; examination from the bottom up reveals a small and almost square form (more horizontal) that becomes a horizontal rectangle, then two nearly equal vertical rectangles, and finally a square again, but this time with a slight vertical predominance.
Considering the pair of horizontal lines (B) and their meeting with the seven verticals (reading from left to right), we see a square repeated in almost the same form on the right (with a slight vertical predominance) that undergoes conspicuous horizontal expansion, contracts again to assume markedly vertical proportions, then returns to the horizontal, and finally becomes a shape in which vertical and horizontal are practically equivalent but now with a slight horizontal predominance.
The space expands and contracts under the pressure of the two contending directions, which attain equivalence and a more stable equilibrium for an instant before opening up again to the more or less marked predominance of one or the other. Equivalences of opposite values are born and dissolve, are lost and found again in forms that are always new. The idea of the square, i.e. an equivalence of opposites, seems to be expressed here too more as a process than a state.
The solid and definite square of the 1920s now appears to undergo dilution on contact with the lines. The latter interact to expand and contract the space, above all in the central area, outside which they become entities in their own right; all horizontals or all verticals, one thing excluding the other. The space becomes absolute and eliminates any possible relationship between the parts.
In the lower right section, the central field flows toward an area of greater synthesis where we can pause to observe a smaller number of planes (Diagram 4c). One of a bright blue color appears as the fourth part of a larger form that recalls the square of the N. III layout by virtue of the position it occupies.
We move from an area of extremely variable space (the central field), where equivalence appears in a state of becoming, to one in which the space is more constant (the smaller field) and then to a more stable synthesis of opposite values highlighted by color. The accent of color seems designed to draw attention to a square, which appears as a sort of model of which the planes observed in the central area constitute a variation.
I recall the compositions of 191819 in which all the measures and the proportions varied on the basis of a constant module. Now there is no longer any prior control.
1  Composition with Yellow, 1930 
2  Composition with Blue and Yellow, 1932 
3  Composition N. 12 with Blue, 193742 
3  Diagram 
3 appears to offer a summary of all the compositions that Mondrian produced between 1929 and 1932 involving variations on the theme of the square, such as for instance 1, with a closed square, an area of slightly greater horizontal development (lower left), a shape of greater vertical development (upper right), one of less greater development (upper left) and a yellow rectangle, o 2 with a large blue square, a smaller yellow square, a white square left open at left and a white similar square which is however left open at left and on top. A whole variety of possible equivalences of opposites. We seem to see all these different proportions brought together in 3.
We move from a sharply defined and definite square placed in a state of dynamic equilibrium by two or three shapes and the surrounding colors (1) to one placed in tension by the prolongation of its sides (2) and finally a "square" in a state of becoming that has undergone total interpenetration with the lines and is expressed as a continuing variation on itself (3). 

1  1932 
2  1934 
3  193742 
Observation of the three works in sequential order reveals how the "white line" running through the center of 1 leads (2) to the multiplicity of 3.
During the 1920's Mondrian often used different shades of white for the square field to evoke synthesis of the surrounding color planes.
White (the space within the double black line of 1) opens up now to complexity which is tantamount to say that unity opens up to multiplicity.
It appears to be a short step from Composition N. 12 with Blue to New York City. In actual fact, however, the process of spatial multiplication was not completed so quickly. 


Composition N. 12 with Blue  193742 
New York City  1942 
The common denominator of all the works produced between 1932 and 1942 is in fact the opening up and multiplication of unity, but the progress achieved was very slow. There were phases of uncertainty with works begun but never completed or taken up later and altered.
The following four charts present examples of works responding to a similar typology. Some of these will be then individually analyzed in detail.
1st CHART
3 
5 
6 
7 
8 
We see here compositions developing a complexity of lines which create areas of different size and proportions. Some of these areas tend toward square proportions which are in some cases highlighted by colors.
2nd CHART
2 
3 
9 
10 
11 
3, 9, 10 and 11 present a square form interpenetrating with a vertical field that runs through the whole composition from the bottom to the top. The vertical field seems to originate from the double vertical lines of 2.
3rd CHART
12 
13 
14 
15 
16 
This type of compositions displays an unstable square generated between the bottom edge of the canvas and one or more horizontal lines in the upper section.
4th CHART
17 
18 
19 
20 
21 
Other works reveal the need to maintain the visibility of a large square generated by the combination of various proportions that interact with one another to evoke moments of equilibrium inside a space that changes constantly in appearance.
As mentioned, the common denominator of these compositions is the opening up and multiplication of the unit representing an equivalence of opposites, that is to say, the square form.
* * * * *
Let us now examine in detail some of these works.
2 
3 


Diagram 2 
Diagram 3a 
Diagram 3b 
Layout II 
In 3 we see the confluence of a square form in the space between the two vertical lines running through the center (Diagram 3a). The square form seems to have originated in the yellow square of 2, which enters the field generated to its left by the two vertical lines.
Diagram 3b: The intersecting of four horizontal and two vertical lines generates a basic structure presenting the development typical of the N. II layout enriched with a larger number of lines in this phase. This almost completely symmetrical layout is penetrated by a red plane in the upper left section, a yellow plane in the center on the right, and two horizontal segments in the lower section of the canvas. These elements disrupt the regularity of the basic layout and transform the composition into an asymmetric whole presenting a circular motion proceeding upward anticlockwise from the bottom.
3 
Diagram 3c 
Diagram 3d 
Diagram 3e 
Two horizontal lines that continue uninterruptedly turn in the lower section into two horizontal segments, limited by two vertical lines (3c). An infinite space becomes a section of finite space. When the lowest segment is considered in relation to the uppermost line, this suggests a potentially square field (3d) that draws the infinite space of the two horizontal lines back toward a finite dimension.
The square field continues upward and the interaction between the opposing directions generates a horizontal area (3e) inside which a vertical yellow plane concentrates the space toward the right, thus creating the impression of a new square form (3f). The initial smaller equivalence thus gives way to a larger one of different appearance but similar nature (3f).
Diagram 3f 
Diagram 3g 
Diagram 3h 
3 
The dialectic between the contrasting directions concentrates and disintegrates the space by transforming rectilinear thrusts undergoing infinite expansion into more balanced situations of finite space (3d) that are opened up (3e) and concentrated again (3f).
The small square in the lower section (3d) is set in a vertical field and contains two horizontal segments; the new square (3f) is inside a horizontal field (3e) and contains two vertical segments (the yellow plane). Opposites generate a variety of situations. The lines again prompt a broadening of our visual horizons. Moving along the four horizontal lines toward the left, the synthesis (3f) merges with the two vertical lines and in so doing gives birth to another square proportion (3g).
The red plane highlights another area of probable equivalence between opposites (3h) that acts as a counterweight in the upper left section to the other two equivalences (3d and 3f). Visualize diagrams 3d, 3f, 3g and 3h in a single sequence. The square form now has very little of the sense of permanence and duration expressed around 1929; there is scarcely time to pause over a possible equivalence before it opens up again to the changing movement of the lines.
Diagram 1a 
Diagram 5a 
Diagram 5b 
5  Composition Blanc et Rouge B, 1936, Oil on Canvas, cm. 50,5 x 51,5 
The square located on the right of two vertical lines (Diagram 1a) is in a state of interpenetration with two vertical lines in 5a. The red plane gives the vertical measurement of a field generated by four horizontal lines contending for the space with the two verticals (Diagram 5c). Moving upward along the two vertical lines the square field (5b) merges with the four horizontal lines. 

Diagram 5c 
Diagram 5d 
Diagram 5e 
Through this interaction the square now assumes horizontal proportions (Diagram 5c  A) that are accentuated (B and C) before regaining vertical development (E) and open up again to an horizontal prevalence (F). The initial square form (Diagram 5b) displays a variety of possible relations between the opposites (Diagram 5c): planes of different shapes and sizes where everything appears in a state of becoming. Unity manifests itself as a multiplicity.
The red plane again draws attention to the left and highlights a new and larger square form (Diagram 5d).
Read upward from the bottom, the smaller square (Diagram 5b) seems to turn into the larger one (Diagram 5d), as though the two forms were successive moments in the transition of the same entity from a state of comparative stability and certainty (5b) to a dynamic condition of less stability (5d).
Under the pressure of color, the homogeneous field of the smaller square opens up and divides into a variable set of parts, a composite unit marked by the alternating predominance of one direction or the other (5c). This is resolved in a unitary synthesis (the large composite square  5d) that then opens up again to an infinite space and is lost (Diagram 5e). A geometry of becoming.
A development similar to the one observed in 5 can be seen in 6, where a variable ensemble of white forms can be read as drawing toward and away from equivalence. The horizontal lines expand the white vertical line formed between the two black lines running close together so that the white vertical line expands to assume the variable proportions of planes. The vertical yellow plane and the horizontal blue plane / line accentuate the expansive motion of the central area toward the sides increasing the asymmetry of the composition. 

6  Composition en Jaune, Bleu et Blanc I, 1937, Oil on Canvas, cm. 55,2 x 57,1 



2 

Layout N. III 
Diagram 2a 
Diagram 9a 
9  Composition en Blanc, Noir et Rouge, 1936, Oil on Canvas, cm. 102 x 104 
The tendency to open up, divide and dynamize the equivalence of opposites takes shape in a new work (9) where a trace of the N. III layout can still be seen.
The lines work in fact to divide the space of the canvas into four large areas of different proportions. Only one of these, underscored by a red plane, is closed on four sides and approaches the proportions of a square (diagram 9a). This square is larger than what is normally seen in the N. III layout.
While the square opens up to a vertical segment in 2, here it increases in size and opens up to three horizontal segments. The central segment is wholly included in the square form while the other two extend outside toward the right. A black accent in the upper left section counterbalances the weight of the segments and the red plane.
1  1932 
2  1934 
3  1936 
9  1936 
In a nutshell, we see a definite square form (1) that opens up to the predominance of the two directions (2) and then accommodates a vertical segment (3) and three horizontal segments (9) that divide its inner field and make it less stable.
10 
Diagram 10a 
Diagram 10b 
Diagram 10c 
9 was produced in 1936 and 10 in 1938, implemented with some color accents in 1942. Comparison of the two canvases reveals that the square area of 9 continues upward in 10 (Diagrams 10a, b, c). The large square of 9 thus becomes a dynamic vertical sequence in 10 where the vertical field is marked by horizontal segments that generate a series of rectangles, one of which is red. By combining these rectangles, we can glimpse square forms taking shape, merging with red and then dissolving toward the top.
11  Composition N. 1 with Red, 193839, Oil on Canvas, cm. 102,3 x 105,2 
Diagram 11a 
Diagram 11b 
Diagram 11c 
In 1938 Mondrian starts working on a a new canvas (11) which presents an analogous development to 10 with a vertical field marked out by horizontal rectangles.
With respect to the layout of 10, the vertical field made up of horizontal rectangles is here shifted to the left. Here too, the dynamic progression of two or three rectangles suggests probable equivalences of the opposing directions, that is to say, square proportions.
The marked presence of vertical lines on the right prompts a vertical reading of the horizontal sections inside the vertical field.
On observing these sections, we note that their vertical component gradually decreases little by little as we move up from the bottom toward the horizontal line running through the middle of the composition, the only uninterrupted horizontal line present in this work. The other horizontals are in fact three segments set between the vertical lines and two in the lower and upper part that continue outside to the right and left respectively.
Reading from the bottom toward the center of the canvas, we thus see a decrease in the vertical component of each horizontal section.
The vertical/horizontal space becomes almost entirely horizontal (Diagram 11a). During this process it is possible to intuit a square form (Diagram 11b).
The horizontal rectangles contract in the center to assume the proportions of a very narrow white plane (Diagram 11a) that has practically the same thickness as the black segment and the line defining it. The narrow plane has in fact the appearance of a white linear segment. The planes underneath become a linear segment. Planes and lines (finite space and infinite space) and black and white are equivalent in this area.
While the space becomes almost exclusively horizontal proceeding from the bottom edge toward the center, the vertical component shows an increase as we move from the center towards the upper part of the canvas.
It is no coincidence that we see an equivalence of opposite values generated in the center of the canvas. Six years earlier Lozenge with Four Yellow Lines shows an increase in the thickness of the lines seemed to suggest their evolution toward potential planes while, in terms of color, yellow was used as an intermediate value between black and white.
Observe the contrast between the only horizontal line and the black segment beneath it. The latter appears slightly thicker as though the black horizontal line became the segment for an instant and the loss of extension were transformed into an increase in thickness. The concomitance of the line and the segment produces a space simultaneously undergoing expansion and concentration. A measured red accent draws the eye toward the lower section and works together with the vertical lines on the right to reopen the space gradually accumulated toward the center. We are thus once again immersed in a vertical movement that gradually tends to become horizontal before reverting to vertical expansion. The red counterbalances and reopens the center, where black and white attain dynamic equivalence for an instant.
A further example of composition we can classify under the above mentioned 2nd Chart is Trafalgar Square. It should be borne in mind on examining that the composition was drafted in 1939 and the small accents of color present in the lower and right sections were added in 194243. The additions strike me as no improvement and indeed as spurious interference with the initial composition, which follows the same layout as 11 with a vertical development of horizontal sections which suggest an open and dynamic square form. 

Trafalgar Square, 193943, Oil on Canvas, cm. 120 x 145,2 
Diagram a 
Diagram b 
Diagram c 
A couple of words about the titles Mondrian gave to some of his paintings such as Place de la Concorde, Trafalgar Square, Broadway Boogie Woogie. These refer to the towns where the artist lived and worked: Paris, London and New York City. Especially for Broadway Boogie Woogie the titles have, however, given rise to no small number of misunderstandings by suggesting superficial parallels with the outward appearance of the city . As if Mondrian would work a whole life to finally represent the streets of New York City and the lights of Broadway. I will return on this when analyzing the painting.
The basic meaning of the process so far examined can be synthetically visualized here.
* * * * *
A group of paintings produced between 1935 and 1938 present a common characteristic: A large square form generated by the relationship between the bottom edge of the canvas and one or more horizontal lines. I have grouped some of these compositions under Chart N. 3. The square form in these new canvases is no longer defined by just two horizontal lines, one in the upper section and one in the lower, as in the N. II layout, but is instead generated between one or more horizontal lines in the upper section and the bottom edge of the canvas (Opposition Lignes Rouges et Jaune). While the square form was left open on one or two sides in the N. II layout, it opens up still further here at the bottom and now coincides with three of the four sides of the canvas. 

Composition with Yellow and Red 1927 (Layout N II) 
Composition 1 with Red, 1931 
Opposition Lignes Rouges et Jaune, 1937 

12  Composition B with Red, 1935, Oil on Canvas, cm. 63,2 x 80 
Diagram 12a 
Diagram 12b 
Diagram 12c 
12 presents a variety of relations between horizontals and verticals with a red plane that is almost square in its proportions (with slightly greater horizontal development).
Below we see a white area that instead displays slightly greater vertical development (Diagram 12a). Each has what the other lacks in order to attain the equivalence that is finally achieved in the plane in the lower left section (Diagram 12b), which is, however, left open to the left and to the bottom.
In a larger area which is almost a square (Diagram 12c) we see a multiplicity of different planes. The space shows here fluid development.
The intersecting of three horizontal and three vertical lines in Composition en Blanc, Rouge et Bleu generates areas of different sizes and proportions. 

Diagram 15a 
Diagram 15b 
Diagram 15c 
Diagram 15d 


15  Composition en Blanc, Rouge et Bleu, 1936, Oil on Canvas, cm. 80,3 x 98,5 
As we follow the double vertical line in the center, the more or less square area (Diagram 15a) becomes a definite square (Diagram 15b).
This vertical shift is accompanied simultaneously by horizontal expansion with the two colored surfaces at either end (Diagram 15c). The sum of the two colored areas visually corresponds to the white square form, being just slightly lower. The white synthesis appears to be divided by color, which spreads beyond the finite field of the canvas, especially to the right.
Visualize uninterruptedly the horizontal rectangle (Diagram 15a) that moves vertically but has scarcely time to become a square (Diagram 15b) before splitting in two under the effect of a dynamic horizontal field (Diagram c). The synthesis opens up to multiplicity (color) while maintaining its unity at the same time (the white square field).
The uppermost horizontal line and the bottom edge of the painting together generate a large square area (Diagram 15d).
Opposites (horizontals and verticals / white and black) alternate creating a variety of sizes and proportions which tend to a synthesis (Diagram 15b), open to variety (the colored vertical rectangles (diagram 15c) and then reach a new synthesis with a larger square proportion (Diagram 15d). Compared with the uniformed white unity (Diagram 15b) the unity shown in diagram 15d consists of a variety of sizes, proportions and colors. Another way to open up unity to multiplicity.
Diagram 16a 
Diagram 16b 
Diagram 16c 



16  Opposition de Lignes, de Rouge et Jaune, 1937, Oil on Canvas, cm. 33,5 x 43,5 
We see here four vertical lines two of which appear to mark out a white vertical line.
We see three horizontal lines with yellow used to pick out the one in the middle, which acts with the bottom edge of the canvas to generate a square form oscillating between a horizontal rectangle (Diagram 16b) and a vertical rectangle (Diagram 16c). Another way to express a dynamic and variable equivalence of opposites.
* * * * *
Three compositions (1, 2, 3) seem to mark a radical departure from everything produced by Mondrian until then.
1  Composition Blanc et Bleu, 193436, 
2  Composition with Red, Yellow and Blue, 193542, 
3  Composition with Blue, Red and Yellow, 193542, Oil on Canvas 
I tend to see these canvases in relation to he vertical field seen in 10 and 11.
As JaffĂ© points out, the height of these three canvases is twice their width. In other words, the proportions of each canvas are equivalent to two squares placed one above the other. While the square form in Composition A with Double Line and Yellow shares three of its sides with those of the canvas, for example, all the space in these three works is generated out of the shifting of a vertically duplicated square field, involving the four sides of the canvas. It is almost as though the proportions of the canvas itself were brought into being with the movement of this invisible dynamic square.
* * * * *
We shall now examine some works pertaining to what I have called Chart N. 4. In 17 seven vertical lines meet one horizontal line and five horizontal segments. Three vertical lines run very close to one another on the right and the white areas formed between them are rectilinear planes; some of them seem intent on turning into white segments. This canvas again displays a vertical field that proceeds from the bottom through the central area of the composition to the top (diagram 17a). A horizontal field of analogous proportions can be seen in the upper area of the composition (Diagram 17b). The intersection of the two opposite fields generate an area close to a square (Diagram 17c). A small blue plane concentrates the space in the lower right section. On the one hand, it attracts the almost square (Diagram 17c), which thus becomes a vertical rectangle (Diagram 17d) of analogous proportions to the blue plane. On the other, it draws attention to a larger form which attains for an instant an equivalence of opposites (Diagram 17e). 

17  Composition de Lignes et Couleur III, 1937, Oil on Canvas, cm. 77 x 80 
Diagram 17a 
Diagram 17b 
Diagram 17c 
Diagram 17d 
Diagram 17e 
The central approxiimate square (Diagram 17c) shows a slight horizontal expansion; the blue plane expands vertically while in the large square (Diagram 17e) the opposites reach equivalence. We are, however, far from the steady large square of the 1920's.
In the meantime, the "white vertical segments" win new space on the right until they regain the proportions of vertical planes that extend from the bottom to the top of the canvas reestablishing the vertical flow of space initiated with the vertical field seen in diagram 17a.
The space is thus opened up again to new measurements and proportions of a variable nature that attain equivalence every so often before overbalancing in one direction or the other.
Diagram 18a 
Diagram 18b 
Diagram 18c 

18  Composition of Lines wit Red (unfinished), 1937, Charcoal and Oil On Canvas, cm. 68,5 x 73 


Along the upper edge of this unfinished canvas we see a red accent of proportions tending towards a horizontal line highlighting an underlying slightly horizontal field which, attracted to the right by vertical lines and downwards by horizontal lines and segments, seems to want to reach the small red area of almost square proportions but slightly more developed vertically. Everything in this composition appears contended between motions of expansion (horizontal and vertical lines and segments) and contrary reactions towards concentration (the small red area, and two small white areas close to it).
A vertical prevalence (Diagram 18a) is succeeded by a horizontal prevalence (Diagram 18b) while an area that overlaps the two shows an almost equivalence of the opposite directions (Diagram 18c).
We again see areas of space moving from the predominance of one direction or the other to relationships tending toward equivalence which lasts just for a moment.
1 
2  19  Lozenge with Eight Lines and Red, 1938, Oil on Canvas, cm. 100 x 100  Diagonal: cm. 140 
Compared with the lozenge compositions Mondrian painted in 1930 (1) and 1933 (2) the one he completed in 1938 (19) shows an increased number of lines.
Eight different lines which, as in the previous lozenge compositions, have different thickness suggest a dynamic, slightly more horizontal square field which expands toward the left while a red accent reestablish the space toward the right. The interspace between the three horizontal lines at the bottom has the proportions of horizontal white lines which become a vertical white plane defined by the two vertical lines on the right and a less vertical plane between the two vertical lines on the left.
21  New York, 1941 / Boogie Woogie, 194142, Oil on Canvas, cm. 92 x 95,2 
Diagram 21a 
Diagram 21b 
Diagram 21c 
While the composition of 21 again develops a large square area in the central area, the lines are no longer only black. Biographical information indicates that the painting was initially exhibited at a show in February 1941, at which time the lines were all black. The artist would then have added the red lines  or perhaps, more probably, painted some of the black lines red  during the autumn of the same year.
The pattern formed by the black lines appears symmetrical and presents a large area in which the horizontal predominates (Diagram 21a). This tends to assume equivalent proportions if seen in relation to a black segment below (Diagram 21b). The red lines bring into play a slightly vertical area (Diagram 21c) that become a horizontal rectangular area (Diagram 21d) which then gradually (Diagram 21e) comes to display a new equivalence if seen in relation to the black line (Diagram 21f).
Diagram 21d 
Diagram 21e 
Diagram 21f 
Diagram 21g 
Diagram 21h 
The relationship between two black lines and two red lines generates an authentic large square (Diagram 21g).
A vertical form and a horizontal form are to be seen in the lower left section (Diagram 21h). A synthesis of these two situations can be seen in the upper left section.
Observation of this painting reveals probable equivalences in which one direction or the other shows a slight predominance without either coming to prevail completely and establishing a permanent condition. Everything reverts to the construction and deconstruction of unitary syntheses of the opposing directions, which are simultaneously syntheses of two colors in this case. The accents of color that the artist must have added in 1942 (above all the small planes in the lower section) do not alter the composition significantly. They add "verticality" in an area that would otherwise be dominated by horizontals but serve above all to enrich the composition with color. Traveling along the lines, the space opens up and then concentrates in the form of more stable relations that are then challenged again. Here too, everything changes while something "between the lines" evokes a sense of greater equilibrium.
* * * * *
1 
2 
3 
4 
While the square form opens up and interpenetrates with the lines in the compositions examined here, other works of same period (1, 2, 3, 4) again present a wholly closed and very visible square form as a homogeneous field of white and sometimes of color. With respect to the classic N. III layout, however, there is an increase in the number of lines, above all the horizontals, and the space appears agitated.
see Neoplasticism Part 3 o1940  1944