A program for Victory Boogie Woogie

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Looking at Mondrians Victory Boogie-Woogie: What Do I Feel?

a painting may induce The Boogie-Woogie was a cultural move-ment of music and dance in the late 1920s, and it is characterized by its vivacity, syncopated beat and irreverent approach to melody This movement fascinated Mondrian as he considered it similar to his own work: “destruction of natural appearance; and construc-

A program for Victory Boogie Woogie

A program for Victory Boogie Woogie Citation for published version (APA): Feijs, L M G (2019) A program for Victory Boogie Woogie Journal of Mathematics and the Arts, 13(3), 261-

Broadway Boogie Woogie Victory Boogie Woogie , created in the

blocks in Broadway Boogie Woogie (1942-1943) and Victory Boogie Woogie , created in the following year, shows that rhythm is an important element in the depiction of jazz music In regard to color, Henri Matisse’s chromatic improvisations in his famous cut-out work, Jazz (1947), show the importance of color to the inimitable nature of jazz music

02/12 - e-flux

Victory Boogie Woogie (1944) and its predecessor piece, Broadway Boogie Woogie (1943), in his own book on the Dutch painter, touching non some of the most compelling aspects of the work: While the space [of Victory Boogie Woogie] is nevertheless very dynamic (not least because of the lozenge format), its dynamism is the result of a virtually

architectonics and abstraction - TTU

Victory Boogie Woogie not so final victory photograph of Mondrianʼs studio on 59th street, New York showing Victory Boogie-Woogie en point on his easel

Lijnen en primaire kleuren - Startpagina

Victory Boogie Woogie Twintig jaar geleden kwam er een beroemd schilderij in 5 Nederlandse handen Het was Victory Boogie Woogie van de Nederlandse schilder Piet Mondriaan, die leefde van 1872 tot 1944 De aankoop van dit werk voor 37 miljoen euro van een Amerikaanse eigenaar werd destijds mogelijk gemaakt door

Coppernickel Goes Mondrian

• Show images and titles of Piet Mondrian’s work, Broadway Boogie-Woogie, Victory Boogie-Woogie and Composition A Allow students time to discuss • Mondrian was inspired by rhythm and music, especially jazz Show Visual 1 • Ask students to determine if image is symmetrical or asymmetrical How many rectangles are in the top row?

[PDF] rapport de stage renault dacia maroc

[PDF] piet mondrian composition with large blue plane

[PDF] red

[PDF] black

[PDF] yellow

[PDF] rapport de stage renault casablanca

[PDF] and gray

[PDF] rapport de stage hyundai pdf

[PDF] rapport de stage graphiste original

[PDF] mondrian arbre

[PDF] rapport de stage agence de communication evenementielle

[PDF] mondrian composition en rouge jaune bleu et noir

[PDF] rapport de stage agence de communication pdf

[PDF] problématique rapport de stage agence de communication

[PDF] mondrian oeuvres célèbres

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JOURNALOFMATHEMATICSANDTHEARTS

2019,VOL.13,NO.3,261-285

https://doi.org/10.1080/17513472.2018.1555687A program for Victory Boogie Woogie

LoeM.G.Feijs

ABSTRACT

bling the originals. In earlier work published in Leonardo, a generic framework was proposed, which turned out flexible and could be adapted to generate many different Mondrian types. Until recently, there were hardly any attempts to target Mondrian"s Victory Boogie Woogie, which is more difficult than most of the earlier Mondrian types. This article describes an extension of the Leonardo approach by including Victory Boogie Woogie. This work poses different chal- lenges because of its uniqueness, its complexity and the fact that it is unfinished. In the extension, three principles for modelling and programming are used: (1) working with cells, (2) nesting, and (3) object-orientation. The program entered and won a Dutch national competition on programming Victory Boogie Woogie in 2013.

ARTICLEHISTORY

Received24February2017

Accepted24November2018

KEYWORDS

Mondrian;VictoryBoogie

Woogie;algorithmicart;

generativeart;composite pattern;DeStijl; object-oriented programming

1. Introduction

in London and nally in New York. He is famous for his abstract and non-gurative paint- ings. He was born as Piet Mondriaan in The Netherlands in 1872 and was trained as a were mostly traditional landscapes and from 1908 there was an inuence of symbolism and theosophy. From 1910 to 1920 the topics got restricted to windmills, coast lines, trees, church towers and owers. While experimenting, Mondrian made the windmills, coast lines, trees and towers more abstract, rst in a cubist tradition, later in his own unique style. Related experiments were done by other Dutch artists such as Theo Van Doesburg and Bart Van der Leck; together with other artists and designers they formed a movement and changed his name to Mondrian and in 1938 he moved to London. Between 1918 and

1940 he made many paintings of the kind for which he became famous, characterized by

in primary colours. A few typical examples are shown in Figure1.CONTACTLoeM.G.Feijsl.m.g.feijs@tue.nlDepartmentofIndustrialDesign,EindhovenUniversityof

This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License

262L. M. G. FEIJS

Figure 1.Typical works of Mondrian: Composition number 3 with colour planes (1917), Checkerboard Figure 2.Piet Mondrian, Broadway Boogie Woogie, 127cm×127cm, 1942-1943, current location

MuseumofModernArt,NewYork(publicdomain).

From 1942 onward, after Mondrian arrived in New York and when he was already in his 70s,hisworktookyetanothernewdirection:thecompositionsgotcolouredlines,new andlively,seeBroadwayBoogieWoogie(Figure 2 ). In an abstract way, Broadway Boogie Woogie and Victory Boogie Woogie (Figure3)seemtorepresentthebusy,livelyandener- getic atmosphere of New York. The last work, Victory Boogie Woogie, is fascinating and it gives rise to many questions, as it was un?nished when Mondrian died. More information on Mondrian can be found in several excellent books [3,15,23] or in the complete catalog of his work [16]. For more information on Victory Boogie Woogie we refer to the book by van Bommelet al.[4]. Mondrian, in his own writings, argued in various ways that art should always move on, searching for a pure beauty. The paintings do not depict anything from the real world. For example in 1937 he wrote a long article in Circle [20], from which we take a short quote:

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Figure 3.Piet Mondrian, Victory Boogie Woogie, 127cm×127cm, 1944, current location: Gemeente- museumTheHague(publicdomain). lifewhichwelive,butthatitistheexpressionoftruerealityandtruelife...inde?nable but realizable through the plastic. as a representation of the Manhattan street grid, it is unlikely that Mondrian would resort to such direct ?guration. This also is the opinion of H. Janssen, co-author of the book on Victory Boogie Woogie [4], as he told me in 2013. Blotkamp [3] sees Mondrian"s work as ing real-life interpretation and even eliminating options for object recognition and Gestalt There is a long tradition of synthesizing Mondrian-like compositions automatically, which was started in the 1960s by A. Michael Noll [18]. An overview is in Section6.The tions is interestingto me, as I have great appreciation for both the aesthetics of Mondrian"s work and the perseverance of Mondrian as a person. Moreover, I live in The Nether- lands, Mondrian"s ?rst country, and know how to program. Combining these interests, I undertook a ?rst curiosity-driven project in the period 1993...2003. The result was a sin- match. The main topic of the present article is a new computer program, developed in 2013 and aimed at Victory Boogie Woogie (1944), Mondrian"s last, un?nished work. This pro-

264L. M. G. FEIJS

mark of honor to both Victory Boogie Woogie and Mondrian. The program builds on the cells,seeSection2.ItiscodedinProcessing[22] instead of the now outdated Turbo Pascal and is speci?c for Victory Boogie Woogie. Processing is an open source project by Casey Reas and Benjamin Fry. The language is essentially Java but packaged in an environment that makes the language accessible and attractive for creative work. The trigger for writing the newprogram wasaCallForCodeissuedbySetupandGemeentemuseumDenHaagin information about the call for code is in Section5. Whereas the focus of this article is on for Mondrian, and a quest for elegance. The quest for elegance is motivated by my long- of theCall for Codecompetition. The process of conceiving, coding and evaluating the program described in this arti- cle began already with my previous project, and built upon many visits to museums and drian in the years 1916-1942, after his ?gurative years and stopping just before the Boogie Woogies. The ?rst step for this new work was to re-implement the program"s essentials in a modern language and test it by generating the type of compositions Mondrian made in

1917. After that, over a sequence of iterations, I modi?ed the program to generate com-

positions ?rst in the style of Broadway Boogie Woogie, and ?nally in the style of Victory

Boogie Woogie.

Sections2-4 describe the development of the program. In Section5the work is evaluated and Section6is about related work.

2. Working with cells

down decompositions of the canvas. One such idea is to take a regular grid and perturb it. This idea ?nds support in works such as Lozenge with Gray Lines (1918), Composition: Mondrian abandoned the grids. Blotkamp [3, p. 126] suggests that Mondrian responded to critique by Van Doesburg who had written that these works were without composition was only for emulating a Composition with Lines (1917). Given my goal of reproducing Mondrian"s later works, I knew that I also had to abandon regular grids (Figure4). obtained is the leftmost image in Figure5.However,thisapproachisnotconvenientto generate the typical lines which cross other lines before stopping, like the middle vertical line which stops at the lower horizontal line in the real Mondrian composition of Figure5 (right). pure bottom-up approaches based on drawing random rectangles will not work either: if

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Figure 4.Examples of Mondrian compositions based on of regular grids. Lozenge with Gray Lines,

1918 (left), Composition: Light Colour Planes with Grey Lines, 1919 (middle), Composition with Grid 9:

Figure 5.Two examples of obvious non-Mondrian compositions (left, centre) and a typical real Mon- drian,TableauI,1921(right). foreground-background Gestalt. My previous approach [7,8] was to let planes and lines compete for space on the canvas and let them align with a process somewhat resembling cell growth. Blotkamp [3, p. 232] that, pushing and pulling, attracting and repelling, succeed in keeping one another in bal- ance and in their place. It is clear that if the lines are ready, the rectangles between them could be ∅ooded with colours. But I have decided not to treat planes and lines as di←erent coloured planes: Only now I become conscious that my work in black, white and little color planes has been ...In painting, however, the lines are absorbed by the color planes; but the limitations of the planes show themselves as lines and conserve their great value. (Blotkamps translation 3 , p. 240]) This is what Mondrian wrote in May 1943, so I used the wisdom of hindsight. Already in paintings in the 1930s the di←erence between lines and planes was blurring.

266L. M. G. FEIJS

Cells grow from initial seeds and interact with their neighbours to ?nd their ?nal posi- tions. This is a generalization of the colour-?ooding of rectangles. The analogy with cell tiply and expand. For most compositions, the canvas never grows; instead the cells expand in empty space until they meet their neighbors. I have to admit that this was not exactly how Mondrian worked: in the early years he used 'doorbeelding" (see Section3); later he shifted lines experimentally after a top-down design. My choice for working with a uni- ?edcelltype uses theinsight,alsoexplainedbyBlotkamp [3], that gradually the di?erence between lines and planes would disappear. One of many examples discussed by Blotkamp lines are actually lines or planes [3, p. 229]. At the same time, working with cells is a prac- tical framework for experimentation [7,8]. The algorithm operates in a manner that does not resemble Mondrian"s way of working but is intended to produce compositions that do resemble Mondrian"s. Now the programming technicalities will be addressed. Acellisatwo-dimensional coloured rectangle with some additional numerical and Boolean properties to regulate the cell"s growth behaviour. Each cell is axis-aligned: its sides are horizontal and vertical. The cells grow from small kernels until they collide, and in this way, eventually, reach their ?nal locations and extents. The growth occurs in steps. In one step, each cell attempts to expand, backtracking if it turns out that the expansion would cause any pair of cells to overlap. Cells may grow only horizontally (for example, cells that will become horizontal lines), only vertically, or both. Some cells grow until they reach the border of the can- vas, others maintain a small distance∩. Some cells grow from time zero onwards, others begin only when a step counter reaches a particular value, itsactivationage. Ideally, as much knowledge about Mondrian as possible is coded as cell instance variables and meth- cells. Initially, the locations of the cells are chosen uniformly at random within the canvas, the probability is high near the edges of the canvas and low in the centre [7]. Taylor [27] argues that Mondrian"s lines are not random and ?nds a higher prevalence of lines close to the edge of the canvas. Every time the program makes its random choices, a di?erent composition appears. Some of these results are 'better" than others, and assessing them is part of the process of continuous adaptation. The advantage of this model and the pro- the code can jump to Section3. We ?rst explain how to produce two types of compositions, called 1917 Composition and 1938 Composition. The program has one important class called Cell. As explained by Bruce, Classes are extensible templates for creating objects, providing initial values for instance vari- ables and the bodies for methods. All objects generated from the same class share the same methods, but contain separate copies of the instance variables. New objects can be created from a class by applying thenewoperator to the name of the class. [5, p. 18]

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Figure 6.Possible congurations of cells.A

will denoteAtogether with the extended area around it.

InthiscongurationAoverlapswithBandC,A

overlapswithB,C,DandE,whereasA F=. classC

1intxMin,xMax,yMin,yMax

2colourclr

3booleanhorfalse

4booleanvertfalse

5booleanstopsfalse

6?oatratioŠ1

7int?0

8intage0

9intactivation0

10intmidlifetriggermaxint

The cell has minimal and maximalxandycoordinates. Each cell has a colour and three booleans that regulate growth: ifhoris true, the cell is allowed to grow horizontally, if vertis true, it is allowed to grow vertically. Ifstopsis true, it will stop when bumping into another cell, otherwise it will cross-over or cross through (in the terminology of Andrze- jewskiet al.[1]alinethatstopsisanon-spanning line). Next,ratiois used to force the cell applies. Then?denesabandaroundthecell(seeFigure6). Finallyage,activationand midlifetriggercontrol the precise timing of the growth, which is important when several types of cells compete. The methods of C analyse the state of the cell, mostly in relation to its neighbours. ?. The most important methods of C are: €O () provides a collision detection mechanism that also detectsalmost- co llisions. Letaandbbe Cells, with associated rectanglesAandB.Then a .O b ?)istrueifandonlyifA intersectsB.Weextendthisdenitionto any cell in the collection intersectsA

R() determines whether a cell is within some tolerance of its desired aspectratio. Small cells are exempt from this test. The code listing is given below.

268L. M. G. FEIJS

case is included; the vertical case is similar and can be easily added by the reader. () simply draws the cell"s rectangle using its designated ?ll colour.

T() is an empty method. Some cells perform special actions upon reaching theirmidlife,buttheprecisenatureofthisactionwillvarywiththecell"stype.Subclassesaretherefore allowed to override T.

We give code listings for

R() and G().

C. R()

1dx?max(0.01,xMaxxMin)

2dy?yMaxyMin

3returnratio<0

4or(dx<10anddy<10)

5or(0.8×ratio)edy/dxe(1.2×ratio)

C. others)

1ifage>activation

2then ifhor

3thenxMin?xMin∅

4fails?thislhcanvas

5or not

R()

6or notO

(others,∩) 7 ifstopsan d fails

8thenxMin?xMin+∅

9xMax?xMax+∅

10fails?thislhcanvas

11or not

R()

12or notO

(others,∩)

13ifstopsandfails

14thenxMax?xMax∅

15ifvert

16thenyMin?yMin∅

17//Continue as in the horizontal case

18ifage++==midlifetrigger

19then()

are the base class which can be extended to have speci?c ?eld values, additional ?elds, and additional methods. The ?rst example of such an extension is the class S. It is meant for generating suchasthe?rstpaintingofFigure1. S is based on speci?c colours and speci?c values forhor,vert,stops,ratioand∩. called , and . The class S extends C.

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Figure 7.Intermediate composition, the snapshot being taken just before the point where all cells wouldexecute

over, there are nine others which are also not large enough and which are to be pruned too (indicated

by arrows). classS(C)

1colourcolour(255,175,175)

2colourcolour(255,175,75)

3colourcolour(170,170,255)

S()

1type"Square"

2setxy(positiononcanvas,uniform)

3clr R(,,)

4hortrue

5verttrue

6stopstrue

7ratio1.0

8?5

9midlifetrigger20

1returnxMaxŠxMin<20

2andyMaxŠyMin<20

S.() 1if()

2thencells.

(this)

Thepurposeofthe()method,calledatage

midlifetrigger,istoeliminatecells that are too small. This is shown in Figure7, an intermediate phase of a composition; the snapshot is taken when all cells have agemidlifetriggerŠ1. Four cells in Figure7will never grow beyond their original 3×3 pixel size (they were conceived in a O position). Another nine cells managed to develop somewhat,

270L. M. G. FEIJS

Figure 8.GeneratedcompositionemulatingthevisualstyleofMondrian"scompositionsfromca.1917. but do not get large enough. They are considered tiny if they are less than 20 pixels in both which has come available, as can be seen by comparing to the ∩nal Figure8. The top-level program is given next. It initializes a globalcellsvariable. In Processing about 60 frames per second. 1917

1size(297,210)

3foricells

1foricells

2docells[i].(cells)

3cells[i].?()

This completes the discussion of the generator for Figure8, which could also generate an in∩nity of similar compositions. Note that the generic cell engine is coded in the class It would be interesting to control the spatial distribution of colours, perhaps avoiding the e←ect in Figure8where the blues dominate the left and right sides of the composition, the growth algorithm has done its work. If the balance could be checked algorithmically, one could search for a minimal colour-change intervention to restore balance. The work of Locheret al.[17] would be a good starting point, I leave it as a possibility for future research. The same genericcell enginecan also beused for other composition types. The compo-

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Figure 9.GeneratedcompositionemulatingthevisualstyleofMondrian"scompositionsfromca.1938. the horizontal lines will stop upon collision (stopsrandom(3)<2). In essence, this is how 15 di←erent Mondrian composition types were coded in the project of 1993...2003 [

7,8]. The above program fragments are taken from a partial 2013

remake, simpli∩ed and polished for readability. This 2013 remake was taken as a basis for undertaking the challenge to program Victory Boogie Woogie.

3. Interpreting Victory Boogie Woogie

Before discussing the modelling and the coding, it is necessary to come to an interpre- tation of Victory Boogie Woogie. Rather than looking only at the features of Victory Boogie Woogie (for example lack of obvious overall structure, greater overall complex- ity, and the presence of many small rectangles), I try to understand the work as a next logical step in Mondrians development. Blotkamp explains Mondrians development in his bookDestruction as art[3]. The termdestructionshould not be taken too literally: it It refers instead of Mondrians desire to remove the ∩gurative interpretation of the work. We should explain one hard-to-translate Dutch term ∩rst:Doorbeeldingis the original Dutch term used by artists of the De Stijl movement for their speci∩c process of continued tion, beyond which there is really no tree, church, windmill, or coastline to be seen; after circa 1920, the goal was to limit the recognition of objects such as individual rectangles or lines. In short, Mondrian did not want any Gestalt.GestaltisaGermanword,essentialin

272L. M. G. FEIJS

Figure 10.Mini-canvasesandsmallrhythmic/intersectionrectanglesinBroadwayBoogieWoogie. and background is also a Gestalt e←ect. The false observation that coloured patches are ∅oating in front of a background is avoided by Mondrians introduction of black lines. The angles. The object-nature of lines is weakened by ambiguities such as doubled lines. The di←erence between lines and rectangles disappears at times almost entirely by their uni∩- cation into coloured lines in the late 1930s. The invention of the Boogie Woogies involves one∩naluni∩cationstep,inwhichthedi←erencebetweenthecanvasand theobjects on the canvases appearing inside (see Figure10). canvas, a small painting in the great work. Therefore I adopt nesting as a key theme in this project. In object-oriented programming, this nesting corresponds to the well-known represent part-whole hierarchies. Composite lets clients treat individual objects and com- positions of objects uniformly [11]. It can also be viewed as a limited type of recursion in the data structures, elegantly re∅ected by the way functions call themselves to process the objects.

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Figure 11.TwinandtripletverticalsinBroadwayBoogieWoogie. without the pieces of tape [4, Chapter 6], which I studied before the present project. And there is information about the process of Mondrian at work on Victory Boogie Woogie: we know that he experimented and changed the painting over and over again. There is also inspiration to be found in earlier work by Mondrian. The ∩rst task was a grid that is Broadway-inspired. It is clear that Mondrian explored certain innovations in Broadway Boogie Woogie which he re-used later in Victory Boogie Woogie. This is Yellow Lines(1933), but the rhythmic rectangles are new indeed. Also, the invention of the mini-canvases is new; they are positioned as bridges connecting the yellow lines. Another interesting detail is given by the small rectangles, each of which is positioned on the intersection of a horizontal and a vertical line. In Victory Boogie Woogie there are similar rectangles, but the situation is not very clear, and therefore it was decided to stay closer to the Broadway inspiration. Even if a vertical crosses a horizontal and is stopped there, then there is an intersection between the hypothetically extended vertical line and the horizontal line. Sometimes there are stray intersection rectangles at quite a distance. rectangles and intersection rectangles. Three of the mini-canvases and some of the small rhythmic/intersection rectangles are highlighted.quotesdbs_dbs35.pdfusesText_40

[PDF] A program for Victory Boogie Woogie