My Drawings and Paintings and a System for Their Classification

Leonardo

My Drawings and Paintings and a System for Their ClassificationAuthor(s): Paul RéSource: Leonardo, Vol. 13, No. 2 (Spring, 1980), pp. 94-100Published by: The MIT PressStable URL: http://www.jstor.org/stable/1577977 .

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Leonardo, Vol. 13, pp. 94-100. Pergamon Press 1980. Printed in Great Britain

MY DRAWINGS AND PAINTINGS AND A SYSTEM FOR THEIR CLASSIFICATION

Paul R6* Abstract- The author presents examples of his drawings and paintings, each based on a basic shape that is derivedfrom one or more closed curves. During the course of preparing three series of works, he chose a classification system wherein each work is designated by a code consisting of four numbers: the number of closed curves employed in constructing the basic shape of a work and three numbersfor line intersections of the types V, Tand Xfound in the shape. The classification system is of interest to him, because it provides a basisfor establishing a kind of order among his works. It also serves as an aid in pointing to shapes that he should consider for use in future works.

I. INTRODUCTION

I shall discuss here 67 of my drawings and paintings, each based on a basic shape that is derived from one or more closed curves [1]. A closed curve is one that has no end points, for example an ellipse or a figure eight. It can consist of one or more loops; a figure eight, for example, consists of two loops.

The basic shapes shown in 46 of the works do not connect to a surrounding boundary. Hence, I refer to such shapes as islands and to the group of which the works are members as the closed-curve group (Fig. 1). I have also done 21 works that contain one Qr more lines that intersect the boundary (open- curve group) (Fig. 2). Some of the shapes in both groups have an organic character. When I began making these two series, I had no preconceived idea of a specific scheme into which the works could be classified. But, after I had done about two-thirds of the works, I chose a classification system that I describe in Part III.

The shapes (Fig. 1, top) in the works in pencil on paper are smoothly shaded to give them a sculptural quality with no flat surfaces. The texture of the shading on the medium-surface paper produces a highly luminous appearance. In their frames the drawings are surrounded by a double mat; the inner one is a medium gray mat, and the outer is white. This provides a 'quiet' setting for viewing each drawing. The inner contour of the mats varies; it may be a rectangle, circle, oval or a rounded arch. Shown in Fig. 3 is the drawing 'II-5: Dolphin' with its inner and outer mats.

In the paintings (acrylic paint on Masonite) I employ islands (Fig. 1, bottom) that are executed in two or three colors. The background is done in white. It is like a 'white ocean' surface covered with tiny wavelets. The texture of the islands of color is

*Painter, 10533 Sierra Bonita Ave, NE, Albuquerque, NM 87111, U.S.A. (Received 15 Jan, 1979)

suggestive of iron filings in a magnetic field, and this texture gives the shapes a sculptural quality as in the case of the drawings. Reproduced in Fig. 4 (cf. color plate) is the two-color painting 'III-4: Madonna'.

II. CONSTRUCTION OF THE BASIC SHAPES

Both 'II-5: Dolphin' (Fig. 3) and 'III-4: Mad- onna' (Fig. 4, cf. color plate) are works whose basic shapes are members of the closed-curve group. The construction of the basic shape of each work is indicated in Fig. 5. In each case one continuous line was first drawn to produce one closed curve. In 'Dolphin', part of the curve was later deleted (dashed line) leaving two loops. In 'Madonna' two line segments were deleted.

The shapes of the closed-curved group that were employed are represented in Fig. 1, except for the first three of the group, which are comparatively complex. (However, the identification number for each of the three shapes is included in Table I, discussed in Part III.) Beneath each shape in Figs. 1 and 2 is the identification number I have given to the corresponding work. Roman numerals II and IV refer to two series of drawings and Roman numeral III refers to a series of paintings. Arabic numerals refer to the chronological order of works within a series. Thus, IV-20 is the 20th work in the drawing series IV. In three cases (see Fig. 1, top: IV-1 (III-19), IV-14 (III-23) and IV-22 (III-7)), both a drawing and a painting contain the same basic shape. However, the soft silvery tones of the pencil drawings and the bold colors of the paintings produce very different responses in viewers. When the drawing and the painting based on the same shape are viewed together, the distinct visual quality of each is striking.

A whimsical aspect was involved in devising the title for works III-19 and IV-1. When viewing the basic shape employed for them, I noticed that it could be seen as containing an intertwined u

94



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Table I. Closed-curve basic shapes in author's works (chronological listing). (Left) Identification number and title; (Right) Classification designation.

Dolphins

Penguins

Snake

11-5: Dolphin

II-7: Bean

III-1: Open Book

III-3: Blue and Green

111-4: Madonna

III-5: Triple Loop

11-6: Banana

III-7: Double Eight

III-8: Blue and Orange

III-9: Front and Back

III-10: Ring with Arch

III-11: Saddle

II3-12: Obil

III-13: Star

III-14: Blossom

III-15: Folded Star

III-16: Amber

III-17: Alpha

1I-18: Bag (Autumn)

III-19: Use

(3,2,16,0) III-20: Sphere (Spring)

(4,0,12,0) III-21: 80

(1,0,8,0) III-22: 88

(1,0,2,0)

(1,0,0,0)

(2,0,0,0)

(2,0,6,0)

(1,0,4,1)

(1,0,2,1)

(2,0,2,Z)

(2,0,4,2)

(2,0,4,2)

(3,0,8,2)

(2,0,8,1)

(1,0,6,0)

(1,0,4,2)

(1,0,8,0)

(1,0,6,1)

(1,0,6,0)

(1,0,4,1)

(1,0,4,0)

(1,0,2,2)

(1,0,4,1)

(without the foot), an s (reversed) and a script e; and so I chose the title 'Use'!

Figure 2 shows the 20 basic shapes of the open- curve drawings. (Because of its complexity, I omitted one shape, but its identification number is included in Table II, discussed in Part III.) Each basic shape in this series of drawings consists of a circular, oval or rectangular boundary enclosing one or more lines. (The boundary is provided by the inner contour of the inner mat.) There are one, two, three or four enclosed lines that intersect with the boundary. Portions of curved lines were omitted in the construction of some of the open-curve basic shapes, omissions of the type found in some closed- curve shapes (Fig. 5). However, in the case of each open-curve basic shape there was the additional consideration of a possible construction showing the 'closing' of all open curves. I imagined lines (completely or partially outside the mat boundary) that would join open curves to form the minimum number of closed curves. Six examples of 'closing' open curves in open-curve basic shapes are shown in Fig. 6. The purpose of this construction is to permit

III-23: Eye

III-24: McUse

IV-1: Use

IV-2

IV-3

IV-4

IV-6

IV-11

IV-13

IV-14: Eye

IV-15: Flame

IV-17

IV-19

IV-20: Sun and Moon

IV-21: R

IV-22: I-ouble Eight

IV-23

IV-24

IV-28: The Auk and The Egg

IV-29: Bone

(1,0,4,1)

(2,0,4,1)

(2,0,4,0)

(1,0,4,0)

(1,0,4,1)

(1,0,4,1)

(1,0,4,0)

(1,0,0,2)

(1,0,2,1)

(1,0,2,1)

(1,2,0,0)

(1,0,2,2)

(1,0,4,0)

(1,4,0,0o) (1,2,0,0)

(1,12,0,0)

(1,4,2,0)

(1,1,2,0)

(2,0,4,2)

(1,4,0,0)

(1,4,2,0)

(1,2,0,1)

(1,2,0,0)

a count of the total number of curves for use in my classification system.

III. THE CLASSIFICATION SYSTEM

For the classification system I chose to indicate for each basic shape the minimum number of closed curves (given by I1) from which each is derived (including open curves that are 'closed') and the number of each of three types of intersections (given by 12, I3 and 14). 14 refers to the number of X- intersections formed by one continuous line crossing another. The angle between two branches is larger than 0? and smaller than 180? (Fig. 7). 13 refers to the number of T-intersections formed by removing one branch from a crossing of two continuous lines. Here one angle is 180? and each of the other two is larger than 0? and smaller than 180?. 12 refers to the number of V-intersections (cusps) formed by removing the loop made by one continuous line crossing itself. One may consider the formation of a V-intersection to be the limiting case in which a loop has shrunk to a point. The smaller angle of a V-

96



My Drawings and Paintings

-5 : DOLPHln m-4: maoornnR

Fig. 5. Basic shapes of the works shown in Fig. 3 and in Fig. 4 (cf. color plate).

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Fig. 6. Six examples of 'closing' open curves in open-curve basic shapes.

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O<O( < 180' 0?< < 180o o'< < IsO,

V- InTERSECTIOn T- IrTERRSECTIOn X-InTERSECTIOn

Fig. 7. Types of intersections considered in the classification of basic shapes.

intersection is more than 0? and less than 180?. The counting of the minimum number Ii of

closed curves is facilitated by making a sketch of the basic shape and indicating by dashed lines the omitted segments of the closed curves that were combined in the construction of the shape. In the case of open-curve shapes, open curves are closed for counting, but the boundary itself is not included in the count of closed curves or of X-, T- and V- intersections. This is consistent with the case of closed-curve basic shapes, where neither the boundary of drawings nor the outside boundary of

paintings is included in the count of closed curves. In the system, a work is classified fully as follows:

W (Ii, 12, I3, 14), where W represents the identification number of the work. For example, the closed-curve drawing '11-5: Dolphin' (Fig. 3) is classified as 11-5 (1, 0, 2, 0), because there are one closed curve and two T-intersections. It should be emphasized that while the number of closed curves is conveniently determined with omitted portions restored by dashed lines, the numbers of V-, T- and X-intersections are determined from the repre- sentation in solid lines (not in dashed lines). While one might think that there are three V-intersections in 'The Dolphin', they are not considered so in the system, because their tips are rounded, admittedly only slightly. A V-intersection (or cusp) is one defining a precise point, just as a point is defined by T- and X-intersections. An example of a V- intersection is contained in drawings IV-21 (1, 1, 2, 0) (Fig. 1 (top) and Figs. 8, 9). Here the V- intersection may be viewed as one resulting from the removal of two successive branches that form a loop. Drawing IV-17 (1, 2, 0, 0) (Fig. 1, top) presehts a basic shape having two V-intersections, each formed by the removal of a loop at each end.

Basic shapes having V-intersections were employed only in the drawing series II and IV. With five exceptions (two in work IV-24, two in work IV-20 and one in 11-4) there is a tonal inversion at the V-intersection. A tonal inversion is shown in Fig. 10. The left side of the sketch is dark below the boundary and light above; the shading is the reverse on the right side. But at the V-intersection point the tones on both sides of the boundary are equal. I find this visually exciting and technically challenging to execute.

Table I lists in chronological order the four- number classification designations of the closed- curve basic shapes employed in 46 works. There are two cases that require clarification. The first con- cerns the painting 'III-11: Saddle' whose basic shape designation is (1, 0, 6, 0). The 4-branch intersection at the top is clearly not an X- intersection as defined above, because the four branches do not describe the crossing of two continuous lines. If one sketches dashed lines to

Fig. 8. (A) The 'R'of the Roy Davis autograph. (B) The basic shape based on the 'R'. (See Fig. 9).

97



Paul Re

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Fig. 10. A tonal inversion at a V-intersection point.

Fig. 9. 'IV-21: R', pencil on paper, 61 x 48cm, 1977. (See Fig. 8)

replace the omitted portions of the single closed curve of basic shape III-11, one restores three continuous lines passing through the intersection. Now, by erasing the two dashed-line branches, one sees that in the basic shape there are one continuous line and two branches off to one side forming a K- intersection. A K-intersection can always be re- solved into two T-intersections by considering each of the two branches to be stems for T's that share common cross bars. Thus, counting two T's at this intersection, I find a total of six T's in the shape.

Another case of interest is basic shape III-6 (2, 0, 2, 2). Here two closed curves are present that coincide over much of their path. There are two intersections that are clearly described as T- intersections. There are, in addition, two points where two lines merge to form one line. I consider that each of these two intersections represents an exceptional degenerate case of an X-intersection in which the angle y is zero. One might consider that these two are kinds of T-intersections, but, because no branch is removed in their formation, I prefer to designate them as X-intersections.

For the earliest works in Table I, 'Dolphin', 'Penguins' and 'Snake', the shapes are comparatively complex. Then, the shapes become pro- gressively simpler until 'II-7: Bean' is reached. Further along there is again an increase in complexity. A roughly similar trend is noted in the open- curve group (Table II), from the rather complex '11-2: Triple Loop' and 'II-3: Wave' to the simpler

IV-5 and IV-10. I regard simple shapes as giving the feeling of wholeness and high strength. But, after employing the simplest shapes, I find that I must turn to choosing more complex ones. But this is not the sole factor determining the order in which I make works. Rather I select from my sketchbook a shape that seems 'right' at the time I am about to make a drawing or a painting. Quite often, it is of a very different character from that of its predecessor. I find this variety very refreshing.

While a chronological listing of basic shape designations is of interest in surveying the course of my work, a systematic tabulation of the designations themselves presents a framework wherein works may be located. I consider such a framework in the following manner: In a designation given by (I 1, 2, 3, I 4) as described above, the total number of

possible different designations in the system (that is, the total number of different locations in the framework) is given by the product of the maximum values assignable to I 1, 2, I 3 and 14. For example, if I allow a maximum number of three closed curves, and the range from zero to nine of each of V-, T- and X-intersections, then the total number of different designations is 3 x 10 x 10 x 10 or 3000. A table could be prepared for which the first column runs as follows: (1,0,0,0), (1, 1, 0,0), (1, 2,0,0),... (1,9,0, 0). And 299 other columns would be formed until all 3000 categories are tabulated. Each of my basic shapes, where I2 does not exceed 3 and where I2, 13 and 14 each do not exceed 9, can be located in the framework. Because a listing of the 67 basic shapes considered here would occupy only a small fraction of the available locations in such a framework, I find it more convenient to use an abbreviated form. This consists of a table that lists, from one column after another of the framework, only the filled designations. Such tables can be constructed easily from Tables I and II.

A number of my works have different basic

98



My Drawings and Paintings

Table II. Open-curve basic shapes in author's works (chronological listing). (Left) Identification number and title; (Right)

Classification designation.

Oeer

II-L: Knot

II-2: Tripee Loof

11-3: W<ove

11-4: Tree

11-6: Open Book

11-8: Tomato

II-9: Landscape

1-10: Grasshopper

II-l1: Plum

IV-5

IV-7

IV-8

IV-9

IV-10

IV-12

IV-16: Dictionary Piece

IV-18: Pine

IV-25

IV-26

IV-27

(1,0,2,0)

(1,0,4,0)

(1,0,6,0)

(2,0,6,0)

(2,0,1,0)

(2,0,2,0)

(1,0,2,0)

(1,0,3,0)

(1,0,3,0)

(1,0,2,0)

(1,0,2,0)

(1,0,0,2)

(1,,0,0)

(1,0,2,0)

(1,2,0,0)

(1,1,1,0)

(1,3,0,0)

(1,0,2,2)

(1,2,0,0)

shapes that have an identical classification designation, for example 'III-7 (IV-22): Double Eight' and '111-8: Blue and Orange'. Such works would be found in the same location in the framework. These works I call 'isomers'. This term is borrowed from chemistry, where it designates two or more chemical compounds that are made up of the same chemical elements and the same numbers of atoms of them (that is, having the same chemical formula) but are different structurally. I have found this particularly interesting here, and I have been prompted to make an analogy. I note that there are four branches at an X-intersection, three at a T- intersection and two at a V-intersection and that a closed curve can be considered to have one 'branch'. I let these four kinds of'intersections' be equivalent to four chemical elements and the number of times each occurs in a basic shape (as given in the classification designation) be equivalent to the number of atoms of each element in a molecule. Thus, a work possessing a basic shape is analogous to a chemical compound, and a family of works having different basic shapes of the same designation is analogous to a set of isomers: the structure variations of the basic shape 'isomers' are analogous to the chemical structure variations in a set of chemical isomers. An exhibition of different works seems to me analogous to a mixture of chemical compounds. I have found that different groupings of my pictures

may result in a gamut of viewer reactions! 'Isomers' IV-11, IV-17 and IV-29 are seen to

possess closed-curve basic shapes with two V- intersections (cusps) (Fig. 1, top); each has a distinctly different appearance. IV-11 appears to me as a highly abstracted depiction of a cavern, IV-17 of a distant mountain and IV-29 of a bone. As the basic shapes that I employ become more complex, 'isomers' tend to bear less and less resemblance to each other. I wish to end this part with a humorous note. I mentioned above how painting III-19 gained the title 'Use'. Since III-24 is 'isom- eric' to III-19 and bears some resemblance to it, I have given it the name 'McUse'.

IV. THE CLASSIFICATION SYSTEM AS A TOOL

The classification system is meaningful to me because I find it provides a kind of order among the basic shapes and among the works containing them. As I mentioned above, I came upon the idea to make a classification system after I had completed about two-thirds of the total number of drawings and paintings. The basic shapes I employed seemed to lend themselves to ordering in such a system, and I felt that in a morphological analysis approach it would lead me methodically to other shapes that I had not considered. The following is an example showing how I use the classification system as a tool: After drawings IV-3 (1, 0, 0, 2) and IV-6 (1, 0, 2, 1) were completed, I noticed in Table I that there was an unfilled location in the closed-curve se- quence at (1, 1, 2, 0). I decided to search for a shape. After a few months I found one in the 'R' of the autograph of Roy Davis written on the inside cover of his book The Path of Soul Liberation [3]. The 'R' is essentially a closed curve as shown in Fig. 8(A), but with a loop omitted, as mentioned above, and, with slight modification, it was made into a basic shape having one V-intersection (cusp) and two T- intersections (Fig. 8(B)). The work containing this basic shape (and including the inner and outer mats) is shown in Fig. 9.

It was mentioned above that in the classification system there are very many locations that are not presently assigned to basic shapes used in my paintings or drawings. But some of these locations would accommodate basic shapes that I have drawn in my sketchbook but have not yet used. Some others correspond to classification designations I have considered, but for which I have not succeeded in coming up with satisfying basic shapes.

I realize that the rules I have chosen for the classification system are not unique and that a more rigorous system might be developed on the basis of morphological analysis [4]. For viewers with an analytical attitude, this system may help them to appreciate my works. I hope that the classification system will serve as an enjoyable intellectual com- plement to the direct emotional appeal of my works. I plan to incorporate the content of this article in a book I am writing on my works.

99



100 Paul Re

REFERENCES 1. A. Newell, Paul Re. Paintings and Drawings, exhibition

catalogue (Albuquerque, New Mexico: Jonson Gallery, UNM, 1978).

2. J. M. Kennedy, A Psychology of Picture Perception (San Francisco, CA: Jossey Bass, 1974) p. 85.

3. R. Davis, The Path of Soul Liberation (Lakemount, GA: CSA Press, 1975).

4. F. Zwicky, The Morphological Method of Analysis and Construction in Studies and Essays (presented to R. Courant on his 60th birthday, 8 Jan. 1948) (New York: Interscience Publishers, 1948).



Top left: Quero, 'Flight between the Sun and the Moon', oil on canvas, 150 x 195 cm, 1978. (Fig. 4, cf. page 134.)

Top right: David Zaig. Superimposed reversed images of a photographic slide, 1976. (Fig. 2, cf. page 137) (cf. also Fig. 3 in text.)

Center: Paul Re. '111-4: Madonna', acrylic paint on Masonite, 48 x 43cm, 1975. (Collection of Helen Re, Albuquerque, NM, U.S.A.) (Photo: K. Cornyn, San Francisco, CA, U.S.A.) (Fig. 4, cf. page 94.)

Bottom left: Alan Wells. Untitled, tempera paint on poster paper, 183 x 244cm, 1977. (Fig. 3., cf. page 106.) Bottom right: Michael Krausz. 'Oracle', acrylic paint on canvas, 183 x 244cm, 1974. (Photo: F. Herrera,

Washington, DC) (Fig. 4, cf. page 143)























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My Drawings and Paintings and a System for Their Classification