Leonardo, Vol. 13, Pergamon Press 1980. Printed in Great Britain

Roland Baladi 

Abstract-The Great Pyramid of cheops near Cairo was constructed so that on its south face a slight dihedral angle would cause theformation ofa shadow at sunset at the spring equinox. The author, an Egyptian by birth, has employedtheprinciple of the periodic production ofshadows by the Sun as the Earth rotates around the Sun and around its axis in his Solar Bas-Reliefs. The objects consist of a surface in relief made of many elements, each capable of casting an individual shadow. The elements are designed to produce different ratios ofsunlit to shaded areas and, in an ensemble, have been employed to produce figurative images.

The author describes in detail Solar Bas-Reliefs consisting of two types of shadow-casting elements. He calls attention to his first full-scale installation (1978) at Les Halles in Paris, which displays the image of a lion cub between noon and 14.00 hours on sunny days.

I.In ancient Egypt one of the tasks of the priests was to predict the time at which the annual flooding of the Nile would occur. They noted (before the time of Cheops, about 5,000 years ago) that the spring equinox occurred when the Sun rose in line with a star in the constellation Taurus, and they assumed that precisely one year had passed when in the following spring the Sun rose again in une with the same star. But this method for the prediction of the passage of one year is not precise; after about 700 years the prediction is in error by about 10 days. The reason is that the precession of the Earth's axis causes the north celestial pole to drift slowly with respect to the starry heavens along a small circle of 470 aperture. One revolution around the circle is completed in about 26,000 years [1].

By the time of Cheops, however, it was known to the priests that the day of arrival of the spring equinox could be >11dicated precisely by the location on the horizon at which the Sun rises or sets. The builders of the Great Pyramid of Cheops (Khufu) applied this knowledge to its orientation and con-struction. One side of the pyramid was made to face the point on the horizon where the Sun rises at the time of the spring equinox. The south face of the pyramid was constructed so that it consists of two planes that intersect at a small dihedral angle (1/30) along a line passing from the apex to the midpoint of the base of the triangular face (2]. The beginning of spring is indicated on the day when the rising and setting Sun casts a shadow for a period of 15 sec on the south face (Fig. 1).

The orientation of the cathedral at Chartres, France, was chosen in the l2th century so that on the anniversary of the birth on 8 September of the Virgin Mary, to whom it was dedicated, it faces the point on the horizon at which the Sun sets. Also, a beam of sunlight passing through a stained glass window on Christmas Day produces a luminous spot on the main altar [3]. The Arch of Triumph at

the Place de l'Etoile in Paris was erected in 1808 50 that on the anniversary of Napoleon 's victory at the battle of Austerlitz on ~ December 1805 the axis of the arch intersects the point on the horizon at which the Sun rises. The above examples are only a few of many others that can be cited where the orientation of structures can be linked to a point of sunrise or of sunset.

In kinetic art, P. K. Hoenich constructed in Israel an installation called a Robot-Picture in which sunlight reflected from polished surfaces prided images on a wall and these images changed in appearance with the time of day and during the year [4]. I also draw attention to the article in Leonardo entitled The Sundial Theme in My Environmental Art by M. L. Faverman [5].

My Sun-illuminated works or Solar Bas-Reliefs make use of shadows produced by the Sun's rays coming from directions that change with the time of day and during the year. A Solar Bas-Relief consists of a planar surface made up of an array of many individual elements, for example notched bricks or blocks provided with shadow-casting metal tabs, usually of the same external dimensions. The por-tion of each element's surface illuminated by sun-light and the portion in shadow contribute to a perception of grayness when the element is viewed from sufficient distance. By the use of elements that produce different ratios of sunlit to shaded por-tions, varying degrees of grayness are perceived. Therefore, by the appropriate arrangement of the various elements in the bas-relief, variations in grayness over its face can be produced when light from a specific direction falls on it. The elements can be designed and arranged to display desired images.

Two examples of my Solar Bas-Reliefs are shown in Figs. 2 and 3. The elements contributing to various levels of grayness combined to depict the portraits of Bob Dylan and of Andrê Malraux in a manner analogous to the gray areas associated with dots of black ink of various diameters surrounded by areas that are not inked in a newspaper illustration.Eight different elements of one notch type (Fig. 4) were employed to produce the Dylan portrait (Fig.2). For a given position of the Sun the face of element 7 would be completely illuminated and would be called 'white' whereas that of the entire element would be in shadow and would be denoted 'black'. Elements from 1 to 6 would show decreasing portions in shadow and, hence, would be perceived from a distance as having grayness of increasing lightness.



The angle 4) of the vertical at a location on the Earth with the plane of the ecliptic varies with the seasons, and on the Tropic of Cancer this angle becomes zero once a year when the Sun passes through its zenith (summer solstice) in the northern hemisphere [6]. If on a particular day of the year, the face of the Solar Bas-Relief is parallel to the plane of the ecliptic, the surface will be sunlit and the plane of the rear of the notches in the surface will be in shadow (Fig. 4). If on the following days the angle 4) diminishes to zero (summer solstice), the southern face of the bas-relief is in shadow. After the summer solstice, 4) increases again, and the face is again sunlit. At the particular value of 4) where the image was seen, the image is present again.

Figure 4 shows eight elements, for example notched bricks, that could be used in a Solar Bas-Relief in the tropical and the subtropical regions. The plane of the rear of the notch and the plane of the front of the bas-relief define angle ~, which is an angle selected to limit the time during which the notch is in shadow while the front of the Solar Bas-Relief is sunlit. For a duration of one day, angle ~ 23 min; it represents the average displacement of the plane of the ecliptic in one day.

If the Solar Bas-Relief is located in a tropical or in a subtropical region, it would generally be inclined slightly either toward the north or toward the south. In the temperate region of the northern hemisphere, it must be inclined to the south. For a given angle 4), the image will appear twice during the year, except when the angle 4) is a minimum for a given location, in which case the image will appear once during the year.

Images can also be made that will appear each day, at specific hours. In this case, the orientation of the Solar Bas-Relief is north-south, and the appearance of images does not depend on the angle 4). In some cases a Solar Bas-Relief can be used as a sundial.

If it is not desired' to present an inclined Solar Bas-Relief (southern exposure, temperate region), one can construct a vertical bas-relief employing bricks with faces inclined at the angle 4) with respect to the vertical (see insert, Fig. 4). In this case the angle ~, which determines the duration of the image, is measured between the plane of the notch and the plane of the face of an element. This arrangement has the advantage of allowing the occurrence of an image on different dates or at different hours by having elements whose faces have different angles 4). Furthermore, by progressively varying the angle

4) for the faces of individual elements it is possible to produce a linked-blend of images during the course of a day.

The model of the Solar Bas-Relief of Bob Dylan contains 8000 elements for which the angle 4) is O degrees and angle ~ is about 2 degrees. To obtain the image shown in Fig. 2, the bas-relief faced the east at the Parc Montsouris in Paris on 24 May 1974. The duration of the image was about two minutes at 8:00 hours.

A different type of element was employed in the model that produces two clear depictions of André Malraux (Fig. 3). Each element consists of a square wooden block provided with one or two shadow-casting rectangular metal tabs (A, B), as shown in Fig. 5 (top). The shadows that the tabs cast when the elements are exposed to sunlight from three direc-tions are indicated. Figure 5 (bottom) shows a portion of the bas-relief illustrating the shadows cast when the Sun was in the west (left), overhead (center) and in the east (right). With the Sun in the east, tabs A cast shadows (Fig. 5, top) showing the appearance of Malraux in his youth (Fig. 3, Leif). At noon (Fig. 3, center) both tabs A and B cast shadows, providing a fading out of the morning depiction and a fading in of the afternoon depiction, the latter showing the appearance of Malraux in old age (Fig. 3, right) that is produced only by shadows cast by tabs B (Fig. 5, top).

The model shown in Fig. 3 faced the south. The depictions of Malraux in his youth and in his old age could be seen clearly when the Sun was inclined at

450 to the vertical. The model consists of 12,000 elements provided with 24,000 tabs.

The depictions in Figs. 2 and 3 were derived from ordinary glossy photographs, which were presented to a Thomson CSF video camera at the Adersa Gerbioz Laboratories at Velizy, France. This video camera delivers signals in response to the local density of small areas in a photograph, corresponding to the equal subdivisions of a grid. In the case of the Dylan photograph, the grid consisted of 8,000 areas, and the camera signals were translated into integer density designations from O (1)lack) to 7 (white) by means of a computer interface conceived by Adersa. (The computer was a Compagnie In-ternationale d'Informatique (CII) Mitra 15.) In the case of each of the Maîraux photographs there were 12,000 areas and a density range from O (black) to 15 (white). (For reasons of clarity only eight of the 16 different elements are shown in Fig. S (top).) For a given grid the integer density designations are proportional to the sunlit area. Since the shaded area identifies a notched element in the series employed in constructing the Dylan Solar Bas-Relief model (Fig. 4), each integer designation specifies a particular element of the series. In the Maraud Solar Bas-Relief model, two integer des-ignations are required to specify a construction element, one applying to the series of metal tabs A for one portrait and the other applying to the series of tabs B for the other (Fig. 5, top).

Prior to the construction of the models that I have described, I obtained a rather good idea of the appearance of the images from dot-density print-outs from the computer. These printouts resemble the depictions on personalized T-shirts being worn in many countries. The integer designations tabu-lated in the array of 8,000 (or 12,000) elements are the computer's instructions to the person having the task of assembling the elements into a Solar Bas-Relief.

I constructed my first full-scale (7 x 9 m) Solar Bas-Relief for La Société d'Economie Mixte d'Aménagement des Halles in Paris in 1978. It shows the image of a lion cub (a symbol of the Sun) that is visible between noon and two PM when viewed from the fountain Les Saints Innocents.

I would gladly give further information on my Solar Bas-Reliefs to those interested.


1. D. H. Merizel, F. I. Whipple and G. De Vancouleurs, Survey of the Universe (Englewood Cijifs, N. J.: Prentice-Hail, 1970).
2. A. Pochan, L'Enigme de la Grande Pyramide (Paris: R. Laffont 1971).
3. L. Charpentier, Les Mystères de la Cathédrale de Chartres (Paris: R. Laffont, 1966).
4. P. K. Hoenich, Kinetic Art with Sunlight: Reflections on Developments in Art Needed Today, Leonardo 1, 113(1968).
Also in Kinetic Art: Theory and Practice, F. J. Malina ed. (New York: Dover, 1974) p. 23.
5. M. L. Faverman, The Sundial Theme in My Enviromnental Art, Leonardo 10, 177 (1977).
6. A. Baladi and R. A. Baladi, Method of Producing a Bas-Relief with a Motif Which Varies with Light and the Bas-R~ief thus Obtained, US. Patent 4,070,216(24 Jan. 1978).


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More about the Solar bas-relief:
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