Oval Leaded Glass Window
Figure 49: A leaded glass window for a house in San Francisco, California. Approximately 1 meter wide.
The following analysis of the leaded glass window shown above, designed and built by this author, is intended to illustrate Alexander's geometric principals in practical use. An analysis of the geometry, in light of the “Fifteen Fundamental Properties,” will be undertaken. The “Structure Preserving Transformations” which occurred as the design and construction progressed will be discussed.
Figure 50: First thumbnail sketch, about 2"x3".
This thumbnail sketch was a rather static first design. It has a series of reasonably strong centres, but they are largely unrelated to one another: there is very little Deep Interlock. Also, there is very weak attempt at a Boundary around outside perimeter.
Figure 51: The first real attempt at a full scale design
Most of the effort in this full scale design went into creating a significant Boundary: a series of ovals, an Echo of the overall shape. There was an attempt to create Alternating Repetition in space between ovals, but this space is not a Strong Center in itself, nor does it create Positive Space like the oval. The central space is not developed significantly. There is no Deep Interlock between the central space and the border. There is a positive child-like feeling to the border, a playfulness and ‘egolessness’ about it. This resulted from the designer’s intent to simply create something pleasing, not necessarily sophisticated or 'modern' - only something joyful, almost like a circus or carnival.
Figure 52: A tentative effort was made at the interior space:
The overlay design shown above gives promising indication of potential Deep Interlock with border. The space between the ovals (here tried as circles) is simplified, creating better Simplicity and Inner Calm.
Figure 53: Full scale design number 2:
Here the circular elements of the Boundary become graduated, with the ovals at the centre becoming smaller circles at the ends where the curve is tighter. This achieves nice Gradients. A small circle is introduced between ovals, unifying them by creating a 'butterfly' motif, employing half of each oval. This creates strong Deep Interlock and Ambiguity around the border. The 'wings' belong to both the butterflies and to the ovals:
Figure 54: ‘Butterfly’ created with the ‘leaves’ of two ovals.
To a lesser effect, this also reinforces the Alternating Repetition of the border ovals.
The interior space begins to take shape with three small central circles and a smaller fourth and fifth circle at top and bottom. These elements sprout an animal or vegetable-like motif. There are not yet Strong Centers visible due in large part to lack of Good Shape or Positive Space. There are reasonable Levels of Scale, from the small circles between the ovals, progressing in more or less equal 1:2 steps, up to the large figures in the centre. There is, however, a strange and uncomfortable feeling, a result of the unresolved central area, the lack of Good Shape and Positive Space. Gradients in the central area begin to show themselves, but weakly, in the way that the central figures get smaller at the top.
Figure 55: Full scale design number 3.
Here the strange feeling has been eliminated, for the most part, with the introduction of Strong Centers and Good Shape in the lines emanating from centre. These lines flow through the ovals/butterflies creating Deep Interlock with the border. Gradients are more pronounced, both in the border, where ovals contract to smaller circles, and in the central figures, that decrease in size as they move up the piece. Local Symmetries have been created in 'arrowhead' elements:
Left figure 56: Strong Centers of the central area are marked.
Right figure 57: Flowing lines create Positive Space, Good Shape and Deep Interlock. Also, dashed arrowhead shape displays Local Symmetry, as well as Deep Interlock and Alternating Repetition
Figure 58: The final full scale pattern used for construction:
In the final design, the central area has been elaborated, with more Strong Centers and Deep Interlock. But there is less of Levels of Scale due to the filling in of central figures and consequently less Simplicity and Inner Calm. The existing feeling is a sort of fertility or fecundity.
Figure 59: The final window as built:
Left figure 60: The bottom half of the built window.
Right figure 61: A close-up of a portion of the window showing some of the textured glass.
Levels of scale
The window has a pretty good range of scales:
From the veins and ridges on the clear glasses (about 2-3 mm); to the small glass drops that divide each circle around the border (about 1.5 cm); to the central beveled glass circles (about 3 cm); to the white elements of the circles/the 'wings' of the 'butterflies' (about 4-5 cm); to the smaller leaf shapes of the central figure (5-6 cm); to the small central elements of the boundary circles (8-10 cm); to the larger leaf elements of the central figures (10-15 cm); to the inward pointing arrowheads (14-16 cm); to the larger of the boundary circles (20 cm); to the two smaller beveled circles top and bottom and their radiating leafs (20-25 cm); to the three central beveled glass circles and their radiating leaf pattern (50 cm); to the entire central oval figure and field excluding boundary (70 cm); to the whole window (1m x 2m approximately).
The strongest ‘center’ is the central beveled circle and its radiating leaf pattern, followed closely by the two other large beveled circles with their radiating leaf structure; then by the circles of the border; then perhaps, by the two smaller beveled circles top and bottom; then by the diamond shapes of the boundary circles. More ‘centers’ include the inward pointing arrowheads, the individual 'leaves' of the central figure and the small coloured drops of the boundary.
There is a reasonable Boundary of the circle/butterflies around the outer edge, although in hindsight, this would have been made larger, perhaps by 10-15%. The white 'wings' of the butterflies create a Boundary around each diamond shape at the centre of each circle. Another series of Boundaries occurs where the leaves of the central figure bound each beveled circle. This is more successful when the eye sees the vibrancy of the beveled circles as light passes through them creating a kaleidoscope of colours bounded by the relative darkness of the sea-green leaves. The four most central arrowhead shapes are strongly bound, on one side by the 'wings' of the boundary ‘butterflies’, and on the other, by the intermediate shapes of ridged glass. The other arrowhead shapes are less strongly bound to various degrees.
There is strong Alternating Repetition of the border circles with the small coloured drops and the arrowhead shapes. The arrowhead shapes also alternate with those elements of the main figure which reach out to the boundary. There is Alternating Repetition in the alternating colours of the diamond shapes of the circles in the boundary. There is minor alternation in the centre of the figure, between the three central beveled circles and the connecting 'leaves'.
The circles of the border display Positive Shape, as do their 'leaves/butterfly wings' and their central diamonds. The leaves of the central figure display positive shape as do the shapes traced by the lines radiating out from the central bevels (see figure 57 above).
The most successful shape in the piece is the upside-down bell shape that extends from each of the three central beveled circles. These reach out to the boundary, curve through it, and return into the central figure in a fluid, sensual way. The least successful shape occurs at the top of the central figure where the two leaf shapes that touch the boundary are bifurcated with a curving line. In retrospect, the design would have left each of these as whole, similar to the formation at the bottom of the central figure.
There is Local Symmetry in each of the circles, as well as in the ‘butterflies’, of the border. It also is evident in the ‘arrowhead’ shapes (see figure 57 above).
Deep Interlock and Ambiguity
This is where the piece manifests its greatest power. The rough, clear glass, which runs from the outer edge, between the circles of the boundary, and becomes the ‘arrowhead’ shapes, strongly interlocks the border with the central figure. This is reinforced by the upside down bell-shaped lines of the central figure, which extend into the border and then curve back into the central figure, again, deeply interlocking them. There is also strong interlock in the way the circles of the boundary each contain half of a ‘butterfly’. There is also a small bit of interlock in the two vertically oriented leaf shapes, at the centre of the central figure, which radiate off the most central beveled circle and also radiate off the respective beveled circles top and bottom.
There is strong contrast in the dark central figure resting on the clear, light background. At night the figure ground is reversed, with the clear glass becoming dark and the central figure appearing lighter.
Gradients radiate from the absolute centre of the piece. The leaf-like elements in the central figure increase in number, while they decrease in size, from the middle, to the top and bottom. Additionally, the circles/’butterflies’ of the border get smaller at the top and bottom where the curve is tighter. Here, the width of the border stays constant, and it may have improved the design to narrow it at the top and bottom.
There are a series of shapes, made with clear ridged glass, that help form the ‘arrowhead’ shape. They contribute very little else to the design, and as a result may appear somewhat odd and arbitrary. But they are important to the Good Shape of the ‘arrowheads’ and contribute Roughness to the piece.
The circular shapes of the border echo the overall shape of the window. Further, there is a repetition of a curving line throughout the piece which contributes to Echoes.
The Void is generally lacking from the piece. There is a small touch of a certain never-ending feeling in the interlocking lines which radiate out from the centre, through the border and back to the centre. But there is no clear area of ‘emptiness’ or blankness.
Simplicity and Inner Calm
The piece lacks this property generally. It is perhaps too sophisticated and too complex. This may be the piece’s greatest weakness.
While hurt by the lack of Simplicity and Inner Calm, the window still manages to make some connection, through the strength of the other properties.
Figure 62: The window in situ.