In , we demonstrated the relationship of two simple forms in a field.
In its initial iteration, the variations show two undeveloped volumes as solids and propose an analysis of their relationship. As the sequence evolves, rela-tionships change, as each of the figures acts as a possible site for further devel-opment. In this way, a combination of two figures offers a relationship that can evolve towards greater complexity. This fundamental observation parallels the dichotomy between external and inward expression, an organizing prin-ciple that inhabits the middle portion of our narrative sequence.
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In , the architects Robert Venturi and Denise Scott-Brown published Learning from Las Vegas. Among their observations was the proposition that archi-tecture offered up two strategic categories: the
and the . The categories prompted lengthy discourse and multiple opinions. For us here, they inform our ideas about design strategies. Build-ings that express complexity externally pay homage to the duck. Those that hold their complexity in a simple volume bow to the decorated shed. We do not suggest that Venturi and Scott-Brown would agree with us, but we admit that their observation lives in our premise.
We begin our investigation of the evolving figure the same way as the pre-vious figure-ground episodes – by dividing a square ground into eighths and twelfths. We then place a single figure into the resulting relational grid and analyze the formal conditions. Generating multiple examples allows us to bet-ter illustrate the role that geometry may play in developing compositional integrity. The sequence that follows is a simple repetitive procedure followed by analysis, in the form of diagrammatic overlay.*
For each iteration, we place a black figure on the ground. Each figure obeys a few simple guidelines. These rules set the stage for later evolution, by elimi-nating extreme variants that might hamper or obstruct the sequence.
There are three guidelines:
No figure touches the perimeter of the square.
The figures’ areas should fall between approximately one ninth and one fifth of the entire field in size.
The figures snap to the grid.
Four example variations appear below (–).
There are three distinct, related ideas to consider in creating the figures:
, and . Placement, in its relation to order, should start with a general intent. Within the relational grid, the fig-ure will reflect the underlying sense of either quarters and centerline or thirds and center space. Wherever placed, orientation of the figure on the grid can be horizontal, vertical or static – without overt direction. Ideas of proportion follow directly from orientation. The object can be tall or squat, wide or stubby, square or squarish – language is remarkably imprecise regarding proportion.
Despite that potential imprecision, the resulting visual gestalt should yield to very simple verbal description – for example ‘A relatively tall figure sits in the upper-left quadrant of a square field, its bottom touches the field’s centerline’
– if for no other reason than to practice verbalizing formal analysis (). If you detect at this point that alternate verbal descriptions exist for the example, then you understand the underlying premise of starting here.
To appreciate the nuances of this seemingly simple scenario, we suggest repeating it through a minimum of eight variations. To understand the spirit of the idea, the eight should display diversity yet remain coherent as a group.
They should achieve differences worthy of consideration yet remain related.
Figures on a relational grid.
In the four examples below, regulating lines in a square ground define a single rectangular figure shown as a gray form. All figures are orthogonal and follow the general guidelines.
The general intent governing the set limit the figures in three ways:
• They avoid symmetrical placement.
• They vary the direction and visual demeanor of the figures
• Each example relates to the one before and/or after.
In addition, the set sequence demonstrates four interrelated variables:
• Placements cover all four quadrants, with three examples spanning the centerline.
• Orientations include horizontal, vertical and static.
• Measurements begin at both corners and edges.
• Therefore proportions interact with both centerpoint and center space geometries.
Figure 1: The figure originates in the upper left quadrant at a corner point defined by the regulating lines for the sixteenth interval. The intersec-tion of the horizontal centerline and diagonal thirds regulating line defines the opposite corner.
Figure 2: The second figure uses the mirror regulating line in the upper right quadrant to define an edge point at the eighth interval. Following the line upward to the twelfth point and across to its semi-mirror in the opposite quadrant completes the figure.
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Once again, we omit exact dimensions for the com-positions. In the classroom, we continue to use index cards for the majority of drawn exercises – in this instance cutting them down to " squares. In some years, we used the entire "×" to introduce students to the Gothic era’s favored proportion. The project works equally well in either case.
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Design discussions generally avoid using the word
‘style’ as it brings along a negative sense of the superfi-cial. This pejorative connotation is leftover from nine-teenth-century ‘style books’ that conflated apparent features with particular styles – e.g., pointed arches indicated Gothic style. ‘Style without substance’ more accurately describes such limited interpretation. In reality, genuine style results from well-applied tech-nique and method – tactics and strategies. Correctly understood, style construes long practice wherein mul-tiple decisions accrue as part of articulating ideas.
Working in simple forms toward internal complex-ity or from aggregate forms toward external expres-sion are complementary styles of design practice. They are working methods that reflect different intentions.
to be remarkably individual. If they follow the rules of engagement, the final group of eight figures will share significant if subtle biases that provide a basis for engaging the ongoing design process.
A single figure on a ground exhibits basic compositional gestures. A hori-zontal figure might sit on top or settle to the bottom (). It may relate to a side or the center, or occupy a particular quadrant. The figure may also either hold its place, or seem to move towards empty space to the left or right. A ver-tical figure – as seen in Figure – acts similarly with differences reflecting the change in axial direction. Squares or other near-static figures seldom exhibit motion, instead appearing to possess a sense of gravity or stability ().
These observations illustrate that while may have a specific defi-nition, the concept of plays over a large range of possible equations.
This seems an obvious point as a concept. In practice, however, refining one’s sense of visual balance constitutes a subtle and ongoing challenge. Describing those observations accurately requires deliberate effort.
Being able to articulate the design act in the context of possible options broadens the capacity for design thinking. Speaking carefully becomes a verbal counterpart to analytic diagrams. Careful discussion of formal results reminds us that seeking one direction in resolving a design results from , not from coincidence.
Language expands a designer’s sense of intention. Taken on robustly, it helps clarify the context for judging one’s own work, and thereby improves both the design and the designer. Addressing a design in language that sug-gests it as the only logical solution to a problem reduces the design act to formula. It also obscures the presence of intent, in pursuit of one tactic over another. We urge our students to separate personal taste from project possi-bilities, not because we eschew instinct, but because critical judgment lays a stronger foundation than instinct alone.* The four examples on the next page (–) further analyze the compositions shown below. Thereafter, a sequence of eighteen variations serves as a visual essay on compositional gesture, as described above.
Figure 3: The third figure origi-nates in the lower left quadrant at a corner point defined by the regulating lines for the eighth interval. The intersection of the diagonal thirds regulating line defines the opposite corner.
Figure 4: The fourth figure uses a subdividing regulating line of the upper right quadrant to define an edge point at the eighth interval. Following the line downward to the center diagonal and locating a point along the diagonal third in the same quadrant completes the figure.
Figure 5: The figure’s place-ment rests on the horizontal centerline. Its upper left corner marks a square, anchoring its position in the quadrant.
Figure 6: The second figure’s placement mirrors the regulat-ing line in the upper right quadrant to define an edge point at the eighth interval.
Following the line upward to the twelfth point and across to its semi-mirror in the opposite quadrant completes the figure.
Figure 7: The third figure origi-nates in the lower left quadrant at a corner point defined by the regulating lines for the eighth interval. The intersection of the diagonal thirds regulating line defines the opposite corner.
Figure 8: The fourth figure uses a subdividing regulating line of the upper right quadrant to define an edge point at the eighth interval. Following the line downward to the center diagonal and locating a point along the diagonal third in the same quadrant completes the figure.
Diagram 5·1: The figure reflects repeated regular subdivision of the quadrant’s square geometry.
Diagram 6·1: The figure uses regular geometric measure for proportion and placement.
Diagram 7·1: Underlying figure geometries show both regular intervals – the square – and the generation of the irregular measure.
Diagram 8·1: Figure geom-etries reveal similar regular intervals of squares and the construction of the offset.
Orderly development of figures and variations
Figure 9: To the left, six related figures with three variations each dem-onstrate a sequential development. As with previous examples (1–4), all figures are orthogonal and follow the same general guidelines.
The general intent governing the set limits the figures in three ways:
• They avoid bilateral symmetrical placement.
• They vary the direction and visual demeanor of the figures.
• Each example relates to the one before and/or after.
The general organization for each row of three also follows a sequence of large to small to medium size – a papa, baby and mamma bear family of shapes.
The set sequence again illustrates four interrelated variables:
• Placements cover all four quadrants, with three examples spanning the centerline.
• Orientations include horizontal, vertical and static.
• Measurements begin at both corners and edges.
• Proportions therefore interact with both centerpoint and center space geometries.
Diagram 9·1·1: Tall horizontal, upper right quadrant.
Diagram 9·2·1: Shorter hori-zontal, upper right quadrant.
Diagram 9·3·1: Wide horizontal, spanning upper half.
Diagram 9·4·1: Narrow vertical, spanning horizontal centerline.
Diagram 9·5·1: Square form touching centerpoint.
Diagram 9·4·2: Taller, narrower, adjacent to vertical centerline.
Diagram 9·5·2: Near-square occupying upper left quadrant.
Diagram 9·6·2: Similar form occupies upper left quadrant.