The first image above shows two figures defined by four horizontal lines drawn on the grid (). Every two lines form a pair. All lines fall on one of two constructed grids of eighths or sixths. The lines do not touch the edge of the field, but instead stop at two elected intersections within the overall grid. The construction follows the pattern illustrated on the previous page and the eleaborated on in , ·.
While multiple compositions might possibly follow the procedure, all will share certain traits based on the instruction set. The resulting composition uses contrasts of size and position, alignment of common edges, and the proximity of the elements to one another and the perimeter to generate a particular spatial character. With that in mind, we can describe the example composition as showing smaller and larger elements or figures. The larger lower figure lies closer to the smaller figure than to any other edge or
-. The upper form’s distance from the top approximates its width. Seen in the context of the bounding lines, the figures’ placement and construction reveal a nexus of relationships within our perceptions. Those observations might result in a diagram representing the spatial gestalt of the composition as seen in the next illustration (). Within the composition, the field most clearly by the two figures lies between them. The other areas identi-fied in the gestalt diagram are that result from the extension of the figures into and across the ground. Both terms refer to gestalt closure*, although implied space is open to more subtle description and understanding.
Defined & implied space
Defined and implied space holds the possibility of envisioning other elements to enrich a composition. Why is this important? The practical version might suggest that because building happens in a context, designers should be good at this. This is, of course, true. However, the larger point is that design pro-ceeds from a central toward greater complexity in response to chang-ing scales of design. Harnesschang-ing complexity through drawchang-ing is one way that designers create order in their projects, leading to buildings of merit and beauty.
The distinction between defined and implied spaces rests on a simple defi-nition, although in practice it often bedevils beginning design students. The
Figure 9: The image to the right shows the previously constructed grid with four abbreviated horizontal lines drawn across the field. The lines align on both edges and are of equal length.
Figure 10: The two resulting figures – shown as black – create the spatial gestalt as described in the text and shown below. The darker area between the two black figures marks the specifically defined area or field. The gradients identify the axial domains for spatial gestures implied within the composition. The relational grid subdivides both the defined and implied areas.
*
Closure, encountered earlier as part of gestalt theory, identifies the perceptual tendency to view a collective of lines or figures as a comprehensive shape – to con-nect the dots. The distinction between defined and implied figures or figural spaces refers to the relative completeness of the provided ‘dots’. Thus four corners define a square, while two corners merely imply it.
In the case of substantial forms – a matter of scale – the shape of the spatial figure may respond to either the inside or outside boundary of the defining ‘dots’.
In the diagrams following on the next page, the dotted lines outline a completed form as defined or implied by four, three or two squares.
terms characterize underlying gestalt features of form and space. Our percep-tions emerge from the collective set of elements that exist in a composition.
Defined spaces result from extending of boundaries present in an array. In the case of rectilinear forms such as our examples, boundaries coincide with the edges (). Any rectangular form will project four boundary lines.
Implied forms, in contrast, generally refer to the underlying organizational structure. In the example below, the proportional geometries of both figure and field account for measurement of two centerlines (). The gray field is thus defined on three edges and implied on the fourth.
In summary, figures generate boundaries that define edges while the geom-etries of the composition (including field geometry), repetition and gestalt closure imply other edges. Both kinds of edges can describe additional fields – or figures – as the composition evolves. The relationship that results from
our four figures arranged as a square composition can develop in several directions depending on design intent. The original intention can be rein-forced directly or subtly by the manifestation of suitable additions as it moves
defined and implied space in several related compositions. Dashed lines mark defined boundary lines while heavier dotted lines denote implied edges. The gray infill areas occupy some of the more apparent fields.
Diagrams 13·1–4 show examples based on four square figures. Diagrams 13·5–6 and 13·7–9 show variations with three and two figures respectively.
Diagram 13·4: Spaces implied by proportion.
Diagram 13·5: Spaces defined by figure boundaries.
Diagram 13·7: Spaces defined by figure boundaries.
N.B. A comparison between Diagrams 13·7 and 13·8 reveals that similar spaces can result from both defined and implied boundaries.
Diagram 13·1: Space defined by interior boundaries.
Diagram 13·6: Spaces implied by proportion.
Diagram 13·8: Spaces implied by closure.
Diagram 13·9: Spaces implied by closure and proportion.
Diagram 13·2: Space defined by figure boundaries.
Diagram 13·3: Spaces implied by repetition.
Figure 11: Diagram identifying the space defined by exterior boundaries of the composi-tion. In this example the four squares occupy the space they define.
Figure 12: Diagram showing a space defined on three edges by the composition with a fourth edge implied by the proportional center line.
toward greater complexity and emphasis. This sort of formal design logic dem-onstrates the presence of a coherent, evolving central idea.
That a central idea underwrites good design may seem so obvious that its significance remains hidden. The word ‘idea’ comes to us from the Greek term denoting form or pattern. In Middle English, the root term idein meant ‘to see’. To have an idea is literally to perceive something as distinct. As complex-ity arises throughout the design process, the designer responds with ideas – hopefully good ones – so that the result may be literally full of good ideas.
However, they are not all of equal importance. At the heart of good design lies the Big Idea, the summoning picture against which we judge the design as a whole.
In a similar way, the first gesture in a design figures not only itself but also sets about creating visual cues for orderly evolution from the simple to the complex. In that sense, we can see in the simplest composition certain pat-terns that emerge within the drawing to define and imply space and form.
Figure 14: The two figure com-position (10) placed within the tartan grid. The analysis seen at the far right corresponds to that underlying structure (16).
Figure 15: The drawing results in two black figures which in turn we mark with extended bounding lines.