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Design insights: Gestalt, Bauhaus and Japanese gardens

Gert J. van Tonder1 and Dhanraj Vishwanath²

To appear in:

Oxford Handbook of Perceptual Organization

Oxford University Press

Edited by Johan Wagemans

1Laboratory of Visual Psychology, Department of Architecture and Design, Kyoto Institute of

Technology 2School of Psychology, University of St. Andrews, Scotland

1. Introduction to perceptual organization and visual design

‘Design’ encompasses a range of concepts that go well beyond vision. The word derives from

the Latin dēsignāre 'to designate,' meaning ‘to mark out’ (Collins English Dictionary 2011). In

terms of visual design (e.g., graphic, landscape, architectural, sculptural, product and fashion

design), this refers to lifting out from the morass of possible connections those aspects which

most clearly convey the intentions of the designer, communicate how the design should be

used, and intuitively reveal the physical constraints imposed by the material design.

With a given utility in mind, the designer shapes an object into a given form, selectively

enhancing the essence of its visual character. Visual style is the framework through which the

clarification of pattern is achieved. The creativity of designers lies in the originality of their

conceptions and style. In good design, perceived form matches perceived function, and both

are consistent with intended function. This, in fact, is not too distant from a broadly construed

definition of perception. Yet, great design is not automatically achieved. Specifying the relevant

goals, environment, primitives, requirements and constraints depends on the talent, skill and

experience of the designer (Ralph and Wand 2009).

Design is hardly experienced as neutral. It is imbued with an aesthetic that, while often

resisting succinct verbal description, offers an immediate affirmation in its resonance with

perception (Arnheim 1969). Some designed objects – a certain car, house, garment, garden or

painting – may be coveted for its visual appearance, while others are not. What, visually, sets

them apart?

When someone creates a design, the more salient perceptual qualities in what is envisaged

and seen, dominate the trajectory of the design process: perception significantly shapes the

design outcome. Any human-made creation therefore reflects back upon perception, offering

potential insight into the constructs that resonate with the internal organization of percepts – a

good reason why vision researchers should have an active interest in visual design. Haptic

perception and motor function is, of course, other fundamental dimensions of design,

especially in design with a human end user in mind. Haptics constrain the range of possibilities

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among visual patterns that would allow a given action. A device built for manual manipulation

needs to suit the physical dimensions, constraints and functionality of the human hand,

regardless of visual appearance. In this chapter, the focus will be on visual perception with the

assumption that we are already considering designs that are within the functional haptic range

of the human body.

A different visual aesthetic results when considerations about functional utility of the designed

item far outweighs those regarding the accommodation of a human user. Craftsmanship is the

art of combining qualitatively and aesthetically rich user interfaces with a high degree of

functional utility. Perception is not infallible: some designs are intentionally made with a high

degree of visual appeal, often as counterfeit products, with the purpose of being more

competitive in the market, but handling of such an object should swiftly expose discrepancies

between its visual ‘promise’ of functionality and its actual frustrating performance. Design can

even deliberately counter the perceptual tendency to match form with function. Cartoons by

Heath Robinson (1872-1944) and Rube Goldberg (1883-1970) depict machines that accomplish

simple tasks through absurdly complex means, to the point of rendering them useless in

practical terms.

Nature may be considered the evolutionary blueprint for perception. While it is likely that all

sentient entities experiencing their own version of ‘reality’ (von Uexküll 1926), human-made

designs can alter, exceed or antagonize perceptual organization that, at the outset, evolved to

deal with a natural environment unfettered by human hands. Of particular interest in this

chapter, therefore, are applied examples where human design aims to recreate some idealized

aspect of nature. The first section will be devoted to the intuitive insight captured in some

instances of classical Japanese design that emphasize the relation between human design and

natural form.

The same perceptual factors implicit in the centuries-old gardening manuals of Japan are partly

incorporated in ideas put forth by the Bauhaus, Gestalt school of psychology and other

movements, nearly a millennium later, as will be shown in the second section. We will also

demonstrate how Japanese design principles more directly influenced Bauhaus design.

In the third section, we show that naturalistic structure, considered by some as the

evolutionary cradle for perceptual organization, shares principles with the visual patterns

emphasized in Japanese design and in Gestalt and Bauhaus approaches, thus serving as their

potential common denominator.

The supplementary online material accompanying the chapter revisits a few recent general

frameworks for thinking about visual perception of the designed structures are presented.

2. Perceptual effects in classical Japanese architecture and designed landscape

2.1. Japanese design concepts

Among the great landscape designs of the world, classical Japanese architecture and gardens

are of special interest, because over the last millennium they have culminated in a canon of

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design effects for enforcing an idealized naturalistic order on design elements; the order in

large naturalistic vistas is usually recreated in relatively limited space. It offers valuable insight

into what a good, balanced natural shape is and how different natural and human-made

structures can be harmoniously combined.

The quintessential Japanese garden contrasts starkly with baroque perspective gardens, such

as the courts at Herrenhausen and Veitshöchheim. These structures impose non-naturalistic,

pure geometries onto natural design elements, usually over large spatial scales. The baroque

garden appears as the continuation of human architectural geometry into the surrounding

exterior space, while in a classical Japanese rock garden the transition from human design to

naturalistic form is more emphasized (Arnheim, 1966).

The key concepts in Japanese design relate to form and visual organization. Nōtan – the overall

gist of light and dark in a design – concentrates on the balance, spatial layout and softness of

light and dark (Tanizaki 1933); it concerns the shape of figure and the shape of the empty

spaces delineated around the figure; the interplay and shapes of light, specularity and shadow,

and any contrasting visual attributes, be it light, colour, size, shape or other qualities. Hongatte

– the way in which the design layout guides the gaze (Kuitert 2002) – refers to visual balance,

asymmetry and incompleteness in the visible parts. Mitate – literally ‘setting up the eye’ –

relates to techniques for bringing a new visual awareness to a familiar object through the

creation of visual allegories. For example, by using the foundation stone of the pillar in a

temple as a washbasin not only introduces novel, interesting stone shapes into a new context,

but creates metaphoric narratives, for example, by linking the foundations of a place of

spiritual practice with a fountain, a life-giving source of purification. Shin-Gyō-Sō concerns the

degree of formality in applying light, shadow, asymmetry and irregularity (Keane, 1996, p.77).

In the design of a stone path, for example, at the most formal level – Shin – stone shapes will

be regular, angular, with little or no variation in colour, shape and size, arranged in a regular

tessellation in a straight path with a straight border. Individual stones and the path as a whole

will tend to fully occupy rectangular frames. However, the stones should not be smoothly

polished, as this is thought to rob them of their simple, natural materiality – a powerful

Japanese design aspect referred to as Wabi-Sabi (Yanagi 1972). At the most informal level – Sō

– stones of varied shapes are spaced at more irregular intervals, with small stones interspersed

with large, light stones with dark, irregular with irregular, rough with smooth, the entire path

winding with a loosely defined, jagged border, as if accidentally stumbled upon in nature.

In actual designs, the combination of the three levels gives rise to very complex variations on

the theme. A formal path may intersect an informal one going in a different direction, creating

the impression that the paths overlap transparently. A path with a formal border may have a

more informal placement of stones within the border, and so forth. Such differences in levels of

formality are found in all design around the globe. Its formalized expression in Japan turned it

into an immensely useful design aid, ubiquitous among all the Japanese arts.

There is no simple recipe for design. Concepts like Nōtan, Hongatte, Mitate, Shin-Gyō-Sō and

Wabi-Sabi directly relate to the appearance of a design, intuitively conveying qualitative

relations between part and whole. Its greatest utility is as a mental tool for increasing one’s

own awareness of, and ability to respond more sensitively to, various perceived visual aspects

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of the design as it is created.

2.2. Visual structure in classical Japanese interior design

A major limitation in the traditional Japanese dwelling was, and still is, the shortage of space

and natural light (Tanizaki 1933). The solution is a system of rectangular architectural frames,

wherein layers of sliding doors can swiftly alter visual access to the exterior. Traditional

Japanese architecture thus naturally lends itself to a style of dwelling where the imagery of

nature is always near, subtly framed by layers of wood, clay and paper.

Figure 1. Tea architecture in Kyoto, Japan. (A) Entrance to the Tai-An tea hut. (B)

Interior of the Saigyō-An tea room. Note the many contrasts between light and

dark, small and large, and regular set off against irregular pattern. Intersecting

lines are carefully avoided, while clearly demarcated T-junctions enhance

spaciousness.

Sliding doors consist of wooden lattices covered in opaque (Fusuma) or translucent (Shōji)

paper. Smaller windows usually consist of shaped openings in clay walls, fitted with a latticed

sliding window panel. This wide array of sliding panels therefore can let in diffuse light, allow a

direct view to the exterior or cut off all visibility. It changes not only the amount of light

entering the room, but also articulates the interior space. First, windows of various sizes create

impressions of spatial depth perspective. At the entrances to tea huts, such as Tai-An and

Saigyō-An in Kyoto, the smallest window is placed furthest from the entrance (Suzuki 1979)

and usually closer to the floor than windows right at the entrance (Figure 1B). Windows are

deliberately not aligned, but arranged in an irregular step-like manner, a strategy also followed

on the architectural exterior (Figure 1A). These effects help engender the appearance of

greater spaciousness in the architectural interior.

Gilded surfaces reflect ambient light back onto surfaces, brightening the room, clearly

delineating shape silhouettes, and appearing as transparent layers beyond which space

continues. Sometimes applied in gilded parallelogram shapes (Naito and Nishikawa, 1977,

colour plate 91), it gives a shimmering impression of spacious floorboards continuing around

corners. Coloured panels are traditionally painted with ink and a mixture of powdered seashell,

ground semi-precious stone and nikawa – a gelatinous glue. This matte pigment results in

nearly equiluminant coloured regions, confounding the definiteness of distance, perceived size

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and the flatness, or shape, of the surrounding walls (Akino 2012). Woven tatami mats reflect

light back from the floor, whereas strips of white washi, Japanese mulberry-bark paper, are

pasted low along walls at locations where various small tasks, such as mixing tea, require

better visibility (Figure 1B).

Straight lines are carefully placed so that repetitive sequences are contrasted with irregular

patterns. This is beautifully demonstrated in the irregular bundling together of built-in bamboo

lattices that act as window meshing (e.g., the far left of Figure 1A). Appearing as a regular

lattice from a distance, its inherent irregularity dominates when viewed up close, creating the

impression of different meshes overlaid – another interesting depth and grouping effect.

Where two wooden frame lines intersect, the thinner line will deliberately be misaligned on

both sides of the thicker line to reduce the degree of smooth continuation. Discontinuity across

a visual junction configures into two adjacent T-junctions, thus implying a greater number of

occluding elements than if there were merely a crossing of two straight lines. This enhances

the perception of spatiality, not necessarily veridical depth. In traditional construction layout of

sliding panels in their frames, three nested T-junctions are overlaid at each corner. By ignoring

such a simple detail in modern design, such spatial articulation is easily lost. Nōtan is thus

expressed through light and dark paper, different hues of clay walls, with wooden beams,

gilded wall panels, and windows carefully arranged into an irregular, balanced pattern with a

subtle interplay of light and dark (Figure 1). Combining these devices culminates in an

open-ended, underspecified (and usually, veridically impossible) visual space of many scales

and heaped layers of potential occlusion. When perception discovers these layers, one

experiences a rich depth articulation and a sense of expansiveness in the surrounding space.

Occluding layers – the rich variety of sliding windows, in particular – hint at the spatial

continuation of whatever is occluded. Traditional architects and gardeners are well aware that

a small section of a garden outside, viewed through layered frames, appears much enlarged,

filled with a great number of components, and that the shapes seen within the frame appear

more beautiful (Nitschke 1993). This traditional design wisdom is supported by psychophysical

observation of boundary extension (Intraub and Richardson 1989) – a consistent perceptual

tendency to recall a greater (reconstructed) portion of what was actually seen through a frame,

as if subjects could see beyond occluding edges.

Irregularity is a key aspect of the visual character of naturalistic landscape design. The careful

attention to irregularity in the architectural interior is therefore a powerful visual link to the

designed exterior landscape.

2.3. The green Gestalt school: visual organization in Japanese gardens

The two oldest surviving texts on Japanese garden design originate from 11th century

instructions. Sakuteiki (note: Attributed to Toshitsuna Tachibana, late 11th/early 12th Century)

presents design guidelines in the context of classical poetic metaphor (Shimoyama 1976), the

other – the Sansui manual (Shingen 1466) (note: Attributed to the teachings of the 11th

century gardener priest, Zōen) uses more concise design statements and illustrations as mode

of instruction. Both texts emphasize gardens as a recreation of the profound mystery and

beauty experienced in nature, but not all of nature is considered essential: the designer is

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instructed to search for and emulate places of unusual natural splendour, but not as an

exhaustive miniature replica of nature: a reduction of the number of parts is implied. This

constitutes one of the main challenges in Japanese garden design.

The texts draw attention to naturalistic landmarks that appear irregular and asymmetric (Van

Tonder and Lyons 2005) as most ideal for emulation, and instruct on how to choose natural

materials for its implementation. They give guidelines on what sizes of rocks are needed given

the garden courtyard space. This sets the scale of whole in relation to the rectangular frame of

the courtyard walls. The relative scale of nearest neighbours is also important: they should not

be of equal size or halve the size of the other, but arranged in a one-third or two-thirds size

ratio (Shingen 1466; Slawson 1987). The rule of thirds (Smith 1797) similar to the golden ratio

is also common in Western art and design

The main rocks are first arranged into a structural ‘backbone’, with smaller rocks later added in

‘good agreement’. The shapes of main rocks should ideally be angular and asymmetrical. Their

placement on the ground should never line up, but follow an irregular winding pattern, with

stones interspersed like the ‘scales of a dragon’. If a rock or rock cluster appears to lean in one

direction, its neighbouring elements, of different sizes, should lean back, creating

counterbalance (Jiroh and Keane 2001). This aspect of asymmetric structure is a key towards

understanding visual balance in naturalistic shape (Figure 2A), and even considered in the

empty spaces between rocks (Van Tonder et al. 2002).

Rocks must not be spaced equal distances apart. Exact repetition is avoided where possible.

Informal analysis suggests that the ratio of the averaged size of any two nearest neighbouring

rocks (or rock clusters) to the distance between their geometrical centroids is roughly kept

constant (Figure 6B). In Ryoanji, this ratio is roughly 1:2 (Van Tonder and Lyons 2005), a ratio at

which textural crowding seizes. Textural crowding is the involuntary grouping together of

elements into a texture pattern in which the shape of individual texture elements are not

effortlessly apprehensible (see chapter 13 on texture perception, by Rosenholtz). Hence the

global tessellation of rocks would be as visually salient as the individual rock shapes. The

method seems like a sophisticated proximity-and-size rule, where smaller rocks are placed

more closely together, and larger rocks spaced further apart – another essential aspect

observed in natural rocky outcrops (Figure 2A).

Japanese gardeners today still use the metaphor that a good design will show its ‘skin, flesh

and bones’ (Ogawa 2011) in one glance, meaning that the overall structural backbone, the

shapes of clusters, individual rocks and their textures must all be visible. A rock should be

placed in the original orientation in which it was found in the wilderness so as not to ‘anger its

inhabiting spirit.’ This taboo is a means to preserve the visual integrity between the shape of

the rock as a whole, and the directionality of its smaller facets and surface textures as chiseled

out by erosion, so that the impression of an entire rocky ridge can be conveyed with a single

design component. Rocks should be buried deeply enough that the visual junction with the

ground plane lends it the appearance of continuing as solid bedrock underground (Slawson

1987), instead of betraying the presence of a small, unconnected design component (Figure

2B). A similar practice prevails among Western masons, who match the orientation of stone in

construction to its original alignment in the quarry. Many cultures also pay heed to the

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orientation of timber: matching the dry and wet (North and South) sides of the wood with

architectural conditions on site increases the durability of a wooden construction.

Figure 2. (A) Exposed bedrock, eroded by wind, sun, ice and rain, remains as

irregularly overlapping heaps, facing upwards against gravity, with similar

triangular shapes appearing at many spatial scales. (B) The most visually dominant

rock cluster in the garden at Ryoanji temple, Kyoto. Note the many instances of

triangularity in whole shapes and surface texture markings, with individual rocks

leaning towards each other. (C) The Ryoanji garden emulates a sparse naturalistic

rock outcrop.

Using triadic rock groupings (Shingen 1466) – where each individual rock and rock cluster is

approached as a triangle – allows the design to be conceived of as a multi-scale composition of

triangles, knit into a whole (Figure 2B). Deliberately using a hierarchy of triangular templates is

thought to simplify the mental load for the designer (Arnheim, 1966, 1969) when having to

simultaneously deal with a lot of visual factors, such as asymmetry, proportion and visual

balance (Slawson 1987).

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Medieval Japanese design influenced the Jugendstil, Art Nouveau, Vienna Secession and

Bauhaus, nearly a millennium later, to adopt a renewed sensitivity to irregularity, asymmetry,

minimalism and other factors that characterize perceptual organization.

3. Gestalt principles of grouping and design

3.1. The Gestalt school, Bauhaus and influence of Japanese design

The Bauhaus design school and the Gestalt school of psychology were contemporary

institutions grappling to understand perception in their own terms. One notable Bauhaus

exercise was developed to hone perception of light and shadow, similar to the notion of Nōtan,

by rapid live sketching of scenery as a reduced mosaic grid with as few cells as possible in

different gray values (Itten 1975). The emphasis was on ‘seeing the gist’ and capturing its

impression through drawing of light, dark, curve, and texture.

It is known that Japanese art influenced the Bauhaus (Behrens 2002), as contact between

Japan and the West increased dramatically towards the end of the 19th century. The

minimalism of Japanese woodblock prints and katagami - paper stencils for silk dyeing -

appealed greatly to Western graphic designers, becoming a major inspiration for renewed

clarity of line and emphasis on non-figural depiction. This appeal was not without major

misunderstandings. For example, numerous layers of katagami sheets are used to stencil in

different sections and colours of a textile design, such as a floral motif with birds. Each

separate sheet by itself, however, appears as a strangely non-figural, abstract design. Unknown

in Europe at the time and becoming very popular among members of the Vienna Secession,

these strange looking stencils were mistakenly regarded as intentional abstract designs

(Shin-tsu Tai et al., 1998, p.89-90). “Idealized nature,” a concept shared with (and to some

extent even borrowed from) Japanese design, neatly fits the late 19th c. Western ideas in art

theory (Hildebrand 1893) that again influenced art nouveau, later art deco, and also Bauhaus.

Written vertically, East Asian kanji script is more pliable to the ideals of balanced composition

followed in landscape and figural painting. For example, even normal fluctuations in the

darkness of ink as the brush runs dry create the impression of spatial landmarks (Figure 3 top

right). East Asian scrolls probably began to influence Western approaches to page layout, so

that it is not really surprising that the design of text enjoyed renewed interest among Bauhaus

instructors, such as Moholy-Nagy.

Some medieval European script is among the hardest to read fluently. Spacing is strictly

uniform, key features on individual letters are virtually undifferentiated, and particular

orientations dominate. Visually beautiful (Figure 3 top left), the letters, words and paragraphs

melt into a grey monoglyph that resists fluent reading.

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Figure 3. Examples of page layout and font design. Top left: Section from an

anonymous medieval vellum manuscript. Courtesy of the National Library of

Medicine. Top right: A section from the Tōhakuateshojō letter (Nittsu,1599)

Bottom: Example of a modern font based on Bauhaus ideals.

Typography designers at the Bauhaus, among others, sought the opposite effect: page format

with clearly articulated flow of text lines and paragraphs, with text and figures interspersed in a

more irregular, asymmetrical composition in an effort to improve font design. Good font

balances the salience of individual letters with that of whole words. Overt spacing is important,

but the shape of extremities on individual letters influences the similarity, alignment and

spacing between parts with significant effect on perceptual grouping of letters into words

(Figure 3 bottom) which is incorporated in the technique of ‘kerning’, in which letters with

salient primitives, such as closed bubbles (‘a’), gaps (‘c’), junctions (‘k’,’x’) and bilateral

symmetry (’w’) resist blending into a uniform texture, promoting legibility. The debate on

legibility against readability of serif vs. sans serif fonts dwells further into this matter (Poole

2008).

The mantras of good design relating to design principles developed at the Bauhaus and other

contemporaneous movements bear testament to the importance of the perceptual effects of

sparse, irregular and asymmetrically balanced patterns. ‘Ornament and crime’ (Loos 1908),

‘form follows function’ (attributed to Mies van der Rohe. See Schulze and Windhorst 2012) and

‘less is more’ (Sullivan 1896) actually refer to aspects of good Gestalt and thus, the principles of

perceptual organization.

3.2. Internal laws of perceptual organization

Cross-pollination between the Bauhaus and Gestalt school is putatively evident in their shared

emphasis on concepts such as figural ‘goodness’ – structural configurations that facilitate

lawful perceptual organization. However, the true extent of their mutual influence remains

surprisingly obscure (Boudewijnse 2012). The idea of Gestalt qualities was first proposed by

Christian von Ehrenfels, and later championed by Wertheimer (1924) who was one of the

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founders of the Gestalt movement. The central idea of Gestalt perception was that the

perceptual whole transcends and modifies the properties of the parts. These ideas originate in

work by Brentano and his school of which von Ehrenfels, Wertheimer and other figures in the

Gestalt movement were students (see chapter 1 by Wagemans and chapter 2 by Albertazzi for

an overview of the origins of Gestalt philosophy).

A significant contribution of the Gestalt movement was the derivation of a number of internal

‘laws’ that seemingly govern perceptual grouping. Every visual experience is perceptually

organized as a figure seen on a surrounding background, the visual qualities of the figure and

background (see chapters 8 and 12 on figure-ground, by Peterson and by Kogo and van Ee)

unfolding even in the absence of clear visual markings, such as when viewing a parabolic

Ganzfeld screen (Metzger 1936/2006). Here, the perceptual figure appears to span the entire

visual field, in the form of a thick bank of fog. In oversimplified terms, perceptual organization

is crystallized along structural constraints, such as smoothness of alignment between parts,

similarity or shared commonality in one or more visual aspects, spatial proximity and density

(on parts, see chapter 24 by Singh), the degree of figural completeness or closure in the

arrangement of parts, and the degree of bilateral or higher order symmetry in the

configuration of parts (Koffka 1935). Convex formations (see chapter 9 by Bertamini and Casati)

appear more salient than concave configurations within the same set of parts (Rubin 1921),

and the simplest potential configuration of parts arises as the dominant perceptual figure

(Wertheimer 1938).

Arnheim (1966) presented a powerful vocabulary of higher-level qualities in perceptual

organization, based on his interpretation of order and complexity. He defines order as ‘the

degree and kind of lawfulness governing the relations among the parts of an entity,’ and

complexity as ‘the multiplicity of the relationships among the parts of an entity.’ Order and

complexity are antagonistic yet interdependent. Great design would display a high degree of

order and complexity.

Disorder is the clash of uncoordinated orders among parts, only possible when within each

part there is a discernible order. Structural definition is the extent to which a given order is

carried through. A relation between parts is rational when it is being formed according to some

simple principle such as straightness, exact repetition or symmetry.

Different kinds of structural order can be discerned. Homogeneity, at a minimum level of

complexity, is the application of a common quality to an entire pattern, whereas coordination,

of greater complexity, is the degree to which all parts constituting the whole have similar

importance and carry similar weight. Parts constitute a hierarchy when distributed along a

gradient of importance with regards to the whole. Accident is highly defined, irrational, and

not achieved by an explicit principle.

Arnheim (1966, 1988) discusses ‘directed tension’ between parts as a quality of gestalt. A

universal design strategy is to present a structural center – analogous to the concept of

perceptual figure – from which various tensions are directed to the other elements of a

composition (see also Alexander 2002). Depending on the perceived directionality of these

tensions, different qualitative wholes are experienced. The tensions may be directed in

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obedience to some larger organizing principle, such as gravity. In triangular composition – a

canon of many artistic traditions – the triangle is a centre with a strong directed tension in

itself. In a mandala, the overall tensions are directed towards and away from the centre.

With this articulation of structural aspects discernible in design, Arnheim provided a

vocabulary that still inspires scientific experiments in the perception of design (eg. Locher 2003,

McManus et al. 2011; see chapter 47 by Palmer).

3.3. Design and Koffka’s analysis of art

The Gestalt psychologist Heinz Werner (1956) investigated, among many other aspects of

perception, the human ability to imitate. This led him to postulate that the world is naturally

experienced physiognomically – as if imbued with mood and personality – when the observer

stops explicitly thinking about the metric properties of what is perceived. The animation movie

sequence of simple geometric figures by Heider and Simmel (1944) is a classical example (see

chapter 36 by Scholl). Deeply influenced by Werner, Koffka (1940) presented an analysis– now

mostly forgotten – on the psychology of art. He proposed that the physiognomy of the

perceptual Gestalt was experienced as a relationship between ‘self’ and the perceived ‘world’,

in what he called an ‘ego-world field’ echoing the idea of perception as intentional acts (after

Brentano) and earlier work on the psychology of aesthetics (Lipps 1903).

In Koffka’s analysis of qualities, also developed by Metzger (1936/2006; see Albertazzi, 2010),

the primary qualities experienced in perception concern both part and whole. Spatial location,

lightness and orientation are examples. Secondary qualities are more holistic, extending

beyond point measurements: round, smooth, elongated, spiky, rough, large and so forth. The

tertiary qualities – physiognomy – transcend purely structural levels. The Gestalt as a

perceptual object in the inner realm of perception could be cheerful, graceful, cheeky, sad,

bold, difficult, revealing their fundamental inner nature, or ‘requiredness’, so that one would

know how to behave towards them. Koffka defines the relationship between the ‘self’ and the

perceptual ‘world’ as a field of which the depth, breadth and directionality characterize the

scope of one’s resonance with the perceived world. When the part-whole relationships in a

Gestalt are not lawful – if a certain part occupies the wrong place in this hierarchy, or if it

contradicts its order, if it seems superfluous, or if it shifts the balance by demanding too much

attention – one senses that there is something ‘wrong’ with the design. When a design is not a

self-contained Gestalt, but demands extraneous relationships to be meaningful, the disruption

to the bidirectional self-world resonance is immediately felt.

Koffka’s analysis and the general principles of perception and phenomenology deriving from

the ideas of the Brentano School has profound implications for the relation between

perception and design. In the design process, the true intentions of the designer resonate,

implicitly or explicitly, with the design. Those true intentions set the requiredness of the

perceived design. Hence, the design truly becomes the interface linking the inner perceptual

realms of designer and user. If it violates the physiognomy of the Gestalt, it will distort the

resonance of the self of the user with the perceived design. In such a case, it may be difficult to

articulate exactly what is amiss, but there would be a sense that the design is dishonest. The

intuitive user experience of the perceptual physiognomy of a design is therefore the truer

gauge of the success of the intentions of the designers, than any structured critique. The

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concept of affordances (Gibson 1979) – the way in which object shapes appear to imply their

intended use – derives from the German word “demand character” (Afforderungscharakter)

used by Koffka, Gibson’s mentor, and also reflected in von Uexküll’s use of ‘funktionale Tönung’

or functional tone. Affordances share some aspects of empathy theory (Vischer, 1873; Lipps

1903) and were seriously considered by Hildebrand (1893) in painting and sculpture. More

modern variants of this idea are found in in the mirror neuron hypothesis (Rizzolatti and

Graighero 2004) and perception-action modeling (Preston and de Waal 2002).

4. Nature and design, chaos and symmetry

4.1. Patterns of growth and decay

Vision, with its internal laws of perceptual pattern organization, evolved in nature as its training

ground. Rugged mountain slopes, swirling clouds and the branched structure of a tree, in fact,

brim with part-whole qualities singled out by the Gestalt school. In natural form, these

structural properties emerge from processes of growth and decay that ubiquitously link part

and whole at many different spatio-temporal scales (Thompson 1942), even if different in their

causative origin. Pressure in the earth’s crust and underlying magma, or erosive forces of sun,

rain, and wind, versus cell growth rate depending on the amount of sunlight, nutrient gradients

and carefully clocked hormones, all conjure self-similar structures. The result is that physical

structures more closely related to the same causative origin are more proximal in space and

time, constituting closed convex hulls. The parts will share similarities in size, shape and other

structural properties, and the structural similarities would populate proximal spatio-temporal

scales. Herein lies a potential evolutionary source for the majority of the perceptual laws

discussed by the Gestalt school (see chapter 58 on Gestalt as ecological template).

Essentially, faster growing parts stretch and break away from their source, slam into slower

growing parts, and pile up until the density of material forces a change in the direction of

structural growth. For example, as a tree branch grows, new potential branches are sent off

into various orientations at each branch node, among which only those that result in receiving

the greatest amount of light thicken as main branches for structural support. Over time, the

structure becomes an undulating structural spine with thinner twigs fanning out to cover as

large a surface area as possible (Fig 4A). Similarly, water flowing through a narrowing cascade

accelerates, stretches away from the slower water behind it, and collides with water that

already passed through and slowed down. The crashing water piles up and deflects further

incoming water sideways, into the opposite direction. Structurally, the rushing water is very

similar to a growing branch (Figure 4B).

These are the shapes aspired to when Japanese designers attempt to capture the essence of

nature. The trained eye can uncoil the complexity of that Gestalt into just a few components

that still evoke a similar naturalistic effect (recall Figure 2A).

13

Figure 4. Natural and hand-made patterns of growth and decay. (A) The undulating

branch of a clover azalea. (B) Splashing white foam in a flowing stream. Where the

flow decelerates, the foam changes direction and sends small eddies swirling

outwards. (C) Tracing detail of swirls on a 1st century BC bronze Celtic mirror,

excavated at Dordrecht. The undulating spine coils over four spatial scales,

branching out at sudden changes in direction. (D) A gilded wooden swirl from an

18th Century Austrian baroque palace, showing one complete cycle of piling

(bottom spiral), acceleration (smooth middle section), deceleration (curl on upper

end) and directional change (outwards swirls at the top).

In our natural environment, perfect symmetry is an exception, rather than the rule. When a

drop falls perpendicularly into a still body of liquid, the ensuing collision is sufficiently

symmetrical to allow a perfect splash crown to emerge. Evolutionarily speaking, symmetrical

bodies should demand less complex genetics and motor control. Symmetrical flowers, fruiting

bodies and the bilateral bodies of animals can be regarded as symmetrical collisions between

two or more equal parts. It signals an unusual occurrence on the natural backdrop of structural

hierarchies. For animals, symmetrical configurations strongly hint at the potential presence of

other intentional agents. The necessity for a rapid flight-or-fight response may be the

evolutionary factor driving the acute perceptual sensitivity to symmetry (see chapter 16 on

symmetry perception, by van der Helm). The perceptual dominance of this tendency surfaces

14

when we make designs, as noticed by Japanese gardeners and Gestaltists alike. It can even

become a hindrance when the aim is to create naturalistic design.

4.2. Visual structure in natural landscape and its implications

In a very large survey on global visual preferences, Kumar and Melamid (1995) found that

landscapes resembling Pleistocene savannah were by far the most universally appealing,

whether tested on subjects hailing from tundra, desert or anywhere else. A savannah

landscape typically has a few trees set in level grassland, with blue skies, a source of water in

view, signs of the presence of other humans, mountains in the distance and a path leading off

into the horizon. Apparently, this is the evolutionary imprint of the homonin eden. Its effect is

most pronounced in visual preferences of prepubescent subjects (Synek 1998), but clearly

asserts itself in designed landscapes. Most gardening traditions employ the components

mentioned above (Dutton 2009).

This preference is also interpreted in the perceptual tuning to fractal patterns. Normal subjects

have difficulties in distinguishing true fractals from pseudo fractals, but consistently prefer

fractal dimensions between 1.3 and 1.5 when comparing fractal stimuli (Spehar et al. 2003). It

is thought that tradeoffs between strategies for visual reconnaissance and hiding are optimal at

this level of visual complexity. Unsurprisingly, savannah grassland has a similar fractal

dimension.

Measured in the 2D visual field, eye movements during a search task trace out a trajectory with

a fractal dimension of about 1.4 (Fairbanks and Taylor 2011). Compared to either fractal

trajectories or linear scanning strategies, the 1.4 search path is more effective in discovering

targets in the visual field. A tantalizing possibility is that preference for 1.4 dimensional fractal

landscapes, and the wider recurrence of self-similar structure in human design, is due to the

close resonance of these structures with evolved search strategies implicit in eye movements,

hence allowing perceptual organization to function in an optimal way not yet well understood.

Natural images display an inverse power distribution in their Fourier power spectra,

reminiscent of the power laws observed by Zipf (1949). Fourier spectra of artistic images from

Western and Eastern traditions also obey the same inverse power law, even if in a dense form

(Graham and Field 2007). The finding is interpreted either as an aesthetic effect (Spehar et al.

2003), namely, that artists implicitly recreate natural scene statistics (see chapter 14 on

statistical features, by Dakin) because of aesthetic preferences, or purely as an adaptation to

scene statistics (Graham and Redies 2010), that is, artists intuitively present visual markings

that the visual system can properly parse, regardless of aesthetics.

5. Future directions for the scientific exploration of perception and visual design.

As discussed above, perception and design share deep connections. Evolution already shaped

the visuo-motor skills necessary for stone knapping hominids in Olduvai, 2.6 million years ago,

demanding acute perceptual sensitivity to the smoothness of convexity on chipped stone

surfaces (de la Torre 2011). By 800,000 years ago, design has evolved into a process of shaping

and assembly of meaningful parts, and has been in practice long enough to assert itself in the

15

perception of Homo sapiens.

With the advent of three and four dimensional printing, the assembly-by-parts approach is

about to become replaced by assembly of Cartesian layers. A motor with all its movable parts,

all made from different materials, can be printed as a complete, fully functional configuration

from the outset (ZCorporation 2010). Virtual three-dimensional folding of shape enables

design unconstrained by physical material limitations imposed in our normal environment

(Hansmeyer 2012). How these new visual forms outside the realm of ‘organic’ assembly will

affect the laws of perception is an open question.

Analytical effort aimed at automating the design process promises to free human designers

from overwhelming repetitive details (Jupp and Gero 2006). In fact, there is such an enormous

amount of bad design in the world, that one may wish for the coming of the great

‘design-o-bot.’ However, as authors with a passion for art and science, we would like to see

greater scientific understanding of design and its process, but not with the aim of removing the

human designer from the loop. It should better equip the coming generation of designers,

instead of planning their extinction.

6. Acknowledgements

The authors thank Johan Wagemans, Steve Palmer and the anonymous reviewers for many

helpful comments. Thanks also to Branka Spehar for finding the 1940 essay on art and

psychology by Koffka.

16

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Supplementary material

1. Measures of designed structure

1.1. Stylistic visual signature

The Shin-Gyō-Sō levels of visual formality in Japanese design, and Gestalt observations of

reification (perceiving a complete whole from incomplete parts) and invariance (perceiving a

constant whole even if parts are distorted) (Lehar 2003) bear on the fact that perceptual

organization of figure and ground continues normally even when the parts are deformed, as

long as a consistent transformation is applied throughout.

Style, at various levels, can be compared to such a broad transformation. Think of a cathedral,

built in the gothic style. First, it is clearly distinct from other architectural styles, even those

that are also intricately hewn from stone. One can conceive of the gothic church as a

featureless house, which is then transformed so that its components are elongated in the

vertical orientation. Each salient part, such as a sloped point, window or corner, is locally

multiplied at slightly different locations and spatial scales. These are then selectively further

elongated, vertically. All upper horizontals are replaced with gothic arcs. With a knotted vine

motif as a final touch along the edges, what started as a normal house will have a distinctly

Gothic appearance.

Second, the same Gothic building can be interpreted and its style conveyed through a different

visual style – for example, as a sculpture made out of scrap metal. Welded into position,

different rusted metal rods can conjure in assembly the visual signature of vertical elongation,

arcs, knotted vines and other features that characterize a structure as Gothic.

Third, either the cathedral or the sculpture can be shown in a picture, in different visual styles.

It can be a photograph – again taken in any of a huge array of photographic styles – or it can be

drawn as an architectural plan, the outlines of every part clearly emphasized in absence of

textures and colours. If sketched in charcoal, the rough, dusty strokes may evoke a granular gist

of light and shadow; it can be painted in oil, with dapples of colour, and not so much boundary

contours, conveying an impression of the arcs, spires and gargoyles. Through copper etching, it

may be shown in a sea of black dots and scrapes that swarm into an instantly recognizable

gestalt of a gothic church. All of these designs, if well executed, will convey a distinctly ‘gothic’

character.

One visual style can therefore be presented in another stylistic mode, with each layer of style

retaining its own character. Style is primarily a qualitative visual system, and mastery of style

implies consistent application of a given transformation to all the parts, embodying the Gestalt

notion of invariance. The fact that the gothic style is still recognizable when depicted in stylized

– often disconnected – markings bears witness to the efficacy of Gestalt reification.

Proportionality is a key feature of natural shape (Thompson 1942), giving distinct species their

unique structures. Proportional systems are already present among the oldest human made

20

visual designs, such as bodily proportions used in Paleolithic art (Francis 2001). Specific

proportions canonize the design shapes of different ancient civilizations, such as the instantly

recognizable proportions of an Egyptian sculpture or funerary mask. In the proportional

systems used in font design, or depicting the human body (Massironi 2002, 35-43) by da Vinci,

Dürer, Le Corbusier and many others, proportion refers to consistent spatial size relationships

between defined parts. In other stylistic effects, proportion can refer to the relative amount of

colour to the amount of luminance contrast, the salience of contours in relation to the salience

of colours (think of Monet’s impressionist painting style versus a cartoon by Hergé), or textures,

or it can relate to the degree to which contours are locally deformed, or even disconnected,

while grouping globally into a specified configuration. If applied to various objects in the same

style, these objects appear to belong together.

1.2. Structured empty space and medial axis representation

Perceptually, the empty space – what artists often refer to as negative space (Arnheim, 1966,

p.130) – is more emphasized in a deliberately sparse landscape composition (Tanizaki 1933;

Nitschke 1993). When the rocks and the empty spaces between them are particularly clearly

articulated、such as the flat gravel courtyard with five rock clusters at Ryoanji temple in Kyoto

(Figure 2C)、even modest analytical means could reveal essential structural aspects of the

design. Here, we will give an example of such an analysis, using medial axis transformation.

Figure 5. (A) Medial axis transformation of the empty space between two points:

any point on the medial axis is equidistant from the two points. (B) The set of

centres of the largest included disks that touch the boundary contours of this

triangle trace out an inverted ‘Y’-shaped medial axis. (C) Medial axis

transformation of a human silhouette appears as a skeletal midline along the body

and limbs. Local maxima - or medial points - are emphasized in black.

Blum (1973) conceived of the medial axis as a means for compact shape encoding. Medial axes

can be thought of as the set of loci that would run along the central skeletal spines of the main

body and protrusions of a shape silhouette (Figure 5C). It can be computed via various

methods, for example, by collecting the centroids of the set of all the largest possible disks that

can be locally fitted into a silhouette shape (Figure 5B). Psotka (1978) showed that points

coinciding with medial axes are highly salient, apparently playing a role in guiding attention

during perception of whole figures. Kovács et al. (1998) suggest that certain sets of stable

points on the medial axis may be perceptually significant when keeping track of biological

shapes in motion. These medial points seem to overlap with the coordinates at which motion

21

sensors placed on a moving agent translate into believable impressions of bodily movement.

The empty space between the stones in Ryoanji would be encoded as a compact structural

skeleton connecting all the open gravel spaces. This reveals the medial ‘shape’ of the negative

space. The empty space globally constitutes a dichotomously branching structure (Figure 6A,D)

resembling small rivulets successively converging into a single axis (Van Tonder et al. 2002).

With counterbalanced branching angles and limb length increasing logarithmically from outer

branches towards the main converging trunk, it resembles the branching structures ubiquitous

throughout nature (Prusinkiewicz and Lindenmayer 1990). A similar branching structure

converges outward from the most conspicuous rock cluster on the left (Figure 6A,C). Adding or

removing any element in the composition significantly disrupts the ordered structure of the

empty space. Even if dissimilar from at a glance, baroque vista gardens can also be represented

as branching networks. This level of abstraction thus enables a more sophisticated comparison

of different landscaping traditions.

Figure 6. (A) Medial axes in the empty space at the Ryoanji dry rock garden form a

four-leveled dichotomous branching tree. Thin lines indicate the architectural

layout of the temple before it was destroyed in 1797. The intended viewing

location is indicated by the letter ‘O’ inside the central hall. (B) Note the relative

size-distance relations between nearest rocks. Taller rocks are shaded darker.

Rocks in the left most cluster (C) and the whole set of clusters (D) do not line up,

but are arranged into irregular folding screen configurations facing the viewing

location.

Medial axes designate information rich loci where maximal amounts of shape boundary

surfaces can be encoded with minimal parameters (Leyton 1987). A practical consequence in

Ryoanji is that the surface facets from the entire set of rock clusters (approximating each

cluster with a convex hull envelope) are best surveyable at the most global medial point Y.

There are obvious evolutionary connotations with placing the viewer in a location that affords

22

high visual access to the surroundings. Strikingly, this point is near one of the intended viewing

points of the garden, the centre ‘O’ of the abbot’s hall in the original architectural layout.

Classical illustrations depict the Ryoanji rock garden from this viewpoint (Akisatoh 1799).

Outlining the central loci of empty spaces, medial axes also map the paths of least obstruction

for spatial navigation.

The original intentions with the Ryoanji garden design are not exactly known, but the

probability of randomly stumbling upon this composition is sufficiently small (Van Tonder 2006)

to suggest that the perception of visual balance and other proportional relationships may be

particularly acute when a subject’s viewing location is physically aligned with the medial loci of

the viewed spatial layout, a perceptual consequence related to natural mapping (see the

section on natural mapping, later in this chapter).

1.3. Isovist theory and Space syntax in urban and architectural layout

Isovist theory (Benedikt 1979), another analytical approach to visuo-spatial accessibility,

predicts the perceived degree of spaciousness of an architectural space. An isovist graph is one

which is computed using the viewing position of the viewer and sampling the sight lines in all

possible directions. The two dimensional isovist in a room can be thought of as the set of rays

or sight-lines that would emanate outwards from the viewer in every direction and terminate

on an architectural structure (Figure 7A, B). The isovist graph is a plot of the length of each

sight-line against angle, with the viewer’s direction of gaze as the zero angle reference (Figure

7C, D). Graph entries can be scaled down with distance away from the direction of gaze to

enhance the predicted differences in perceived spaciousness. Using the technique, a

rectangular room is predicted to appear more spacious when viewed from a corner than when

it is looked at from the middle of a wall (Figure 7C, D). The isovist theory was developed by an

architect trying to address the discrepancy between physical floor space – a fixed number of

square meters regardless of where the entrance is – and how the architectural plan and

placement of entrances influence the appearance of spaciousness. In tea architecture (Figure

1), entrances are placed in room corners to convey a sense of greater spaciousness (Suzuki

1979), a device underscoring the predictions of isovist theory. Combining isovist theory with

medial axis transformation, space syntax theory (Hillier and Hanson 1984) successfully predicts

the known density patterns of traffic and pedestrian flow in major cities and architectural

spaces around the world. The Olympic Delivery Authority (ODA) used space syntax in planning

the complex 2012 London Olympics and Paralympics infrastructure. Its success underscores the

observation that humans visually assess a path for greatest visual accessibility, simplicity and

depth of sight-line.

23

Figure 7. Isovists projected from the (A) corner and (B) side of a rectangular room,

and their sight-line graphs (C,D). Here, sight-lines are linearly scaled down away

from the direction of gaze (center red bold line) to emphasize the influence of the

viewing direction. The area under the isovist graph is (C) larger for the corner

projection than from the side (D), predicting that the room will look more spacious

from this viewpoint.

1.4. Bilateral symmetry and self-similarity in human design

In the use of bilateral symmetry, perceptual organization completes a full circle, from nature as

the driver of perceptual evolution, to the internal laws that shape how we see, and affect what

will become salient in our designs. Even the oldest known human-made engraving on an

80,000 year old stone blade reflects our resilient natural tendency toward symmetrical design,

attention to the central axis of symmetry, exact repetition of shape and interval, and smooth

alignment between parts (Henshilwood et al. 2002).

Strictly speaking, self-similarity, reflections, translations, rotations and other transforms are all

scalar aspects of symmetry (Weyl 1952), but at an intuitive glance, self-similarity and symmetry

– bilateral symmetry in particular – appear qualitatively different enough that designers and

artists distinguish between the two.

In hindsight, it is obvious then that the self-similarity of natural form would emerge,

throughout many epochs in human design (see chapter 17 on hierarchical patterns, by Kimchi).

Cathedral and temple architecture in particular complements a high degree of various aspects

of symmetry with a repetition of the whole in its parts, in some cases over many spatial scales

24

(Bovill 1996). Medieval Japanese garden design guidelines developed from the refined

observation of actual rock formations and many attempts to recreate nature’s essential

balanced asymmetry, in spite of the innate human perceptual bias towards more pronounced

bilateral symmetry.

The self-similar circular layout of Ba-ila villages in southern Zambia (Eglash, 1998, p. 27) recurs

over at least three spatial scales. The gates to Ba-ila villages, compounds and the entrances to

individual dwellings are arranged along various axes of symmetry that relate to a global

structural centre onto which all the constituent parts converge. The layout of Tang Dynasty

capitals represents self-similarity in a rectangular format (Nitschke 2000). The city as a whole,

its aristocratic quarters and normal compounds, down to the main hall of each compound, are

laid out as bilaterally symmetrical rectangles, centred along a central north-south axis with a

protective barrier and deity on the north side, and a main entrance toward the south - a

self-similar arrangement spanning four orders of magnitude.

Flourishes, knots and mazes commonly adorn an infinite range of designs throughout the ages

(Gombrich 1979), appearing in African carvings, textiles and basketry, Greek mosaics, Roman

frescoes, Celtic mazes and accessories (Figure 4C), engraved Mayan masonry, Islamic

arabesques, curling vines in Indonesia, lattices depicting lightning and smoke in East Asia, leafy

branches in European cathedrals, and shell motives in Baroque palaces (Figure 4D). In essence,

these decorations are stylistic signatures of undulating growth and decay, patterns fitted into

symmetrical, regular frames to suit rectilinear human-made objects. While on the surface, the

possibilities for doing so may appear infinite, there is a surprisingly limited set of unique spatial

arrangements for tiling such motifs into one, two and three dimensional patterns (see chapter

45, by Koenderink).

The drip paintings by Jackson Pollock exhibit unexpected fractal properties (Taylor at al. 1999).

Created before the advent of the formalization of fractal geometry by Mandelbrot (1977),

Pollock obviously acted upon his perceptual experience, whether that involved implicit

perception of fractal structure or some other equivalent order. In his own words, he tried to

‘capture the language of nature’.

1.5. Natural mappings

Natural mapping (Norman 1988) emphasizes the importance of resonance between form and

function. Specifically, natural mapping refers to a design methodology where the layout of

controls is intentionally arranged to resemble the spatial layout of the designed object or

environment. Consider, for example, a gas stove top with four burners arranged into a square

layout. By aligning the control knobs for the burners in a straight line, it is not clear which knob

maps to which burner. Even after repeated use, users may still make mistakes, when all it

would take to create a flawless interface would be to place the four knobs into a square

pattern that visually matches the layout of the burners. According to Norman, great designs

require neither labels nor manuals, but are sufficiently intuitive to be used on the fly. The

alignment between the user, controls and the design itself is also important for fluent use. We

know from experience how difficult it can be to navigate from a map that is rotated relative to

the actual surroundings, even if it is an accurate mapping of the terrain. Through the use of an

intentional viewing point, classic Japanese gardens place the viewer within a natural mapping

25

from which the visual balance and other features of the design can be most acutely

experienced – a form of natural mapping for aesthetic enhancement.

On the scale of architecture, the new Seattle Central Library, by Koolhaas and Prince-Ramus

(Goldberger 2004) presents a natural mapping of the romanized alphabet. The entire floor

space in the building consists of one long alphabetically indexed walkway, coiled into a huge

helical spiral. One can thus literally walk from book indices A to Z in one single stretch, a very

efficient design for both staff and users; although in this case the mapping is not directly

perceptual but requires cognitive knowledge of the relation between letters and organization.

The design has been met with mixed emotions, for reasons other than the successful helical

design (Cheek 2007).

Natural mapping can be extended to the structural mapping of the physical human body. The

chair is an example of a hugely successful design because it naturally maps to the body. The

seat, arm rests, opening for the legs, and rest for the back and head nearly resembles the

visual layout of the user’s anatomy, resulting in an intuitively grasped design. Grasping a design

this fluently reveals some discrepancies in perception of the actual qualitative experience of

physically interacting with that design: some of the most beautiful design chairs have also been

note for the extreme discomfort they deliver, to the surprise of both their makers and users.

Ba-ila villages and Tang dynasty cities represent large-scale examples of natural mappings with

bilateral symmetry along a central axis, and with a clearly directional head-and-tail assignment.

As with a chair, these design layouts are suggestive of the human body. In fact, in traditional

maps showing the layout of Zen temple complexes in Kyoto, the names of architectural gates,

paths, halls and facilities within the temple complex are typically inscribed on a human

silhouette (Masuno, 2008, p.150), where the human silhouette is spread in the ‘Vitruvian man’

style, with different parts mapped to specified body parts.

Self-similar urban layouts mapped to the body are doubly powerful. First, there is the mapping

with the familiar body. Second, grasping the mapping of urban organization at any spatial level

informs one’s knowledge of its organization at other scales.

26

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