2004 Dresden Archaesth Vantonder (1)

7/28/2019 2004 Dresden Archaesth Vantonder (1)

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INCOMPLETE INFINITY: STRUCTURE IN A JAPANESE GARDEN

VAN TONDER, Gert J akobus,

Lecturer in visual cognitive science,Dept. Architecture & Design,

Kyoto Institute of Technology,

606-8585, J apan

email:[email protected]

J apanese dry rock gardens are synonymous with naturalistic, even if abstract, landscape design.

Appropriate composition, executed with natural materials, overrides the potentially uninteresting emptiness

of a sparse garden courtyard. Drawing from karesansui gardens in Kyoto, this paper considers their calm,

rich visual appearance as the outcome of visual mental completion. In karesansui, one can see only partial

views of garden elements. Rather than presenting the viewer with a literal recreation of nature, such

elements evoke a strong sense of the holistic natural structures which they potentially can form a part of.

For the sake of clarity, I show examples of global and local structural analysis, in rock clusters, and in the

empty spaces between them. The analysis derives from previous work, linking the medial axis

transformation (Van Tonder, Lyons & Ejima,2002), with human perception of visual structure in Ryoanji.

Comparison reveals that visible elements, like rocks, serve as local `seeds from which subliminal global

shape can be perceptually completed. Local shapes suggest an infinity of scale in global structure, and vice

versa. This complementary relationship leads to ordered visual complexity of a very natural kind, even if

mostly not directly visible. Advances in fractal geometry suggest a close relationship between natural

structure and infinity of scale. Thinking in terms of rich structural infinity in a paradoxically empty garden

courtyard may serve to deepen our understanding of the visual effects achieved in J apanese rock gardens.

It may also offer inspiration for improving the naturalism of other architectural settings through the use of

hidden structures of infinity.

1. Background

J apanese karesansui, or dry rock gardens, are well known for their natural, yet empty,

appearance. Their aesthetic appeal seems to go beyond existing cultural and

philosophical interpretations, since karesansui is usually appreciated by individuals

unfamiliar with esoteric and theoretical concepts in Zen gardens. As a visual cognitive

scientist, I am interested to see if the intrinsic visual qualities of dry rock garden design

enable some objective insight into the visual appeal of these gardens, and if such

insights are applicable to landscape design, on a wider scale.


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This presentation shows part of ongoing research, that investigates how karesansui

design affects the brain mechanisms of human visual perception, in an attempt toobjectively understand (1) the design effects, and (2) visual appeal of this style of

J apanese garden.

The intention with the work is not to discard non-scientific interpretations, but to add

some otherwise inaccessible insights to the current understanding of J apanese gardens.

2. Mechanisms of visual perception

The visual system constantly needs to distinguish between object figures for attention,

and the surrounding background, to provide contextual information for planning of the

appropriate course of action (Gregory, 1998). However, retinal signals serve as limited

information of shape, and the brain has evolved with various mechanisms to reconstruct

incomplete visual parts, and group them into meaningful global wholes.

The gestalt school of psychology (Koffka, 1935, Wertheimer,1938) observed various

factors that describe which visual parts group. The author distinguishes between

dominant grouping factors, i.e. symmetry, good continuation, and contour closure, and

subtle grouping factors, namely, proximity and similarity. A discussion of the

neurological basis of the grouping factors is beyond the scope of this presentation, yet,

the vision research community has researched this topic extensively (Kovacs, 2000,

Elder & Goldberg, 2002).

The natural visual surroundings in which humans evolved, teems with fractal structure

(Mandelbrot,1977). In a nutshell, fractals are patterns where subparts and wholes

resemble each other. For example, the shape of a branch is approximately the same as

the shape of its parent tree. A smaller subsection, cut from this branch, would again

resemble its parent branch, and the whole tree, as well. Mathematical description of

fractals allow for infinite repetition of scale, whereas fractal structures of nature repeat

the same structure only over a limited range of scales. The fractalness of natural shapes

must have influenced the evolution of our brain mechanisms of perceptual grouping. For

example, more proximal parts in natural shapes are usually also more similar in shape,

and parts of the same natural object are usually more similar in shape than parts

belonging to other structures.


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It then comes as no surprise that grouping factors, like proximity and similarity, are

effective indicators of how well visual parts would be grouped together. Psychophysicalexperiments confirm that humans perform better in perceptual tasks where local parts

resemble global stimulus shape (Navon, 1977, Kinchla & Wolfe,1979).

3. Naturalness: The aesthetic ofkaresansui

The two oldest surviving J apanese garden design manuals, the Sakuteiki, an

anonymous 11th century scroll (Shimoyama, 1976), and the text, Sansui narabini

yagyounozu, (Zouen, 1466), both emphasize that capturing the essence of nature is the

chief aesthetic ideal of J apanese gardens. Since fractal structures form such a

fundamental part of nature, the question, of whether karesansui gardens are recreations

of fractal structure, naturally arises.

The two old texts provide various design guidelines that engender the creation of

gardens with, among other qualities, a natural, infinite, asymmetrical and simple

appearance. This suggests that the old garden manuals were compiled by masters with

a keen eye for visual (perceptual) effects in gardens. In fact, previous research draws

parallels between the old garden design guidelines and the grouping factors, observed

by the gestalt school (Van Tonder & Lyons, forthcoming).

The old texts caution against the use of bright colours, striking textural contrasts,

symmetrical shapes, and smooth alignment of design elements, like rocks. It suggests

irregular spacing of plants and rocks, in winding patterns, and give many guidelines on

how to create visually balanced rock compositions. For example, the guidelines

describe relations between the size of the garden courtyard, size of rocks and distance

at which clusters and rocks should be spaced. It further recommends that rocks must be

chosen and planted such that their natural textural grain matches their overall shape,

and again, that shapes of rocks and rock clusters should appear roughly triangular.

Rocks are supposed to be set firmly, with about two-thirds of the rock below the ground,

to ensure a natural appearance. The list of design effects described in the old manuals,

contains many other instances of critical visual factors that bear upon perceptual

grouping. Recent work (Van Tonder & Lyons, forthcoming) suggests that the karesansui

style not only avoids patterns of dominant perceptual grouping, such as symmetrical

shapes and compositions, but engender many levels of subtle grouping, through


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repetition of similar shapes on many scales (similarity factor), and relative spacing

(proximity factor) that gives figure and background (i.e. rocks and empty sand,

respectively) equal visual salience.

4. Infinite structure in dry rock gardens

The texts describe rocks and plants as forming the structural backbone of the garden.

This global structure has previously been investigated via medial axis transformation.

The latter was conceived as a mechanism to describe biological shape (Blum, 1973).

The transform is analogous to spreading grass fires, that terminate where no grass is

left to burn. For example, three fires (Fig. 1A, black dots) will spread and die out where

the grass is burnt up from all sides, i.e. along the black lines. These lines reveal the

medial axis structure of the space between the three points. If the fires were started all

along a triangle, the medial axis resembles an Inverted y-shape (Fig. 1B). The medial

axis of a human figure looks like a skeleton (Fig. 1C). Psychophysical experiments

revealed that the human visual system is subconsciously sensitive to medial axes

(Kovacs, Feher and J ulesz,1998).

Medial axis transformation reveals an unsuspected degree of structural organization in

the visual ground, or empty space, of Ryoanji, a representative example of Zen gardens

(Van Tonder et al., 2002). Similar structure, of visual ground, occurs in various other

examples of karesansui (Fig. 1D-1G). The medial axis structure of such gardens

explicitly shows that the empty spaces between rocks and rock clusters are arranged

with the same statistical self-similarity, characteristic of natural structures, where global

shape and its local subparts are alike in shape. In fact, the structure of visual ground

here resembles the branches on a tree, or alternatively, many small rivulets flowing

together along a connected network of larger and larger confluent rivers.

Even when only a limited section of a mountain, rock, or tree, is visible, humans have no

trouble in perceiving the shape in its entirety. Especially in fractal structures, a few

levels of shape is sufficient to enable our visual systems to interpolate, and so

reconstruct, the entire structure as it would unfold over an extended range of spatial

scales. The self-similarity of structure in visual ground is therefore significant: It is the

structural seed from which the mind perceptually completes visual ground as an

infinitely extending, naturalistic structure. Similarly, the self-similarity of visual figure

(arrangements of plants, rocks, rock clusters, etc.) is the perceptual cue from which the


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visual system can complete the backbone of the garden as an infinitely extending

naturalistic structure.

Figure 1. Medial axis transformation (MAT) of three intuitive visual figures, A-C. MAT reveals structure in

the empty spaces of rock gardens. In D-G, the MAT between rock clusters is indicated by dark branching

patterns. Where relevant, architectural structures are indicated by rectilinear boxes.

Natural textures often display an inverse relationship between spatial frequency and

spectral power (Fig. 2A). Such patterns are called 1/f textures. In the experience of the

author, free viewing of 1/f textures causes perception of various dynamic shapes. Most

people are familiar with the perception of faces, animals or other shapes in the textures

or carpets, soil, or an earthen wall, such as those erected around many karesanui

gardens (Fig. 2B). Leonardo daVinci remarked that inspiration for a difficult visual


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composition can be found in the dirt stains on an old wall.

Thus, infinity is further suggested through natural textures on surfaces of most gardenelements, such as rocks, courtyard walls, and gravel. Whereas perceptual grouping in

such (noisy) textures should not favour any particular shape, the similarity factor

prompts the prediction that a given shape, X, placed next to a natural texture, would

bias perception into grouping texture elements such that the whole would resemble

shape X. Thus, when placed in the vicinity of a given rock shape (Fig. 2D), perceptual

grouping in a nearby 1/F texture, such as an earthen wall, becomes biased toward that

shape, and the viewer is likely to perceive the biasing shape of the rock recurring within

the texture of the wall (Fig. 2C). Here, the simple wall thus serves as virtual extension of

the structure of rocks and rock clusters, thereby altering the perceived fractal dimension

of the garden.

Figure 2. Perceptual grouping in natural textures is biased by shapes of nearby objects.

Again, this is an instance where appropriately chosen materials lead to perceptual

completion of the garden as an infinite structure. This is an area left open to rigorous

investigation, and part of future research on human visual perception in J apanese

gardens.

Perceptual completion can also be induced by visual cues that signal visual occlusion

between object surfaces. For example, a Kanizsa figure (Fig. 3A) is an instance where


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visual cues (the four black pacman shapes) induces the completion and perception of a

vivid white square occluding four black disks or spheres. Specialized mechanisms in the

visual system, triggered by the tangential visual junctions on the pacman shapes (Fig.3B), perceptually complete the surface and boundary contours of the white square, and

at the same time complete the missing parts of the disks, so that one grasps and see

complete objects (Fig. 3C and 3D). The visual system relies so strongly on this

ecological assumption that one literally sees the white square, as an explicit shape with

explicit outlines. The effect is so strong that it can override the seemingly more logical

groupings of other visual cues in the same scene (Purghe,1998), such as a mountain

landscape (Fig. 3E).

Figure 3. Perceptual completion due to occlusion junctions may create the impression of rich, infinite

structure in a karesansui rock composition.

In a garden, occlusion cues trigger perceptual completion of shape. The clearer and

stronger the occlusion cues, the more vivid the completed structure. By placing rocks

deep in gravel, gardeners ensure strong occlusion junctions between the rocks and

sand (Fig. 3E). The author believes that the angles at which stones are set, are carefully

chosen to direct perceptual completion outwards, so that instead of completing the

shapes of individual rocks, one rather senses their potential completion into

neighbouring objects. Of course, most of this completed meta-rock cluster is only virtual,


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perceived as extending under the gravel of the garden courtyard (Fig. 3G and 3F).

Smooth alignment serves as a very strong cue to perceptual completion of occlusion

structure. By arranging rocks and rock clusters at irregular intervals relative to eachother, gardeners prevent perceptual completion from finding a simplistic terminus.

Perceptual structure of rock clusters is therefore again spread out, towards other garden

elements, as the visual system reconstructs the continuation, of each rock, below the

gravel. Similarly, strong occlusion junctions between rocks, and between plants and

walls and hedges, provide occlusion cues from which perceptual completion ensues. In

a visual scene ofkaresansui rocks, the combined effect of occlusion junctions and the

visual system`s sensitivity to self-similar patterns, should therefore give rise to

perceptual completion of a complex fractal structure (Fig. 3H), thus literally imposing a

rich, infinite structure t be perceived in an obviously sparse composition. Could this

underlie the intuitive sense of paradox when looking at karesansui?

5. Conclusions

This presentation introduces (1) previous work on the visual structure of a Zen garden,

and human visual perception of J apanese gardens, and (2) ongoing research, on visual

cues that support perceptual completion of structure, and self-similar, naturalistic and

possibly, infinite, structure, in karesansui.

If the hypothesis turns out to be correct, some of the major compositional achievements

of J apanese dry rock gardens lie in (1) the activation of brain mechanisms for

perceptual completion of visual structure, (2) selective activation of completion

mechanisms, towards the reconstruction of self-similar (recursive), infinite structure, (3)

elimination of visual cues that would support simplistic, non-recursive, completion, and

(4) the activation of completion mechanisms by the appropriate use of sparse visual

compositions.

This approach to landscape design enables the creation of complex, naturalistic

perceptual structure through a minimal number of design elements. Even if the explicit

visual structure of such a composition could be considered incomplete, its implicit,

perceptual equivalent is not just complete, but also infinite.

Here, I would like to point out a practical implication for current architectural landscapes.

It raises the tantalizing possibility that designs, with perceptually infinite structure, can


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be created by the appropriate placement of only a few structural seeds, in an otherwise

relatively empty setting. In a town surrounded by mountains, for example, sensitive

setting of appropriate rock clusters in a public space could engender a powerfulperception of the greater landscape being richly innervated, and drawn into, that space.

The success of such a minimalist approach depends on how well the visual cues

essential to perceptual completion, as presented in this paper, are presented in the

design. I would like to suggest that the 1466 illustrated manual on karesansui design, in

which the priest Shingen transmits the 11th century teachings of Zoen, already provides

good instruction on how this task may be accomplished.

This work shows that various compositional effects have to be considered to

successfully implement perceptual completion as a design strategy. Irregular placement

of design elements, creating appropriate occlusion junctions for their extension behind

other surfaces, ensuring their internal self-similarity, and covering the surrounding

empty surfaces with naturalistic textures to extend the self-similarity of structural seeds,

are examples of aspects that must be taken into consideration. May this inspire you to

create wonderful new landscapes!

6. Acknowledgements

I would like to thank Gunter Nitschke, for many insightful discussions on issues related

to the topic presented here. This research was supported by the Kyoto Institute of

Technology.

7. References

1. Blum, H. (1973). Biological Shape and Visual Science (Part I). J ournal of

Theoretical Biology 38, 205-287.

2. Elder, J .H. & Goldberg, R.M. (2002). Ecological statistics of gestalt laws for the

perceptual organization of contours. J ournal of vision, 2(4), 324-353.


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3. Gregory, R. (1998) Eye and brain: The psychology of seeing. 5th Edition. Oxford:

Oxford University Press.

4. Kinchla, R.A. & Wolfe, J .M. (1979). The order of visual processing: Top-down,

bottom-up, or middle-out. Perception & Psychophysics, 25, 225-231.

5. Koffka, K.: 1935. Principles of Gestalt Psychology. New York: Harcourt, Brace &

Co.,

6. Kovcs, I. (2000). Human development of perceptual organization. Vision

Research Special Issue on Attention, 40(10-12), 1301-1310.

7. Kovcs, I., Feher, A. & J ulesz, B. (1998). Medial-point description of shape: a

representation for action coding and its psychophysical correlates. Vision

Research 38(15/16), 2323-2333.

8. Mandelbrot, B.B. (1977) The fractal geometry of nature. New York: W.H.

Freeman and company.

9. Navon, D. (1977). Forest before trees: The precedence of global features in visual

perception. Cognitive Psychology, 9, 353-383.

10. Purghe, F. (1998) Can illusory figures be transparent and opaque at the same

time?, Perception, 27(3), pp. 337-340.

11. Shimoyama, S. (1976). Translation ofSakuteiki: The Book of the Garden

(Tokyo: Town and City Planners). Attributed to Toshitsuna Tachibana, late

11th/early 12th Centrury.

12. Van Tonder, G.J ., Lyons, M.J . & Ejima, Y. (2002). Visual structure of a J apanese

Zen garden. Nature 419, 359-360. Manuscript supplement available at:

http://www.cis.kit.ac.jp/~gert/publications/selected_publications.html


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13. Wertheimer, M. (1938). Laws of organization in perceptual forms. In W. D.

Ellis (Ed.), A sourcebook of Gestalt psychology(pp. 71-88). London, UK:

Routledge and Kegan Paul.

14. Zouen. Senzui Narabi ni yagyou no zu (Illustrations for designing mountain, water

and hillside field landscapes). Published in Sonkeikaku Library, Sonkeikaku Soukan

series. Tokyo:Ikutoku Zaidan. Transmitted by Shingen in a manuscript dated 1466.

Original teachings thought to date from 11th century (11th Century).

2004 Dresden Archaesth Vantonder (1)

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