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Rock Gardens-Planning and Visual Perception in Rock Garden Designing

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Abstract and Figures

A rock garden, also known as a rockery or an alpine garden, is a small field or plot of ground designed to feature and emphasize a variety of rocks, stones, and boulders. Gardeners who enjoy growing a wide variety of plants are the best advocates of rock gardens. This type of garden can contain a mixture of evergreens, deciduous shrubs, bulbs, perennials and annuals. Collectively, the design they create is a myriad of colour, form and texture. Rocks, purchased or on-hand should provide the basic framework of the design. The best arrangement will look as if nature had a hand in it’s creation. Observation of natural outcroppings along highways and hillsides can be copied on a miniature scale. We can group small rocks together to give the impression of larger masses worn away by time and weathering. Medium stones should be used in groups of two or three. Bury large boulders halfway in the ground for stability. Cohesiveness is best achieved by using only one kind of rock in the garden. Limestone and sandstone are the two types readily available in this area.
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Rock Gardens
Planning and Visual Perception in Rock Garden Designing
CONTENTS
I. Introduction
II. History
- Rock Garden in Chandigarh, India
III. Visual Perception in Rock Garden Design
IV. Rock Garden Plants
V. Terrace Rock Gardening
Innovative approaches
VI. Conclusion and Discussion
VII. References
Introduction
A rock garden, also known as a rockery or an alpine garden, is a small field or plot of ground
designed to feature and emphasize a variety of rocks, stones, and boulders. Gardeners who enjoy
growing a wide variety of plants are the best advocates of rock gardens. This type of garden can
contain a mixture of evergreens, deciduous shrubs, bulbs, perennials and annuals. Collectively, the
design they create is a myriad of colour, form and texture. Rocks, purchased or on-hand should
provide the basic framework of the design. The best arrangement will look as if nature had a hand in
it’s creation. Observation of natural outcroppings along highways and hillsides can be copied on a
miniature scale. We can group small rocks together to give the impression of larger masses worn
away by time and weathering. Medium stones should be used in groups of two or three. Bury large
boulders halfway in the ground for stability. Cohesiveness is best achieved by using only one kind of
rock in the garden. Limestone and sandstone are the two types readily available in this area.
The soil in a rock garden should be well-drained with only a moderate amount of humus or compost.
Most rock garden plants do not like rich soil or heavy fertilization. Well-rotted manure, worked
around the crown of the plant in early spring, is sufficient feeding for the growing season. Good rock
garden plants are drought resistant making them choice candidates for hard-to-water areas such as
slopes and shallow ground. Water deeply and allow soil to dry thoroughly. Watering is most
efficiently done in early morning or evening. Rocks hold moisture and release it slowly. Crevices
around them provide planting spaces for those plants requiring more than the average amount of
moisture. Mulching helps to control weeds and keeps the soil cooler. Mulched beds reduce water
splashing on the plants lessening the chance of fungal problems during hot muggy days and nights.
Japanese gardens are rock gardens well known for their sophisticated, minimal design and for the
calm yet profound atmosphere which they engender. After an opportunity to witness garden designers
at work, the authors realized that successful garden composition partly results from the application of
intentional, complex design principles, with anticipated visual eects. We therefore asked how the
visual elements of a garden, its rocks, moss and shrubs, and the compositions that gardeners create,
are interpreted by the brain. How do gardens achieve particular expressive and artistic eects? In this
paper we consider possible implications of intentional garden design eects, by interpreting how
design principles aect two of the fundamental processes associated with human visual perception,
namely segmentation of the visual scene into meaningful parts, and perceptual grouping of parts into
meaningful structural wholes. It is suggested that principles of visual psychology shed new light on
the aesthetic issues related to Japanese garden design.
History
- Rock Garden in Chandigarh, India
The Rock Garden of Chandigarh is a sculpture garden in Chandigarh, India. It is also known as Nek
Chand's Rock Garden after its founder Nek Chand, a government official who started
the garden secretly in his spare time in 1957. Today it is spread over an area of 40 acres
(161874.25 m²). It is completely built of industrial and home waste and throw-away items (The Times
of India, 2012). It is near Sukhna Lake (http://www.thehindu.com/life-and-
style/kids/article2081192.ece). It consists of man-made interlinked waterfalls and many other
sculptures that have been made of scrap and other kinds of wastes (bottles, glasses,
bangles, tiles, ceramic pots, sinks, electrical waste, broken pipes, etc.) which are placed in walled
paths (V. S. Bhatnagar, 1996).
Figure A: The garden is most famous for its sculptures made from recycled ceramic
Figure B: Waterfall and path at Rock Garden, Chandigarh
Figure C: Nek Chand’s Rock Garden, Chandigarh
In his spare time, Nek Chand started collecting materials from demolition sites around the city. He
recycled these materials into his own vision of the divine kingdom of Sukrani, choosing a gorge in a
forest near Sukhna Lake for his work. The gorge had been designated as a land conservancy, a forest
buffer established in 1902 that nothing could be built on. Chand’s work was illegal, but he was able to
hide it for 18 years before it was discovered by the authorities in 1975. By this time, it had grown into
a 12-acre (49,000 m2) complex of interlinked courtyards, each filled with hundreds of pottery-
covered concrete sculptures of dancers, musicians, and animals (T. Shakur and K. D'Souza, 2003).
His work was in danger of being demolished, but he was able to get public opinion on his side. In
1976 the park was inaugurated as a public space. Nek Chand was given a salary, a title ("Sub-
Divisional Engineer, Rock Garden"), and 50 laborers so that he could concentrate full-time on his
work. It appeared on an Indian stamp in 1983 (The Indian Express, 2011). The Rock Garden is still
made out of recycled materials. With the government’s help, Chand was able to set up collection
centers around the city for waste, especially rags and broken ceramics (The Times of India, October
2009; The Times of India, March 2009). When Chand left the country on a lecture tour in 1996, the
city withdrew its funding, and vandals attacked the park. The Rock Garden Society took over the
administration and upkeep of this unique visionary environment (Sajnani, M., 2013;
https://www.pbs.org/independentlens/offthemap/html/travelogue_artist_3.htm?true;
http://www.nekchand.com/).
Visual Perception in Rock Garden Design
- Japanese Rock Gardens
Figure 1: Japanese Zen Gardens
This leads to the realization that a set of design principles described in a Japanese gardening text by
Shingen (1466), shows many parallels to the visual eects of perceptual grouping, studied by the
Gestalt school of psychology. Guidelines for composition of rock clusters closely relate to perception
of visual figure. Garden design elements are arranged into patterns that simplify figure-ground
segmentation, while seemingly balancing the visual salience of subparts and the global arrangement.
Visual ‘ground’ is analyzed via medial axis transformation (MAT), often associated with shape
perception in humans. MAT analysis reveals implicit structure in the visual ground of a quintessential
rock garden design. The MAT structure enables formal comparison of structure of figures and ground.
They share some aesthetic qualities, with interesting dierences. Both contain naturalistic
asymmetric, self-similar, branching structures. While the branching pattern of the ground converges
towards the viewer, that of the figure converges in the opposite direction.
Intentional design effects in Japanese Gardens
Japanese garden designers, today, would be familiar with the following list of the key techniques used
in garden design:
• Rocks form the backbone of the garden composition.
Triangular rocks and rock clusters are preferred. As compositional units, or so-called triads, they
express earth, man and the divine through horizontal, diagonal and vertical lines, respectively.
• Odd-numbered groupings of rocks are preferred; the total number of clusters should also be an odd
number.
• The largest rock in each cluster is set first. Smaller rocks must then be placed such that they are in
‘good agreement’ with the main rock of each cluster.
The composition can be rounded o through various techniques of adding rocks. For example,
‘base stones’ are typically placed at the foot of the dominant rock in a cluster, to extend its base and
make it look more triangular; Sute ishi, literally meaning thrown away stones, are low, inconspicuous
stones that appear as if scattered in a random manner. These techniques are used to make a
composition look more natural.
Arranging rocks like the scales on a fish (also called the folding screen technique), creates the
impression of a vast, deep landscape with mountains.
• Suggested landscape features, like streams, should never be straight, but curved in a manner
suggestive of an endlessly winding structure.
• Asymmetry of all aspects of the design should be considered.
Design elements, such as rocks, moss and gravel, should have uniform textures, without bright
colouration or excessively striking textural patterns.
Origins of the above list of design principles can be traced back to two gardening manuals, the earliest
being a medieval text known as the Sakuteiki, translated by Shimoyama (1976). The other, an
illustrated text (Shingen, 1466), dates from the Muromachi (13331573) period. The latter text
contains both verbal and diagrammatic descriptions of dry landscape gardens in particular. The
previous list of design principles is actually a summary of the main tenets of the text by Shingen.
The Visual Psychology of Perceptual Grouping
The Gestalt psychologists (Koka, 1935; Wertheimer, 1938) stressed the importance of the process
whereby the human brain groups together various visual cues into meaningful perceptual wholes.
Visual grouping can be interpreted as segmentation, the division, by the visual system, of a scene into
possibly meaningful parts, as an early step in the analysis of a visual scene. Koenderink et al. (1992)
analyzed the segmentation process further into the active description of a scene, in terms of the
surface regions and bounding contours of objects. At this level, local contour elements and surface
texture elements are grouped into outlines and regions of segments, respectively. In a more complex
stage of grouping, the segmented image is arranged into figure and ground the next step in the
analysis of a visual scene. The process of visual segmentation, central and fundamental to the
understanding of human vision, is not yet completely understood. The Gestalt school provided a set of
intuitive guidelines for predicting the outcome of perceptual grouping, that is, the formation of
meaningful arrangements of visual elements.
The most fundamental independent guidelines, often called Gestalt laws, are still relevant in
perception research today (Palmer, 1999), and is summarized by the following:
Proximity: More closely spaced cues are seen as belonging together
Similarity: Elements that look more similar are grouped together
Smoothness: Elements group together if their spatial alignment follows a smooth path
Enclosedness: Objects group together if they are arranged on a closed path
Simplicity law: The objects actually perceived correspond to the ecologically simplest configuration
of parts.
The above does not imply that distinct features independently aect the grouping of visual elements
into boundary contours and surface regions. Rather, the superposition of features with dierent gestalt
qualities is not linearly additive, but complex. Gestalt formation at one scale aects gestalt formation
on another. Similarly, the proximity factor has complex implications for grouping. For example, the
formation of boundary contours, and hence image segmentation, is aected by the ratio of visual cue
size to the spatial distances between them. Zucker and Davis (1988) found a salient change in contour
perception at a cue size: empty space ratio of about 1:5. More sparsely sampled contours fail to
generate various classical illusions associated with the reconstruction of incomplete boundary
contours. Cues on such sparse contours fail to be integrated into a whole figure (Kova´ cs, 2000).
Caelli and Julesz (1978) proposed that local visual cues are organized into texture elements, or so-
called textons, which represent local geometrical characteristics of the given visual cues. They
suggested that boundary contours, formed during image segmentation, are based on gradients in
texton distribution. Van Tonder and Ejima (2000) have argued that tessellation, and hence the ratio of
cue size of textons to the relative spacing between them, strongly influences visual grouping. The
local geometry of the empty spaces between textons also plays a role in perceptual grouping. At
specific intermediate cue size: empty space ratios one may find that local geometry of both the texture
elements and the empty spaces between them contribute equally to perceptual grouping of the whole
design.
Design Effects related to Visual Figure
Texture eects
Japanese gardeners use comparatively homogeneously textured materials. Saturated colours and high
contrast texture markings are avoided, possible since low contrast objects tend not to dominate visual
attention. The textures used are natural, and therefore visually more complex than a mere blank slate.
Uniform surface regions with even textures simplify the creation of boundary contours. The process
of visual segmentation is thus simplified through the reduction of the number of sub-segments within
the interior of each object.
Figure 2. (A) Examples of textures preferred by Japanese gardeners. (B1) Oddnumbered groupings of stones usually
result in odd-numbered visual junctions, which disappear (B3) among distractors, whereas even arrangements (B2)
lead to even junctions that are more salient (B4). Patterns with many even junctions (B5) result in competing figures.
A base stone (white circle) (C1) strengthens visual grouping within the cluster (C2). Deliberate alignment (C3) creates
an unnatural looking closed figure. Without a base stone the composition visually appears as two separate groups
(C4). (D1, D2) Images after Bahnsen (1928) demonstrate how bilateral symmetry dictates to figure-ground
perception. (D3) Inducing bilateral symmetry in one rock cluster causes it to ‘pop out’ in the Ryoanji design. (D4)
Local bilateral symmetry weakens grouping between clusters. (D5) More subtle eects of similarity and proximity
are dominated by artificially induced global bilateral symmetry.
The use of coarse, light-and-dark mottled gravel as background for most of the garden somewhat
reduces the unavoidable contrast created between rocks and visual ground. Both the rocks and moss
have a similarly mottled appearance. The contrast between figure and ground would be much greater
if fine white sand were used instead. attention drifts between dierent competing figures without
revealing any additional global structure. Traditionally, the technique of arranging the rocks to
overlap alternately, like scales on a fish, was considered evocative of space and depth. Such overlap
gives the impression of a series of folds jutting out behind one another along a deep mountain valley
(Figure 3A4). The role of occlusion junctions as vivid monocular depth clues is known in visual
psychophysics. Alternating overlap of rocks ensures the creation of odd (or trilateral) junctions.
Spacing between rocks
The garden manual by Shingen (1466) expresses the maximum size of rocks as a ratio of the size of
the garden as a whole. The extent to which rocks visually fill a garden will aect the perception of
spatial dimensions of the entire garden. Adaptations to spacing between rocks can thus be used to
create various moods, such as emptiness or liveliness. Just as with the texton textures , the degree to
which stones group depends on the size ratio of the rock arrangement as a whole compared to that of
individual rocks. Downscaling of rock clusters (i.e. decreasing the ratio to 1:5) exposes the
tessellation pattern of the global composition, but impairs the clarity of visual relationships between
individual objects in rock clusters. With the rocks scaled to appear much larger (1:1), clusters form a
closely knit unit in which subparts of clusters, rather than clusters themselves are visually discernable,
and the tessellation scheme of the overall pattern becomes obscured.
Contour junctions
Gardeners carefully consider the visual appearance of spatial junctions (boundary contours) between
rocks, as well as surface textures of rocks themselves (surface regions). Visual junctions are created in
such a way that an odd number of contours meet (e.g. Figure 2B1), whereas even numbered junctions
are avoided (Figure 2B2). According to the Gestalt law of good continuation, an even junction will
appear more perceptually salient than an odd junction if seen against a background of random texture
elements, such as shown in Figures 2B3 and 2B4. Adjusting the formation of odd and even junctions
gives gardeners control over the salience of contours, and hence, the process of visual segmentation.
Where even junctions abound, such as the pattern in Figure 2B5 (after Marroquin) segmentation is
ambiguous: instead of shifting across the image in a structured manner, visual attention drifts between
dierent competing figures without revealing any additional global structure. Traditionallly, the
technique of arranging the rocks to overlap alternately, like scales on a fish, was considered evocative
of space and depth.
Figure 3 (A1) Sute ishi, or ‘thrown away stones’ (A1) increase the number of triangular groupings in the original
rock cluster (A2) to extend more widely into the rest of the garden (A3). An enlarged view of rock surface texture
(B1) and successively more global views (B2B4), reveal a recurrence of triangular arrangements in this garden
(Dokuzatei, Kyoto).
Such overlap gives the impression of a series of folds jutting out behind one another along a deep
mountain valley (Figure 3A4). The role of occlusion junctions as vivid monocular depth clues is
known in visual psychophysics. Alternating overlap of rocks ensures the creation of odd (or trilateral)
junctions.
Analysis of the structure of visual ground
Medial axis transformation is not only useful for compact description of shape regions, but also
reveals structure in empty spaces between figures. It could therefore be an appropriate method to
analyze minimalist designs often encountered in Japanese dry landscape gardens. A summary of our
previous work on structural analysis of the Ryoanji dry rock garden (Van Tonder et al. 2002) is
presented here. Ryoanji hardly requires an introduction as it is well known among designers as well as
the lay public. With five clusters of rocks on a rectangular bed of raked gravel, visitors to the garden
are intrigued by the sophisticated simplicity of the nearly empty composition. Compared to more
typical garden designs, the visual ground in Ryoanji is strongly emphasized. It covers the full extent
of the garden. Looking for structure in the empty regions between rock clusters therefore seemed like
a reasonable way to proceed in the analysis of the garden’s global shape.
Figure 4. (A1) The medial axis between two points is the locus of equidistant points between them. (A2) A two-
dimensional shape (dark outline) and its medial axis transform (internal shading) computed with our model. (A3)
Contrast sensitivity enhancement data of Kova´ cs et al. (1998) of a triangle, with vertical and horizontal cross
sections to show data in detail, were replicated with the model by Van Tonder and Ejima (2003). (B1) Medial axis
transformation of Ryoanji. The layout is after Oyama (1995). The outlines of rocks appear within the rectangle of
gravel. The verandah and main hall are also outlined. The central room appears as a bold black outlined square.
Rock contour values are scaled to relative rock heights. (B2) The simulation, with rock contour values all set equal.
(B3, B4) The medial axes for the original simulation and perturbed simulations are highlighted in white, for clarity.
(C1) An enlarged view of the medial axis tree of the left most rock cluster. (C2) The global medial axis tree. (C3)
Horizontal reflection and enlargement of a section of the local tree reveals a close similarity with the global structure
(C4).
Medial axis transformation revealed a well defined global pattern (Figure 4B1) with several unusual
qualities. The medial axes constitute a global structure that converges toward the main viewing area,
forming a very simple tree shape with three hierarchical branching levels (with a main trunk, two
secondary branches and four tertiary branches). The branching point closest to the building, where the
tree bifurcates into the first two branches, is a location of maximal global Shannon information
(Leyton, 1987). The structure of the entire garden design can therefore be described most compactly
at this point. The transformation reveals a self-similar dichotomously branched structure, with a
naturalistic appearance reminiscent of both organic (from the myriad of phytomorphic and
zoomorphic examples) and inorganic (geological and meteorological formations) patterns of nature.
The shape of the tree is asymmetrical.
The same computational model (Van Tonder and Ejima, 2003) for medial axis transformation was
used throughout with a fixed set of parameters, adjusted to fit the human perceptual data described in
Kova´ cs et al. (1998). Medial axes do not converge towards the viewing area upon deletion or
addition of clusters, or following random placement of the five rock clusters. After such alterations,
medial axes of the garden lack a consistent branching rule and in most cases do not even
approximately resemble a tree structure (supplementary material, Van Tonder et al. 2002). The
structure defined by the shape of the ground in the original layout of Ryoanji is nonaccidental. The
input stimulus was perturbed to test the robustness of the computational model used. Whereas
boundary contours of rocks where scaled to their corresponding relative heights in the initial
computation, we set contours of both small and large rocks to equal values. The resulting medial axis
transform (Figure 4B2) shows that the global tree structure is still largely the same, except for the
addition of small, noisy branches. The main medial axes are highlighted in white (Figures 4B3, B4)
for clarity.
Note that the left most rock cluster in the perturbed version produces a branch that meets the main
trunk of the original tree structure (Figure 4B4) in the main viewing area of the garden. Closer
inspection reveals that this local tree (Figure 4C1) shares various qualities with the global (Figure
4C2) tree structure. For illustrative purposes we horizontally reflected and enlarged a section of the
local tree (Figure 4C3). Both local and global (Figure 4C4) structures are self-similar dichotomous
branching patterns of the same hierarchical order, and both converge towards the same viewing area.
Rock Garden Plants
The ideal location for a rock garden is a natural slope or terrace, such as those found at the side or rear
of a house based on a split level or garden-level design. We can use rocks of one geological type. A
common rock is native granite covered with lichens (moss rock). Rocks are available from nurseries,
landscape contractors and rock dealers. An effective rock garden should have several large rocks,
some weighing 200 pounds or more. We can set the rock into the ground so at least one-third is buried
or place rocks in a natural way, following the grain of the rock. One can position rocks to control soil
erosion between rocks and to allow soil pockets of various sizes for plants and use smaller, similar
rock as a mulch. For most plants, incorporate organic matter into heavier clay soils to improve texture
and provide better drainage. A rock garden should be no larger than can be easily maintained.
Rock gardens have high maintenance requirements. Weed control is the biggest problem. Most rock
garden plants need low to moderate watering amounts and frequency. Rock gardens are traditionally
thought of as positioned on a slope in full sun. An east or west exposure can provide a respite from all
day sun. Some reliable plants for the rock garden include the evergreens and conifers which come in
many shades of green, blue and yellow. Juniperus squamata ‘Blue Star’ has bright blue dense foliage
all year and has a mature height of 14 inches by the same width. The Pinus strobus ‘Nana’ (Dwarf
White Pine) is an irregular globe of soft green needles growing to about 3 feet tall with an ultimate
spread of 6 feet. Thuja occidentalis ‘Tom Thumb’ (Dwarf American Arborvitae) has flattened green
foliage and this tight little globe achieves a mature height of 14 inches tall by 12 inches wide.
Figure 5 Japanese pine trees tower over rock garden at Takamatsu's Ritsurin Park by Manmaru
Deciduous shrubs have a dual purpose. They give us lovely flowers and their twiggy appearance in
winter provides variety in texture. Spiraea japonica ‘Alpina’ grows to only 14 inches high with a
profusion of pink flowers in late spring. Deutzia crenata ‘Nikko’ gently sprawls over the ground
barely achieving one foot in height. This little gem is covered with white flowers in early spring.
One can try planting some perennials in the rock garden. Anemone pulsatilla (Pasque flower) is one of
the earliest bloomers. This plant produces ferny foliage with purple, red or white flowers. The foliage
stays nice all summer. Geranium sanguineum (Hardy Geranium) develops a spreading mound of
finely cut leaves with many brightpink flowers in mid-spring. The foliage will turn red in autumn.
Herniaria glabra (Rupturewort) makes a great ground cover.
Good between stepping stones, the dark green tiny leaves will become topped with white flowers in
early spring. Oenothera macrocarpa (Missouri Primrose) is a sprawling native glade plant which
provides night blooming sulfur-yellow flowers all summer. Small bulbs such as anemones,
snowdrops, scilla and grape hyacinths can also be added along. Miniature narcissus and botanical
tulips return reliably each year and complete the bulb collection. Annuals of small stature such as
pinks, ageratum and verbena give the summer season a color boost. The extensive array of plants to
choose from for rock gardens truly offers the opportunity to satisfy the palette of every gardener. The
following list of plants are especially noted for their adaptability to rock gardens in the Midwest. We
can plant a variety of species, repeating some species several times to make the garden look natural.
Ideally, rock garden plants should spread slowly. However, we must take care not to overplant.
Plant Selection
Many types of plants are suitable for rock gardens. Generally, plants that are low growing and have a
clumping habit are preferred. Perennial plants are most common in rock gardens, although some
annuals can be used. Table 1- Table 6 lists many rock garden plants, most plants listed should be
hardy to 8000 feet, some higher (www.plantselect.org).
Table 1: Recommended rock garden plants (Bulbs)
Scientific Name
Common Name
Anemone blanda
Windflower
Allium aflatunense
Ornamental Onion
Chionodoxa sardensis
Glory-of-the-Snow
Crocus vernus 'Purpurea'
Dutch Crocus
Iris danfordiae
Bulbous Iris
Iris reticulata
Bulbous Iris
Narcissus cyclamineus 'February Gold'
Daffodil
Narcissus cyclamineus 'Peeping Tom'
Daffodil
Narcissus cyclamineus 'Tete-A-Tete'
Daffodil
Narcissus jonquilla 'Suzy'
Jonquil
Narcissus 'W. P. Milner'
Daffodil
Tulipa batalinii
Tulip
Tulipa greigii 'Heart's Delight'
Tulip
Tulipa praestans 'Fusilier'
Tulip
Tulipa (species)
Tulip
Table 2: Recommended rock garden plants (Spring Annuals)
Scientific Name
Common Name
Agrostis nebulosa
Cloud Grass
Linaria maroccana
Toadflax
Viola tricolor
Johnny-Jump-Up
Table 3: Recommended rock garden plants (Shrubs)
Scientific Name
Common Name
Berberis thunbergii 'Kobold'
Japanese Barberry
Buxus microphylla 'Koreana Wintergreen'
Boxwood
Cotoneaster horizontalis 'Perpusilis'
Rock Cotoneaster
Forsythia viridissima 'Bronxensis'
Golden-Bells
Fothergilla gardenii
Witch Alder
Genista x 'Lydia'
Broom
Stephanandra incisa 'Crispa'
Lace Shrub
Table 4: Recommended rock garden plants (Perennials)
Scientific Name
Common Name
Acanthus mollis 'Latifolus'
Bear's-Breeches
Anemone pulsatilla
Pasqueflower
Arabis alpina 'Snowcap'
Rockcress
Artemisia absinthium 'Lambrook Siler'
Wormwood
Artemisia schmidtiana 'Silver Mound'
Mugwort
Campanula porscharskyana
Bellflower
Coreopsis verticillata 'Moonbeam'
Tickseed Coreopsis
Dianthus alpinus 'Alwoodii'
Alpine Pink
Dianthus graniticus
Granite Pink
Dianthus grantianopolitanus Tiny Rubies'
Cheddar Fmk
Engelmania pinnitifida
Engelmann Daisy
Euphorbia myrsinites
Myrtle Euphorbia
Geranium renardii
Alligator Leaf Geranium
Geranium sanguineum
Hardy Geranium
Geranium macrorhizum
Big Root Geranium
Gypsophila repens
Creeping Baby's Breath
Herniaria glabra
Common Rupturewort
Iberis sempervirens
Candytuft
Papaver atlanticum
Atlantic Poppy
Oenothera macrocarpa
Missouri Evening Primrose
Potentilla nepalensis
Nepal Cinquefoil
Potentilla recta 'Warrenii'
Cinquefoil
Potentilla tabernaemontana
Spring Cinquefoil
Salvia jurisicii
Salvia
Salvia superba
Perennial Salvia
Saponaria ocymoides
Rock Soapwort
Stachys byzantina
Lamb's Ear
Verbascum chaixii 'Album'
Chaix Mullein
Veronica alpina 'Alba'
Alpine Speedwell
Veronica incana
Woolly Speedwell
Veronica teucrium 'Crater Lake Blue'
Hungarian Speedwell
Veronica longifolia 'Subsessilis'
Clump Speedwell
Table 5: Recommended rock garden plants (Annuals)
Scientific Name
Common Name
Ageratum x hybrida
Flossflower
Antirrhinum majus
Snapdragon
Cosmos bipinnatus 'Sunny Red' & 'Sunny Gold'
Cosmos
Dyssodia tenuiloba
Dahlberg Daisy
Evolvulus x 'Blue Daze'
Evolvulus
Gomphrena globosa 'Buddy'
Globe Amaranth
Lobularia maritima
Sweet Alyssum
Verbena x 'Aphrodite'
Vervain
Zinnia angustifolia
Narrowleaf Zinnia
Table 6: Recommended rock garden plants (Fall Blooming Annuals)
Scientific Name
Common Name
Allium senescens 'Glaucum'
Curly Chives
Chrysanthemum 'Golden Dream'
Garden Mum
Gallery of Rock Garden Plants
Figure 6 Blue Rug Juniper Plants
Figure 7 Purple Fountain Grass
Figure 8 Moonbeam coreopsis
Figure 9 Lavender
Figure 10 Yarrow
Figure 11 Sedum Autumn joy
Figure 12 Royal Candles Speedwell
Figure 13 Columbine Flowers
Figure 14 Dianthus alpinus
Rooftop Rock garden
Here’s where gardening can get really creative by using ones imagination. Roof gardens are a
common sight of Europe, where this seems to be a long tradition. Hen-and-chicks (Sempervivum) and
various kinds of Stonecrop (Sedum) are often grown directly on top of terracotta or slate roof tiles
where they cling by their tiny roots and take advantage of any little bits of soil or debris that gather at
their base, supplying nutrients. Roof tiles are less common in most parts of North America, and it is
not advised towards attempting to grow plants on top of asphalt or cedar shingles or other roof
surfaces where standing moisture could cause problems over time. However, garden sheds and other
small structures a dog house or play house is the perfect opportunity to do some experimenting
with rooftop gardening. Upon considering first laying down a thick rubber or vinyl barrier (the type
used for water gardens should work, or other types from roofing supply stores) before installing the
final roof surface. Relatively shallow-pitched roofs are a better choice than steep ones, where the
plants might wash away in the first heavy rain storm.
Tiny little alpines can also be nurtured with need of some little help in adhering to the surface. In a
doghouse, for example, the entire roof surface had a layer of soil a couple of inches thick, covered by
sheet sphagnum moss and then finally topped by a layer of chicken wire. It was a riot of colour from
all kinds of succulents and other alpines. A roof garden planted as densely as this example requires
regular watering.
Figure 14 Dog house Roof Garden at the Chicago Botanical Garden
On higher roofs, like on a shed, it might be possible to take the individual rosettes of a Hen-and-
chicks and actually glue them to the tiles using a hot glue gun. Another method is to make small soil
pockets using pieces of dead sod (one just needs to have a roll or two after discarding the old stuff).
After one has flipped the sod upside down, a layer of sheet moss is added, and then fixed down with a
final layer of chicken wire attaching this firmly to the tiles. Then one can poke in rosettes of Hen-and-
chicks and little bits of Stonecrops, which will quickly root themselves into the soil below. Watering
these lightly every few days for a month or so, and then just leaving them alone will take care of the
rest.
Figure 15 Hen-and-Chicks on a Tile Roof in Austria
Green Roofs
Figure 16 Green roof at the British Horse Society headquarters
The example of very simple rooftop garden above is quite different from the serious, large-scale
approach to creating a green roof. Many commercial buildings are now integrating green roofs into
their design in cities all over North America. It’s a whole science involving a lot of high-tech
materials and building a green roof will require the help of professionals with experience.
Crevice Gardens
Figure 17 Crevice Garden at Montreal Botanical Garden
This is a fairly new technique for growing alpines, first started in Czechoslovakia. The result is very
simple in construction and absolutely stunning to look at. If we imagine large pieces of flat flagstone
rocks standing vertically out of the ground, one next to the other with a gap of a few inches in
between. This gap is filled with soil, then covered in gravel mulch and the alpines are planted in these
long and narrow crevice spaces. The standing rocks could be gently curving, jagged and angular in
shape or even neatly trimmed into rectangles or very geometric shapes. On a tight budget, even pieces
of broken patio stones could be used to good effect. For support, the lower portion of each stone is
buried below the existing ground level before filling the gaps between the stones with the special
alpine soil mixture. The result is a free standing rock structure that has a lot of great textural character
and can easily be created for a large or a small space. One can even adapt this idea to containers and
troughs, using flat pieces of thin slate, either natural or cut.
Rock Gardening with Waste
Rubble Gardens
Here the core idea is to make use of things like bricks, broken concrete, clay, stone or other hard
materials salvaged from building demolition, and give these a second life as a home to alpine plants.
It’s a fairly rustic look that results, and perhaps not to everyone’s taste. One can work in layers, just
like you would with rocks, so that as you build upwards the spaces between the rubble is filled with
an alpine soil mixture. Save your best reclaimed bits and pieces for the surface layers so that you can
really take advantage of their unique features. Water this rubble pile well, and wait a few days so the
soil has a chance to settle into the crevices before topping it up if needed, then adding your plants. As
a final touch, consider covering the soil surfaces with a gravel mulch, to sort of tie the whole thing
together as well as to reduce maintenance (http://www.rockstargardens.com/).
Figure 18 an amazing Rubble Garden at an Austrian Nursery
Found objects
Figure 19 Creativity with stacks of old flowering pots
Figure 20 Re-usage of Plastic water bottles
Figure 21 Plastic bottle Green house
Figure 22 Plastic bottle scultures
Figure 23 Waste throw away materials used to build artistic vintage structures
Figure 24 Glass and plastic bottles re-used to build fancy monumental structures
Figure 25 Utilization of waste for creating innovative structures
Figure 26 Green house shelters and houses made of Plastic and glass bottles
Any object that will hold a bit of soil and can provide drainage (perhaps with the help of a drill) can
be pressed into service for growing alpines. Keep this in mind the next time you’re scouring a garage
sale or flea market. Old pieces and doodads from farm or industrial equipment, from vehicles and
from buildings might make a truly unique character container for a focal spot on your deck or patio.
And consider all kinds of materials, from metal to wood, clay, stone or even plastic. Maybe this is the
perfect thing to do with your brother’s old drum kit, a beat up guitar or a French horn that suffered an
unfortunate accident.
Boots and Hats
Gardeners sometimes do charming things with boots, shoes or hats that have outlived their wearable
purpose. They could sit as a collection at the edge of a step, or you could even nail them to a fence or
wall before filling with soil and planting. The longevity of such a container will depend on the
condition and what it’s made of, but it could at least be fun for a season or two.
Living Sculptures
Figure 27 Steel I-Beam Sculptures at IGA Garden Show at Germany
One can make it big or make it small. Planting opportunities are through the sides of broken pots, or
in the gaps between pots when you change from a large pot to a smaller one. Just stuff these with soil,
a few plants and some sheet moss. And of course, we can incorporate other materials to make facial
features, for instance.
• Three sheets of welded woven wire to be fastened together into a free-standing triangle, lined on the
inside with sheet sphagnum moss, coir fibre or burlap and then filled with soil. Alpines could then be
planted in the small square gaps between the wires. Literally, this was like a living column. •Clay pots
are stacked one inside the other, then wired together through the holes. These can then be shaped into
a three dimensional sculpture, anything from a freeform design to a terracotta person. • Heavy steel I-
beams of varying lengths are set into concrete so they stand vertically, and about six inches apart.
Rocks are then shoved down into the gaps between the beams. Between the rocks, create planting
pockets from chicken wire, sheet moss and soil.
Discussion and Conclusion
A Muromachi-era gardening manual (Shingen, 1466) contains drawings of rock configurations, and
verbal descriptions of their associated visual eects. The work here resulted from the realization that
these guidelines are analogous the Gestalt laws of visual perception. The application of Gestalt
principles of perceptual grouping to gain new insight have been applied into how karesansui design
deals with aesthetic qualities such as asymmetry, tranquility, simplicity and naturalness (Nitschke,
1993). We hypothesize that gardeners manipulate the process of visual segmentation into figure and
ground by controlled use of various design elements. Specifically, they engender naturalness and
avoid excessive local pop-out of visual elements. Likewise, symmetry, even-numbered junctions and
excessive heterogeneity with respect to scale transformations lead to unnaturally complicated scenes
which disrupt visual tranquility, and goes against the creation of naturalistic design. This work
provides a new interpretation of structure in Japanese garden design. Structure is embedded in
hierarchies of trilateral junctions arranged into multi-scale, dichotomously branching patterns in both
visual figure and ground, with the main dierence being that, while figure converges away from the
viewer, the structure of ground converges in the opposite direction. The human sense of aesthetic is
closely linked to visual perception. Since the latter comprises an understanding of visual structure, our
work therefore suggests a new link between structure and aesthetic understanding of this type of
garden design. In our work, medial axis transformation was applied to uncover the implicit structure
of the visual ground. The resultant pattern exhibit various non-accidental qualities, such as self-
similarity. We suggest that the analysis of the Ryoanji garden presented here provides a novel
extension to Arnheim’s earlier ideas in terms of order and complexity in the garden (Arnheim, 1966).
He pointed out that classical French gardens typically employ axial symmetry in the form of a focal
point that centers on a radially symmetrical section of the garden and a central axis or lane, leading to
the focal centre, whereas Japanese rock gardens do not. However, our analysis of visual ground
reveals that hierarchical structure resides not only within each cluster, but extends from clusters across
the entire garden. Even if perception of medial axes remains at a subconscious level, the branching
structure gives a clear sense of the holistic shape of the design, which moreover reflects the inverted
branching structures suggested by the textural features and triangular compositions of each rock
cluster. Medial axis transformation thus enables formal comparison of order and complexity in rock
clusters and the entire design. The concept of MA is an important aspect of Japanese design in more
than one way (Nitschke, 1966), yet the best understanding of MA remains at an intuitive rather than a
rational level. While we do not argue against this approach, as visual psychologists we are curious to
know why the empty space or intervals between objects should have an impact on our visual
perception. The subtlety of eects hints at perceptual mechanisms working at a subconscious level
and in this investigation we may have established a meaningful link between perceptual mechanisms
in vision and the MA in Japanese dry landscape design. Designers have to simultaneously deal with
objects and their surrounding empty spaces. Good designers probably do this eectively, already.
However, we would like to suggest a reversed approach of conceptualization, where the structure of
empty space is designed first. The resemblance between the tree structure in Ryoanji and natural
materials used in other art forms, suggests direct applicability of techniques from one discipline on
another. This may sound counter intuitive at first, but the implied role of empty space in the
perception of holistic composition makes it a potential tool for the creation of more harmonized
designs. The well defined structure of local symmetry axes could assist designers to better understand
processes they may already use semi-intuitively in rock garden designing.
References
[1] Alexander, C.: 1979, The Timeless Way of Building, Oxford University Press.
[2] Arnheim, R.: 1966, Toward a Psychology of Art, Berkeley: University of California Press.
[3] Bahnsen, P.: 1928. ‘Eine Unterschung uber Symmetrie und Asymmetrie bei visuellen
Wahrnehmungen’, Zeitschrift fur Psychologie 108, 129–154.
[4] Blum, H.: 1973. ‘Biological Shape and Visual Science (Part I)’, Journal of Theoretical
Biology 38, 205287.
[5] Caelli, T. and B. Julesz: 1978. ‘On Perceptual Analyzers Underlying Visual Texture
Discrimination: Part I’, Biological Cybernetics 28(3), 167–175.
[6] https://timesofindia.indiatimes.com/city/chandigarh/Chandigarh-Rock-Garden-to-get-a-face-
lift/articleshow/4267789.cms?referral=PM
[7] http://www.nekchand.com/
[8] https://www.pbs.org/independentlens/offthemap/html/travelogue_artist_3.htm?true
[9] http://www.rockstargardens.com/
[10] http://www.thehindu.com/life-and-style/kids/article2081192.ece?
[11] Koenderink, J.J. A.J. Van Doorn and A.M. Kappers: 1992. ‘Surface perception in
pictures’, Perception & Psychophysics 52(5), 487–496.
[12] Koka, K.: 1935, Principles of Gestalt Psychology, New York: Harcourt, Brace &
Co.
[13] Kova´ cs, I.: 2000. ‘Human development of perceptual organization.’, Vision Res.
Special Issue on Attention 40(1012), 13011310.
[14] Kova´ cs, I., A. Feher and B. Julesz: 1998. ‘Medial-point Description of Shape: A
Representation for Action Coding and its Psychophysical Correlates’, Vision Research
38(15/16), 23232333.
[15] Kova´ cs, I. and B. Julesz: 1994. ‘Perceptual Sensitivity Maps within Globally
Defined Visual Shapes.’, Nature 370, 644–646.
[16] Leslie Umberger, Erika Lee Doss, Ruth DeYoung (CON) Kohler, Lisa (CON) Stone,
Jane (CON) Bianco, 2007, Sublime spaces & visionary worlds: built environments of
vernacular artists. Princeton Architectural Press, ISBN 1-56898-728-5, pp. 319- 322.
[17] Leyton, M.: 1987. ‘Symmetry-Curvature Duality’, Computer Vision, Graphics, and
Image Processing 38, 327341.
[18] Leyton, M.: 1992, Symmetry, Causality, Mind, MIT Press: Cambridge, MA, USA.
Marroquin, J.L.: 1976, Human Visual Perception of Structure. Master’s thesis, MIT.
Nitschke, G.: 1966. ‘MA: The Japanese Sense of ‘Place’, Architectural Design 36, 116–156.
[19] M. Sajnani., 2013, Encyclopaedia of Tourism Resources In India, Vol.1, Gyan
Books , ISBN 10: 8178350173 ISBN 13: 9788178350172
[20] "Night tourism to light up 'rocks'". The Times of India. 2012-07-01. Retrieved2012-
10-30.
[21] Nitschke, G.: 1993, Japanese Gardens, Koln: Benedikt Taschen Verlag GmbH.
[22] Oyama, H.: 1995, Ryoanji Sekitei: Nanatsu no Nazo wo toku (Ryoanji Rock Garden:
Resolving Seven Mysteries). Tokyo: Kodansha.
[23] Palmer, S. E.: 1999, Vision Science: from Photons to Phenomenology, Bradford
Books/MIT Press: Cambridge.
[24] Salingaros, N.: 2000. ‘Hierarchical Cooperation in Architecture, and the
Mathematical Necessity for Ornament’, Journal of Architectural and Planning Research 17,
221235.
[25] Shimoyama, S.: 1976, Translation of Sakuteiki: The Book of the Garden (Tokyo:
Town and City Planners). Attributed to Toshitsuna Tachibana, late 11th/early 12th Centrury.
[26] Shingen: 1466 (original text)/1930, Senzui Narabi ni yagyou no zu (Illustrations for
designing mountain, water and hillside field landscapes). Manuscript dated 1466, published in
Sonkeikaku Library, Sonkeikaku Soukan series. Tokyo: Ikutoku Zaidan.
[27] Taylor A. P. Micolich and D. Jonas1999Fractal Analysis of Pollock’s Drip
PaintingsNature399422.
[28] The Indian Express. 22 November 2011. Retrieved 12 February 2017.
[29] TNN (1 October 2009). "'Pricey' weddings at Rock Garden". The Times of India.
Retrieved 12 February 2017.
[30] T. Shakur and K. D'Souza, 2003, Picturing South Asian Culture in English: Textual
and Visual Representations, ISBN 0954446305, 9780954446307
[31] Van Tonder, G. J. and Y. Ejima.: 2000. ‘From Image Segmentation to Anti-textons’,
Perception 29, 12311247.
[32] Van Tonder G., J. M. J. Lyons and Y. Ejima: 2002. ‘Visual Structure of a Japanese
Zen garden’, Nature 419, 359–360.
[33] Van Tonder, G. J. and Y. Ejima: 2003. ‘Flexible Computation of Shape Symmetries’,
IEEE Transactions on Systems, Man & Cybernetics, Part B 33(3), 535541.
[34] V. S. Bhatnagar, 1996, Chandigarh, the City Beautiful: Environmental Profile of a
Modern Indian City. APH Publishing, ISBN 817024790X, 9788170247906
[35] Wertheimer, M.: 1938, ‘Laws of organization in perceptual forms’, in W.D. Ellis
(ed.), A sourcebook of Gestalt psychology, London, UK: Routledge and Kegan Paul, pp. 71
88.
[36] www.plantselect.org
... and are placed on the surface of the soil and part of it is buried in the ground, while the newly broken parts are hidden in the ground and show only the surfaces that were previously exposed to external conditions. The stones are positioned in a slightly oblique position to form pockets where plants can be grown and large stones are placed at the top of the garden, while small stones are placed at the bottom (Mitra 2018). Some basic rules should be followed when using stones in the design of rock gardens, namely: not stealing stones from the countryside, avoiding the use of broken concrete as a replacement for stones, using the same type of stone in each garden and not exaggerating the use of more than one type buy stones from A local quarry preferably visiting and choosing the stones required by the designer personally, choosing a group of stones in different sizes and preferably weighing 12.7 -101.6 kg (Hessayon 2000). ...
... Tufa: A porous Limestone form which contains plant residues. Its lightness is the exceptional advantages.(half the weight of ordinary limestone) and its ability to support plant growth (Hessayon 2000, Mitra 2018) Rocky garden plants: Plants that growing up among the rocks usually come from weeds and bulbs. Plants are cultivated in groups and require fertile soil. ...
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