Using Art and Math in Garden Design

By Mary Warren

Using art and math to create a garden design might seem like artificially superimposing incompatible sets of rules on plant placement in garden beds. However, in concert, art and math can actually provide good mechanics for building a garden that will be a joy to behold. In this article, the experienced and the hobby gardener alike will find suggestions for a successful layout that will also aid in the best plant choices, all based on artistic and mathematical principles.

Coulter’s pinecone
Coulter’s pinecone

To begin, one doesn’t have far to look to find a planting grid. Nature provides a few. The structure of the fronds of a fern or the scales of the Coulter’s pine (Pinus coulteri) can suggest a garden diagram. Follow the downward spiral of the cone’s scales or the fern’s unfurled fronds, and a three-dimensional, conical display emerges. If plants are placed to mimic the swirl, with attention paid to the distance between plants, the result is that each plant is simultaneously visible and also contributes to the entire scene. When painting in oils, this layering is referred to as working lean to fat, building pigments from the bottom layers up and across the canvas. When applied, this principle creates a garden with many levels. The garden becomes a living painting as its plants layer up and across the bed.

Logarithmic spiral.
Logarithmic spiral.

Gardeners who choose the pattern of the scales of the Coulter’s pinecone or the furls of the fiddlehead fern are actually using what the mathematicians dubbed “The Golden Ratio”. To put it simply, the gardener must give plants space, according to growth rates, so that they don’t spoil their neighbors by growing into them. One can find conifer growth rates and sizes in the American Conifer Society’s Conifer Database (conifersociety.org). Other plant specifications are available on the Internet. Knowing how large plants will get assists in choosing the right ones for the space the garden affords.

In selecting plants for the garden, color, texture, and shape provide visual stimuli, evoking a sense of beauty that is unique to each person. For one gardener, the arms of Cupressus nootkatensis ‘Green Arrow’ (Green Arrow Nootka cypress) might appear too zigzagged and visually disruptive. For another, ‘Green Arrow’ symbolizes a skyward motion, a reaching-up, like an arrow shot into the sky. Another gardener might prefer more conventionally shaped conifers like Picea glauca var. albertiana ‘Conica’ (Dwarf Alberta spruce), with its classic Christmas tree shape. Regardless, the choice of plants expresses the gardener’s individuality and personal vision.

‘Green Arrow’. Photo by Ron Elardo
‘Green Arrow’. Photo by Ron Elardo

In addition to the proportions suggested by the Golden Ratio, other possible bed designs can be inspired by both art and math. Buddhist mandalas, for example, combine both art and math and are meant to portray perfection. A mandala can be simple or complex. A Google search will yield a plethora of examples. From Western art, there is an even simpler mandala, based on Leonardo da Vinci’s Vitruvian Man, man within a circle within a square, the so-called “squaring of the circle” (Carl Gustav Jung, Symbols of Transformation). From my design education and experience, modifying the square shape of this model to create a rectangular-shaped bed affords the gardener a much more flexible layout plan.

Da Vinci’s Vitruvian Man.
Da Vinci’s Vitruvian Man.

The ancient Greeks applied “golden/sacred numbers” in the creation of the great architectural works they dedicated to their gods. The mathematically precise, rectangular spaces between the columns in the Temple of Athena Nike, at the top of the Acropolis in Athens, can be copied on a smaller scale in the construction of garden beds. Those rectangular shapes can accommodate more easily even or odd numbers of plants than square beds can. Avoid beds planted in rows. They lose dynamic energy and look like a production nursery. Lean to fat planting, as described above, produces a soft and relaxed reaction as the eye begins at the top of the design, pans downward to a flared-out base, and then around the bed back up to the top.

Columns of the Temple of Athena Nike.
Columns of the Temple of Athena Nike.

A fundamental rule in sketching and painting is to refrain from working solely from one corner outward. Gardeners should shape the garden from all directions simultaneously. They should engage with the entire planting area, in the same way that a tree is pruned aesthetically. The tree is simultaneously viewed from all angles. Gardeners should strive for the best possible three-dimensional look, recognizing that plants will inevitably steer their own way. Height, transparency, density, and color may require particular placement for best effect.

One last consideration is the inclusion of different soils, rock formations, structures, and figurines into the garden. These elements may require rethinking plant placements, while maintaining balance and the impact of a well-rounded display.

When modifying existing gardens, rely upon the inspiration art and mathematics can provide. Those mechanics will provide a framework for design decisions. The purpose in utilizing time-worn methods is to produce a garden that will refresh both the eye and the soul.

Enjoy this journey in artistic and mathematical design.

Mary Warren is the Owner of Gardening Artists located in Seattle, WA. She holds a Bachelor of Fine Arts Degree from the California College of Arts and Crafts and a Master of Fine Arts Degree in Sculpture from the University of Washington. She has been gardening since she was four years old, when her mother showed her how to plant fragrant sweet peas.

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