I have been fascinated by the Fibonacci ratio, particularly since this pattern occurs so frequently in the natural world. Its proportions can be seen in the spacing of joints in the human fingers, the arrangement of seeds in a sunflower, and the spiral of a nautilus shell, for example. The numerical sequence begins with 0, 1, 1, 2, 3, 5, 8, 13, and continues indefinitely – each number is the sum of the two previous numbers (as illustrated in the first image below). It can be theorized that many of these patterns have evolved for efficiency: to maximize the number of leaves, seeds, etc., that are exposed to sunlight. This ratio is also very pleasing to the eye, and has therefore been used in various types of design.
 
Landscape architects sometimes incorporate Fibonacci proportions in their projects through a variety of means, such as with pavement design, scaling of spaces, and object/plant groupings. In many cases, these designs have focused on numbers and rectilinear shapes, although the spiral has also been used in artistic ways. A couple examples of the rectilinear usage of this ratio include Dan Kiley’s design for NationsBank Plaza in Tampa, Florida; and Lawrence Halprin’s scheme of structural spaces at Riverbank Park, in Flint, Michigan. An example of a spiral design in the landscape is shown below (last image).

The Fibonacci ratio and associated spiral

A beautiful example of Fibonacci spirals in False Queen Anne’s Lace

The “eyes” of the peafowl’s feathers spiral in toward the bird in Fibonacci proportions.

Aloe polyphylla – Photo credit: J. Brew

Fibonacci numbers were used in this woven scarf to create a transition from one color to the next.

Fibonacci spiral in a railing detail

The Core education center, Eden Project, in Cornwall, U.K., was designed using Fibonacci proportions and spirals. Photo credit: Pauline Eccles

Spiral Fountain in Darling Harbour, Sydney, Australia – Photo credit: Greg O’Beirne
 
All photos and images not credited otherwise were taken/created by Alice Webb. Photos by others were obtained from Wikimedia Commons.