Phyllotaxis describes the arrangement of leaves on a stem and in relation to each other.

Read about the relationship between helical leaf arrangements and the patterns on shells through the

See Ron Knott and the University of Surrey’s website for a thorough introduction to Fibonacci sequence: http://www.ee.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html

The Biological Modeling and Visualization group at the University of Calgary study the development of natural forms and patterns using computer science methodology. These techniques—modeling, simulation, and visualization—enhance our understanding of the development of plants.

Visit their website to explore the field of Algorithmic Botany

The seeds of a sunflower, the spines of a cactus, and the bracts of a pine cone all grow in whirling spiral patterns that are remarkable for their complexity and beauty. Over eighty percent of plant life exhibits spiral growth patterns. Spiral growth patterns are so prevalent because they give plants the maximum access to sunlight and water. Spiral patterns are also widespread in seedpods. The spiral pattern helps plants pack the greatest number of seeds into the smallest space. These growth formations also show consistent mathematical patterns such as the formula known as Phi or the Golden Ratio.

For in-depth information visit Smith College’s website on Phyllotaxis,

an interactive site for the study of plant pattern formation.

The golden ratio, also known as the golden mean, golden section, or divine proportion is a number frequently found in the ratios of distances in simple geometric figures, including the rectangle, pentagon, and dodecahedron.

The simplest way to think about the golden mean is in terms of a rectangle with the shorter side equal to 1 and the longer side equal to the number φ (phi), which is approximated by the decimal 1.61803399. If you subdivide the rectangle into a square and another rectangle, the new, smaller rectangle will have the same proportions as the first

rectangle. If you divide the new rectangle in the same way, you will get a third rectangle with the same proportions as the first two, and so on. This pattern can be seen in the graphic above. If you draw a curved line connecting the division points of the rectangles, you get a particular kind of spiral—a logarithmic spiral. The figure is known as a whirling square.

Read more about phi under Architecture and Contemporary Art.