Sunday, February 10, 2008

Fibonacci Sequence

I often use the Fibonacci sequence when designing quilts and landscapes (I retired my landscape design business in 2007). The formula was devised by a 13th century mathematician called Leonardo of Pisa. Also called Fibonacci, he first introduced the sequence in his Liber Abaci in 1202. Begin with 0, add 1, and the sum is the previous 2 numbers. It goes like so:

0+1=1
1+1=2
1+2=3
2+3=5
3+5=8
5+8=13
8+13=21
13+21=34 and so on.

The top image is one of my landscape designs. I used upright evergreens (cedars and Blue Arrow Junipers) and ornamental grasses in groups of 3, 5 and 8 to visually tie together different areas of the garden, and to create a rhythm around the property. I used specimen plants in the lower sequences of 1, 2 and 3 to provide focal points.

I took the photo at right at Fort Jefferson in the Dry Tortugas Islands in the Gulf of Mexico. The bays are equidistant, and this is a great illustration of perspective. In landscape design, the Fibonacci sequence can be used to force perspective. For example, if you have a long narrow property and want to create the illusion that it is shorter and more intimate, you can plant something on the long axis, spaced apart from your viewpoint in the sequence: 13', 8', 5', 3'. This will visually compress the property. Conversely, if you have a shallow property and want to make it seem longer, space your plants apart from your viewpoint like so: 3', 5', 8', 13' etc.

For designing quilts, I use this sequence in it's simplest form. For example, on the Healing/Protection Quilt, I sewed buttons on in Fibonacci sequence groups e.g. 3, 5, 8 buttons in a row. Or I may design a quilt that will measure 21" x 34"; a pleasing proportion.

The Fibonacci sequence is commonly used by designers and architects, and is one of my favorite devices for pleasing design.

1 comment:

Jack L said...

Thanks very much for your article! How would you calculate Golden Ratio borders an art quilt that measures 27x32"? To make matters more challenging, it needs to fit in a 36" square space.