Happy Halloween, my lovely blog reading friends. No, I’m not going to talk about scary things in this post, but if you say Fibonacci in kind of a squeaky door, Vincent Price voice it does sound kind of scary : )
One thing that can be really scary for any artist is a painting that is seemingly missing something, it’s just WRONG and you can’t figure out what it is or how to fix it. Most of the time, these problems have something to do with design fundamentals like scale, color, proportion, etc, which all make up the COMPOSITION. Composition is a complicated, multi-faceted spooky mystery that baffles even the best of us, but knowing a few simple guidelines like The Golden Ratio and the Rule of Thirds can make all difference. The Fibonacci Sequence is another tool for you to add to your composition toolbox and is the one I use most often in my own work.
The Fibonacci Sequence is named after Italian mathematician Leonardo of Pisa, also known as Fibonacci. The Sequence, illustrated below, begins at 0, 1 then those two numbers added make up the next number in the sequence, which is 1, then those last two numbers added make up 2 and so on into infinity. In addition to being used extensively in other mathematical formulas, these versatile numbers are also proportionately related to the Golden Ratio, have been used in poetry and are seen in the growth rate of biological forms nature such as trees, sunflowers, pinecones and pineapples, even human skeletal growth. When these numbers are utilized in any kind of art or design, that design is said to be more pleasing to the eye-it just feels right.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144….
I first learned about this Sequence as an undergrad in a class called Math for Design and I was fascinated. Later, when I was working as a textile designer, we applied these numbers to our stripe patterns, tile designs and anything else that required repetition. Last, I return to the Sequence again and again in my personal work whenever I have a question about repetitive elements or where an element should be placed within the painting.
To utilize the Sequence in stripe patterns, we applied the numbers to inches, mixed up the sequence and naturally applied color. Illustrated below is a stripe pattern (created in candy corn colors for Halloween : ) that is first shown in the sequence as it stands (1), then the numbers in the sequence are mixed up (2), then another stripe pattern in a random number of inches (3). Which is more pleasing?
Addendum: In response to Tess Stieben’s comment regarding which stripe pattern is more pleasing, I added repeat patterns below to illustrate my response. Thank you, Tess!
Tess: Interestingly I prefer #3, it is dramatic, #1 is boring, #2 ok but #3 has a bold punch in the way the colors are divided making the dark contrast with the lighter colors.
My Response: Thanks for your comment, Tess. I see what you mean. Looking at it as is, without repeating, as if we were looking at a painting is quite lovely and I see what you’re saying. Now, think of the stripe as a repeat pattern, floor to ceiling running across a wall or even on a large sofa. Still think the same? The Fibonacci Sequence and the other ratios are used in design because they make the design more pleasing, more comfortable. The dynamic quality of pattern #3 may be more exciting as a painting, but not necessarily if it was covering the four walls of a room. While making paintings, this is also something to consider.
According to the theory, stripe pattern 1 and 2 would be most pleasing. You certainly could have chosen 3, which is totally arbitrary and follows no compositional rules. Feel free to comment, I would be interested to know which stripe pattern is most interesting to you and why-the comment button is located at the top left of this article.
See the images below for examples of how you can apply this Sequence in your own work. I used this Sequence in grad school and beyond by applying inches to the spacing between repetitive elements as well as in the measurements of squares, circles and ovals themselves. Read this post for more about my early work as a designer and how/why I make the work I make today. When you begin to apply this sequence to your own work, please let me know how it’s working for you and if/how it’s made your compositional life easier.
It is important to keep in mind that all of these compositional tools I’ve been writing about in my last few posts are just tools and can be kept in your mental toolbox to use when you need them. As Francis Bacon is attributed to saying, “Knowledge is Power”, so learn what you can and use it wisely.
Addendum: In response to Shary Bartlett’s comment on this post, I created a gallery below where the areas in which I used the sequence are most prominent in the work. In the paintings below, the sequence is also used in the regularly spaced intervals of information in terms of measurement, however the sequential numbers are not used. Thank you, Shary!!!