Sunday, July 19, 2015

Fibonacci Sequence, Divine Composition or The Golden Ratio

three yellow sunflowers on a white background
Sunflower Bright, copyright 2015, Stephanie Maatta Smith
Recently I had the pleasure of participating in a local artists’ challenge. While the subject of the challenge was “sun flower” and our artistic interpretations of this subject, the discussion began with Fibonacci Sequence, or the Golden Ratio. This is, of course, a foundational concept of artistic composition, and one that occurs naturally in nature.

Without going into a long explanation the Fibonacci sequence is a mathematical sequence that forms a spiral as the numbers become larger and are combined into squares. (Here’s a link to a quick and easy explanation of the math.) The start of the sequence is 0, 1, 1, 2, 3, 5, 8, 13; the sequence develops by adding succeeding numbers together (0+1 = 1; 1+1 = 2; 2+1 = 3 and so on). What’s even more intriguing is the aspect of ratio in the sequence, with each pair of successive numbers having the same approximate ratio of 1:1.61.

looking down the lighthouse stairs, showing the spiral staircase
Ponce Lighthouse Stairs, copyright 2012, Stephanie Maatta Smith
The Golden Ratio is sometimes considered a "souped up version" of the Rule of Thirds. Ah, yes, we all nodded our heads sagely; we’ve heard of the Rule of Thirds. Using the rule of thirds, the artist or photographer creates an image by imagining a 3 x 3 grid overlaid on the frame and positioning the subject carefully on one of the intersecting lines; thus, drawing the viewer into the image and leading him or her to the subject. By employing the Golden Ratio of 1:1.61 and envisioning the resulting spiral in conjunction with the Rule of Thirds, creative works become harmonious and pleasing to the eye.  It’s the foundational principal that makes a work of art, photography, and architecture feel right and all visual elements in proportion to each other.

center of a daisy
Daisy Central, copyright 2014, Stephanie Maatta Smith
The spiral and corresponding mathematical sequence are seen repeatedly in nature. For example, the seed heads of a sunflower are formed in outward reaching spirals with the seeds becoming larger as they reach to outer edge. The same pattern is seen in the carpel and stamen of a daisy. In nature, this design not only looks pleasing, but also serves a purpose. Seeds, petals, leaves grow in this pattern to give stability to the plant structure and to allow all of the leaves and seeds to receive light and water, ensuring growth and reproduction.

For more on the Fibonacci sequence and Golden Ratio in photography, check out this Digital Photography School article.

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