Monday, January 26, 2015

Wild Sunflower on a Winter's Day

Helianthus divaricatus, Laurel Highlands, 2012

" Sunflower heads form an intriguing geometric pattern that is characterized by spirals that extend from the center outward in both clockwise and counter-clockwise directions.  The spirals are formed in the achenes as they develop, their position relative to proceding achenes optimized to maximize exposure to the sun.  The angle that they form is related to the Golden Ration, Phi, a number that is approximately 1.618034.  The Golden Ration has the unique property that Phi-1=1/Phi.  The Golden Ration is related to the Fibronacci numbers (1,2,3,5,8,13,21...).  As one extends this ration to infinity, the ratio of any number to the one that precedes it approaches Phi (thus 21/13=1.62).  Because of Phi, the number of spirals in either direction on a sunflower head will always be one of the Fibronacci numbers, such as 8, 13, or 21."
- Hiker's Notebook, Wild Sunflowers

While considering Van Gogh's representation of turbulence in 'Starry Night', I wondered about the science and math in the form of wild sunflowers, or even domesticated sunflowers since they follow the same pattern.  Van Gogh wrote to his brother Theo, "The sunflower is mine," and though he created a series of sunflower paintings, I can't see that the Golden Ratio or the Fibonacci Sequence influenced his work, at least in an overt way.

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