Fibonacci was an Italian mathematician in the late 11th and early 12th Century, credited with bringing the Arabic numeral system to Europe and introducing the use of the number zero and the decimal place. His name is today remembered for the Fibonacci Sequence; an integer sequence whereby each number is the sum of the two preceding numbers:
1, 1, 2, 3, 5, 8, 13, 21, 34 (and so on)
Although it may not seem obvious, there is a strong connection between this mathematical sequence and the composition of artwork. By visualising each number as a square (increasing in size, in the same way as the sequence) and connecting the opposite corners of each square, you can create the Fibonacci Spiral.
The Fibonacci Sequence is intimately connected with another mathematical construct, the Golden Ratio (two quantities whose ratio is the same as the sum of the total to the larger ratio). If this is all getting a little confusing, don’t fear, we shall now leave the numbers behind.
The Golden Ratio is sometimes called the Divine Ratio. Mathematicians found that it was abundant in nature, in places as diverse as the proportions of the human face, the flowering of an artichoke, and the ancestry of the ideal bee.
Artists recognised that the Fibonacci Spiral is an expression of an aesthetically pleasing principle – the Rule of Thirds. This is used in the composition of a picture; by balancing the features of the image by thirds, rather than strictly centring them, a more pleasing flow to the picture is achieved.
From the Renaissance onwards, artists have – whether purposefully or simply by instinct – created dramatic and attractive paintings which demonstrate the Fibonacci Spiral in their composition. One excellent example is Robert Greenham’s Tango Final of British Championship, Blackpool, 1969.
As you can see in the image above, the entire composition is perfectly outlined by two Fibonacci spirals, which trace the line of the spotlit dance floor, the skirts and arms of the dancers, and even the curve of the central lady’s neck, and place the focus perfectly on the two foremost couples. This complex, abstract composition makes it very easy to see the Fibonacci sequence at play, following the bold lines as it does, however it can also be found in other, more naturalistic compositions.
In David Oyens’ Young woman reading in the studio, 1901, the Fibonacci spiral can be seen in the model’s pose; the innermost point of the spiral is placed on her eye, lending focus to her peaceful activity. From here, it takes in the curve of her head and shoulder, with a line extending along her forearm, before sweeping out to encompass the chair, the vertical line of the window, and the angle of the easel in the background.
The same principle can also be discerned in paintings without the human element; Hugh Wilkinson’s View of a New Forest Stream, 1909 also shows the flow of the Fibonacci spiral. In this landscape, the outermost curve of the spiral is echoed roughly in the shape of the darker clouds, the upper right square is delineated by the horizon and one of the higher treetops, whilst the lower sweep of the spiral is echoed by the bank. The centre of the spiral curves around the vanishing point of the stream itself, again creating the perfect focal point.
In our final example, George Weissbort’s The white coffee pot, with fruit and wine illustrates the potential for use of the Fibonacci spiral in the composition of still life paintings. Here, the outer sweep of the spiral is echoed in the varying height of the items, anchored in an apple, which is only partially in the frame on the left, and tracing around the base of the pear on the right. The edges of the component squares line up with the handle of the coffee pot, the stem of the wine glass and even the contents of the glass, creating a pleasing and yet apparently natural arrangement.
The most interesting aspect of the Fibonacci spiral is, perhaps, the fact that it can be forced or simply found. Last year, it was even observed in a journalist’s photograph of brawling Ukrainian parliamentarians.