Fibonacci Circle Curves

“How does an artist take inspiration from a Mathematical concept and transform it into a work of art?”

This is a question people have asked me many times. Each artist follows her own path, but translating the aesthetic elements of a mathematical topic into the visual realm of Art is my personal journey. I will discuss the process I developed to to create my most recent series of drawings, which I refer to as “Fibonacci Circle Curves”. I will map the artistic process from my selecting a Mathematical theme, through the many steps it takes to complete a drawing. This is a process that took 18 months to develop.

Through the years I have made many drawings exploring the Fibonacci Sequence. The recursive nature of the sequence makes it an interesting subject for abstract drawing. My new series of drawings investigates the visual qualities of intersecting circles whose area measurements are in proportions related to the Fibonacci Sequence. This experiment is a different way to look at the ratios of consecutive Fibonacci numbers.

EPSON MFP image

The measurement of the area of the first circle in the sequence determines the area of each subsequent circle.The measurement of the area of the second circle is the same as that of the first circle. The measurement of the area of the third circle is twice the first. The measurement of the area of the fourth circle is three times the first. The measurement of the area of the fifth circle is five times the first, etc. This series of circles illustrates the Fibonacci Sequence: 1,1,2,3,5,8…, though  the measurements of their areas.

EPSON MFP image

I made templates for the first eight circles in the series and started to experiment. I started off by drawing the circles in a straight line. I drew the first circle and marked  its center point. then I began the second circle at that center point. Then each subsequent circle started at the center point of its predecessor. In this format it is possible to draw a straight line connecting the center points of each of the circles. I immediately noticed there were some aesthetically interesting shapes created by the intersecting circles, but I was not satisfied. I decided to continue to manipulate the circles. I broke up the straight line connecting the center points into angled line segments. Instead of having the center points of the circles line up, the line segments connecting the center points should create angles less than 180 degrees. After some time it became clear that the best angle to use was the Golden Angle. The golden angle has a measurement of approximately 137.51 degrees. It is the smaller of the two angles formed by two radii that divide the circumference of a circle into two arcs so that the ratio of the measurement of the large arc to the small arc is equal to the ratio of the  measurement  of the total circumference to the measurement of the larger arc.

EPSON MFP image

After curving the series of circles, the space created between the arcs started to look much more interesting. I was still not satisfied with the image, however. I began a process of using this curve as my basic building block. I made a number of curves on transparent paper and I began to superimpose and shift the images. I did not want the drawing to look static but wanted the image to have a sense of movement. I came up with a method of drawing using the line segments created by connecting the center points of adjacent circles. Using these line segments as a guide, I dragged the template of the first circle, so that the center point stayed on the guideline. Then I drew multiple circles until the first circle was completely inside the second circle, sharing one circumference point. I repeated this with each of the circle templates. The finished product was finally an image with potential.

EPSON MFP image

This elegant structural unit is the starting point for all of this new work. I have made numerous drawings using multiple Fibonacci circle curves. either shifted or rotated or, and superimposed on top of each other, creating some surprising interactions. I continue to explore the shapes produced through this process. I have made work emphasizing the negative spaces, painstakingly filling in between the lines. By cutting up the drawings and rearranging the sections I have made collages and Artist’s books allowing the viewer to focus on small sections of the curve.

Fibonacci Circle Curve Red

Fibonacci Circle Curve Red

I hope this detailed explanation of my artistic practice offers an interesting behind-the-scenes tour of my process, beginning with my thinking about Fibonacci ratios and circles, and progressing through experiments leading to new drawings.

– FibonacciSusan

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