Fibonacci Flower

Concept

Fibonacci Ellipses

The Fibonacci Ellipses collection shows arrangements of ellipses whose major axis (height) and major axis (width) are two consecutive Fibonacci numbers. The length of the large main axis of an ellipse becomes the length of the small main axis of the following ellipse. From the property of the Fibonacci numbers it follows that the major axis of the following ellipse is the sum of the major and minor semi-axes of the previous ellipse.

The Fibonacci Flower image uses the ellipses to bring to bloom the petals of a mythical and fabulous flower that vaguely resembles a lilac water lily. The petals are continuously rotated around the center by the golden angle and touch the innermost ellipse (a circle). Similarly, many plants in nature do this to minimize shading of their leaves and maximize sunlight.

Arrangement

The smallest ellipse is a 1×1 circle and has been colored red as the origin of the image. It symbolizes the core of the plant from which the petals grow. The first petal (a 1×2 ellipse) is arranged horizontally to the right. The following ellipses are each rotated counterclockwise by the golden angle 137.508º and positioned below the preceding ellipses. Each petal touches the core with its main axis of the ellipse. The last two truncated ellipses indicate the infinity of the Fibonacci sequence and thus also the Fibonacci flower.