The Sunflower Mandala:
A Universal Growth Pattern of Expansion and Contraction
The Sunflower Mandala exercise will remind you of a dynamic motion found in the Natural World. Experience the beautiful principle of infolding and unfolding as you work and participate in a creative process which is timeless and universal.
The sunflower unfolds in a double logarithmic spiral pattern of Golden Mean proportion of approximately 1:1.618 . . . . A similar double logarithmic spiral pattern based on the diagonal of a square, or approximately 1:1.414 . . . , is illustrated in this exercise.
The overall pattern is created by a series of proportionally related squares arranged concentrically around a central point. The proportional relationship is between the side or edge of any square and the diagonal, such that:
- The side of any square is equal to the diagonal of the adjacent smaller square.
- The diagonal of any square is equal to the side of the next larger square.
- This relationship can be mathematically expressed as follows: 1 : square root of 2.
These two images were created with 7 concentric rings of squares, each of which is in a similar relationship to the previous ring and to the following ring. The resulting pattern appears to spiral in or out to infinity, depending upon your intention and focus.
You will need a few simple tools and supplies to create this image. The exercise has been planned such that young children, as well as adults, can create the pattern, so the basic materials list is simple and inexpensive. If the following items are not available to you exactly as listed, improvise with some creative alternative.
You will need the following:
You can start with a square of any size to achieve this pattern, as it spirals in and out infinitely; however, for your first mandala, I suggest you begin with a 1-inch square for the largest square and proceed inward with the proportionately smaller squares. You will be cutting 12 squares of each size.
The images shown below have 6 concentric rings of proportionate squares, so they require 72 squares. Of course, you can add more if you like, and the proportionate squares will become infinitely smaller or larger.
In these two examples, the pattern is identical, but the overall effect of each image is different. The spiraling Sunflower image is Dynamic, while the Rose Window image is Static. The pattern on the right is actually the concealed Geometry underlying some of the Great Cathedral Rose Windows.
“Rose Windows” by Painton Cowen is an excellent book describing this Geometry in detail, as are other works by Burckhardt, Critchlow and Lawlor.
If you follow the guidelines illustrated in the two line-drawing images above, your creation will fit nicely on a 10-inch-diameter paper plate, which also adds a sturdy circular frame for displaying your work.
To begin, start with a point on your page, and it draw a vertical line and a horizontal line perpendicular to it, also through your center point. Next, using your compass, draw a circle with a 3.4-inch radius. Then with the same compass radius, further subdivide the circumference of your circle into 12 segments. Remember… the radius of a circle exactly cuts the circumference into 6 equal segments. It is easy to then divide these arcs in half, resulting in 12 segments.
Draw light guidelines with your straightedge from the circumference into the center. The corner point of the largest square (with 1-inch side length) should be placed so that it just touches the guideline circle. The rest of the exercise will unfold to you as you work.
|Use your compass to draw more circular guidelines as you need them and as you progress proportionally in toward the center. If your guidelines are drawn lightly with a pencil they will not distract from the completed image.|
This type of pattern is referred to as a Mandala, a Star Polygon, a Rose Window, and other names as well, depending on the culture, tradition or application where it is used. The image can be developed into a Tessellation or Field Pattern if repeated in a way such as the last image shown here. The possibilities are infinite! Let your imagination soar!