Does our Datura Painting Represent a Golden Spiral?

Does our Datura Painting Represent a Golden Spiral?

Scott and I have been working hard on this Datura painting.  We just finished the background behind the flower bloom.

Datura photo with grid

On social media, a friend asked if this blooming Datura flower contained a Golden Spiral?

For years, since learning of the golden spiral I have been interested in this subject.  The golden spiral is related to the golden mean, the golden proportion, the golden ratio and the Divine proportion.  The Golden Ratio is called Phi, similar to another famous ratio, Pi.  To learn all about the math of the Golden Ratio, click here.

golden spiral created from the golden ratio or golden number

"The Golden Spiral", from www.csun.edu

The golden ratio has been used in art and architecture at least as far back as the ancient Egyptians in the Great Pyramids.  The Golden Ratio was also used by the Ancient Greeks to construct the facade of the Parthenon. 

Parthenon with golden proportion

This, perhaps, invisible math in the architecture of well known religious monuments was meant to enhance the divine nature of these manmade sites. 

To the Western eye, the golden proportion is considered innately beautiful and pleasing and divine in nature.

The golden spiral and it's ratio are found in plants, animals and human proportions.  A good example is in a pinecone.

golden spiral in nature, pinecone

From https://www.goldennumber.net/spirals/

So does our unfolding Datura flower exhibit a golden spiral?

I could have purchased some software and upload our image to analyze the spiral,  but I decided that I wanted to measure and draw out the spiral myself, using paper, pencil, compass and ruler.  Thankfully, I learned how to draw the Golden Spiral at Waldorf training last summer!

Golden Spiral using geometry

Golden Spiral at Waldorf Training, Rudolf Steiner College, July 2018

I printed a copy of the Datura picture and outlined one of the spirals in black sharpie.  Then, using the inner part of the spiral to determine the basis of the ratio, I started measuring out squares using the Fibonacci sequence, for example, the innermost squares are 1 x 1.  The next biggest square is 2 x 2; this is where the spiral begins in the center.  The next square after that has is a 3 x 3 square, then a 5 x 5 .  Next there is an 8 x 8 square and finally a 13 x 13 square.  I accomplished this using geometry rather than measuring, because getting a precise measurement on a photocopy was difficult (I needed more precise tools for that).  

Datura analyis, does it contain a golden spiral?

My analysis of the Datura using a method to draw the Golden Spiral

Each adjacent set of squares makes an approximate of the ratio of Phi, for example, 13/8 is 1.625.  To make an actual golden spiral, you must take a compass with a radius of one of the sides of the square and draw a quarter circle from one corner of the square to the diagonal corner of the square.  This will give you the unfoldment of the Golden Spiral.

Unfortunately, the Datura spiral did not quite line up with the actual golden spiral implicit in the unfolding squares.  Its prettty close and in some of the squares the curve fits.  But I would conclude that the Datura spiral is not technically a Golden Spiral, based on Phi.

However, Gary Meisner does a great analysis of a nautilis shell which also does not technically contain a golden spiral. I invite you to compare and see what you think.

 

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