Fibonacci, Phi and Art

If you enjoy math, geometry, mystery and science, this subject might interest you. It is too complex for a simple blog post. Here are some highlights and I will include links if you find this subject as intriguing as I did. Enjoy.

Phi, also known as The Golden Ratio or Divine Proportion, Golden Section, Golden Mean, is represented by the number 1.61803399. The digits can go on forever without repeating. We will simplify it to 1.618. 

The Fibonacci Sequence is nature's numbering series and provides another way to derive Phi mathematically. The sequence of numbers is quite simple. Starting with 0 and 1, each new number in the sequence is simply the sum of the two before it, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. The approximate ratio of each successive pair of numbers in the sequence is 1.618 or Phi. (Example: 5 divided by 3 = 1.666.) As you go further into the sequence and more digits are added, the ratio gets closer to the exact figure of Phi.

Both The Fibonacci Sequence and Phi represent the same number, 1.618, therefore they are inseparable. When Phi is mentioned, know that The Fibonacci Sequence is also there. 

Why were the early Greek and Renaissance artists, scientists, architects, musicians and astronomers so fascinated by this number? Why did Dan Brown use Phi as a plot element in his novel, The Da Vinci Code? Why do we still use Phi today?

“Phi creates a sense of balance, harmony and beauty in the designs we find throughout our natural world and the universe thereby creating a sense of harmonic relationships and spiritual connections.”  Since ancient times, man has applied both Phi and The Fibonacci Sequence consciously and unconsciously to achieve balance, harmony and beauty in art, music, architecture, design and religion.

The influence of Phi may be seen in the works of the early artists such as Da Vinci, Raphael, Botticelli and Seurat, right up to present day artists. Musical scales and compositions and the dimensions of musical instruments, such as the violin, all show the influence of Phi. Architecture, such as the Notre Dame in Paris and the Greek and Roman Temples are another example. Industry uses Phi in the design of their logos and products, such as cars and fashion. In medicine, Phi is used as a guide in both facial plastic surgery and cosmetic dentistry.

The Fibonacci Sequence and the influence of Phi appear everywhere. In nature they are is seen in the leaf and petal arrangement in plants and flowers, the bracts of a pinecone, the scales of a pineapple, the arrangement of seeds in a sunflower. Many insects and animal dimensions are based on Phi, such as the spirals of seashells, the body sections of ants and other insects, wing dimensions, etc. Even in the arrangement of the bones of our hands and the spirals of human DNA. Astronomers have found Phi and the Golden Ratio relationships in our solar system and the universe.

We didn’t invent Phi or The Fibonacci Sequence. It was always there. It is as old as the universe. Some Theologians believe that Phi is linked to the Creation. 

Pretty interesting reading.

Two related topics that you might find interesting:

The Golden Rectangle – the most pleasing rectangle with sides having a ratio of 1.618. (Phi again).

Rebatment – the two squares within a rectangle and its importance in composition and the formation of the Fibonacci Spiral.

And the links:

http://www.goldennumber.net/

                  

http://emptyeasel.com/2009/01/20/a-guide-to-the-golden-ratio-aka-golden-section-or-golden-mean-for-artists/

http://emptyeasel.com/2009/01/27/how-to-use-rabatment-in-your-compositions/

Thanks for visiting.

Celene

www.CeleneFarris.com

April's Virtual Paint Out - Sri Lanka

This month we visit, via our computers, Sri Lanka (formerly known as Ceylon). A small tropical island slightly larger than W. Virginia, located south of India in the Indian Ocean and home to over 22 million people. A land of rain-forests, rolling plains, lush farmland and beautiful sandy beaches. The climate is tropical with abundant rainfall and fairly constant temperatures ranging between 60 and 90 degrees year round.

Mirissa, Sri Lanka, 9x12, oil  SOLD

This painting was available in my Ebay Store - Virtual Paint Out.

Thanks for visiting,
Celene

To see all my paintings from our Virtual Paint-Out tours, please click here.

www.CeleneFarris.com

Jazz

I’m watching a wonderful Ken Burns series on Public Television called “Jazz”.  The similarities between music and art are striking and worth thinking about.

Jazz is a combination of many musical styles. It’s distinctive sound ranges from smooth, classic jazz and swing all the way to extreme jazz. The jazz musician takes an ordinary melody and transforms it into a new sound. Some musicians push it even further until the music resembles an abstract painting. It is music that we can feel, as well as hear. Music with a soul. In painting, a good artist takes an ordinary scene and shows us more. I’ve heard it referred to as the “Wow Factor”.

The elements of jazz, like a painting style, are difficult to define. One key element is Improvisation, which is a very personal response to the music. Improvisation is a part of our everyday life, our inner being, influencing how we live, how we dress and speak, what we do and how we act. And it is constantly changing and evolving. The dictionary defines Improvisation as - “Creativity; spontaneous or unplanned changes; the ability to create something personal; a unique process of expression”.

In the movie, “The Glenn Miller Story,” Miller (played by Jimmie Stewart) was an unsuccessful, struggling bandleader. Out of desperation, he came up with the idea to modify the reed section of his band and alter the pitch. Success! His distinctive new sound was born. He said,” A band ought to have a sound all its own. It ought to have personality.”

The traits these successful musicians all had in common were hard work, dedication, a love of music and a determination to find their own voice. We all start as beginners producing the technically correct but stiff painting or music. Somewhere along the line, our inner muse begins to take over and we begin to feel the freedom of self-expression developing. Our paintings begin to have “personality and a sound all its own” -  and how far we take it is up to us. 

As Duke Ellington said, “It don’t mean a thing, if it ain’t got that swing.”

Can you put the swing into your paintings?

Happy painting,

Celene

www.CeleneFarris.com

Marshal Pt. Lighthouse, Port Clyde, Maine

Still going through my stash of photos and memories.

I love living near the Maine coast. This is one of my favorite lighthouses. We visited here last summer and stayed to watch the sun go down. The light in the tower came on just a few minutes after I snapped this picture.

I was there with a painting group a few years ago when the weather quickly changed and a heavy fog rolled in. Suddenly the fog horn started and the noise was deafening. We packed up and left. No sense staying to paint. You couldn't see anything but fog or hear anything but that horn!

  

End of the Day at Marshal Pt. Light, 5.75 x 12, oil

Thanks for visiting,
Celene

To see all my paintings from our Virtual Paint-Out tours, please click here.

www.CeleneFarris.com

Memories of St. Augustine, Florida

I was going through my stash of photographs the other day and found this one in my Florida section. It brought back so many wonderful memories. For many years my husband and I spent the months of February and March in Florida. We rented a house at the beach just south of St. Augustine. I can still remember this day, the warm Florida sunshine and the sights and sounds of colorful St Augustine.

We haven't been to Florida in a number of years. Can you believe that we actually missed Maine in the winter? We did.

Shopping in St. Augustine, 6x8, oil. SOLD

This painting was available in my Ebay Store - Small Treasures

Thanks for visiting,
Celene

www.CeleneFarris.com

Using Up Spare Tubes of Paint

I received this email the other day. “Oil paint is so expensive. What can I do with all the tubes of paint that I’ve bought and never used? I hate to buy more when I have all these extra tubes in my studio.”

My suggestion would be to experiment with these extra tubes and try to mix the colors that you normally use, especially the more expensive colors.

For example, here a few ways to mix an acceptable Yellow Ochre Light:

Yellow Ochre Light = White, Yellow Ochre or Raw Sienna and a bit of Yellow.
Yellow Ochre Light = White, Permanent Green Light and Permanent Rose.
Yellow Ochre Light = White, Yellow, a bit of Olive Green and Orange.

Naples Yellow = Add more White to the above mixtures.
Olive Green = Black and Yellow.
Cobalt Violet = White, Purple, a touch of Red.
Various Reds = Alizarin, Orange and/or Yellow.
Various Oranges = Permanent Rose and Yellow.
Cerulean Blue = White, Ultramarine Blue and Viridian.

The Earth Colors – Burnt Sienna, Light Red, Venetian Red and Indian Red are all variations of a Brown with varying amounts of Red. Experimentation will show you that Red and Green = Brown. By adjusting the amounts, you can easily make these colors. Add White to produce Yellow Ochre and Raw Sienna. Add a bit of Ultramarine Blue to produce Burnt Umber and more Blue to produce Raw Umber.

The list could go on………

(Note: I use the word Brown for illustration only, as we know that Brown is really the darkest form of Yellow.)

Technically you only need the three primaries, Yellow, Red and Blue, plus Black and White, to mix all colors but having tubed colors is certainly convenient, especially for Plein-Air work. But in the studio you can experiment with and slowly reduce the number of these extra tubes. The results might surprise you.

Tubed colors are evenly mixed, while your new colors, if left slightly unmixed, will be vibrant and exciting. By varying the amounts and choice of colors used, you also vary the results and you can tweak a color in a new direction if you choose. Also tubed colors vary by manufacturer so if your mixtures are a bit different it’s okay. And, who knows, as you become more comfortable with color mixing and substitution you might prefer your own mixtures to some of the ready-made colors.

Oil paints are expensive and we all have tubes of unused paint lying around. This is a good way to learn color mixing while reducing this extra inventory and save a little money in the process.

Happy painting!

Celene
www.CeleneFarris.com

March's Virtual Paint Out - New South Wales, Australia

This month our painting group traveled (via our computers and Google Street Maps) to New South Wales, located near the south-east corner of Australia. It's a diverse region of rugged mountains, arid outbacks with opal and silver mines, rainforests, fertile valleys known for vineyards, wineries, vast sheep and cattle ranches, and a beautiful coastline of long, sandy beaches. Temperatures extremes have been recorded as low as minus 10 degrees in the winter mountains to a sizzling 120 degrees in the summer inland arid regions. Discovered by Capt. Cook in 1770, it was colonized in 1788. Covering an area of 312,528 square miles, the current population is approx. 7½ million.

Sheep Farm
New South Wales, Australia, 9x12, oil  SOLD

Cape Byron Beach
New South Wales, Australia 9x12, oil  SOLD

I do enjoy these virtual painting trips and spend quite a few hours touring the countryside and reading a bit of the history, all from the comfort of my studio. Many thanks to artist, Bill Guffy, our travel manager, for all the hours he must spend coordinating and maintaining the Virtual Paint Out website. Thanks, Bill, I'm looking forward to next month's destination.

To see all my VPO paintings from all our destinations, please click here.

These paintings were available in my Ebay Store.

Thanks for visiting,
Celene

www.CeleneFarris.com