March 1, 2013

# Fibonacci, Nautilus Shells, and Photography

I’ve been spending a lot of time thinking about composition lately.  I am really trying to push myself to get beyond the rule of thirds and try  out some new methods.

The method I’m experimenting with now is called the Golden Spiral.  It’s based on of all things an ancient sequence of numbers that often repeats in nature.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144

The sequence is often called the Fibonacci numbers and is named after  Leonardo Fibonacci who was an Italian mathematician.  He didn’t actually invent the series (it’s though to have originated from the Hindu–Arabic numeral system.

The sequence is based on adding the adding adjacent numbers in a string, then carrying the results.

0+1=1, 1+1=2, 1+2=3, 2+3=5, 3+5=8, 5+8=13, 8+13=21, 13+21=34 (and so on)

A tiling image with squares whose lengths are successive Fibonacci numbers
By Borb — Wikimedia Commons

If you draw  circular arcs to connect the opposite corners of squares, you end up with an approximate shape of the golden spiral.  This shape actually takes on the exact look of a nautilus and expresses the number Phi (or golden ratio).

By Dicklyon — Wikimedia Commons

Okay, enough match class…  but you have to admit it’s a little creepy how often this appears in nature… the most obvious is here.

Detailed photo of a halved backlit shell of a chambered nautilus (Nautilus pompilius) isolated on white
Photo by Fyletto — iStockphoto

But it shows up in lots of other places too… by using this ratio, you can often add some energy into the composition.  The good news is that you can also get here trough cropping in Photoshop or Lightroom.

1. Open an image with Photoshop or Lightroom.
2. Choose the Crop tool.
3. Press the O key to cycle through the crop methods.
4. Press Cmd+O (Ctrl+O) to rotate the asymmetrical options.
5. Crop as desired using the Golden Spiral as a guide.

There you have it… the Golden Spiral applied to postproduction as well.  Give it a shot and see that you think.  Aim for in-camaera composition for the best results, but use the Crop tool where needed.

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### Join the conversation! 9 Comments

1. FYI, on Windows it’s Shift-O, not CTRL-O to rotate the circular grid

2. John, is that in Photoshop or Lightroom?

3. If I am not mistaken from my art classes — the rule of thirds is a simplified version derived from the golden ratio.
i.e. 1/1.618… = 0.618… is too hard to estimate on the fly, so instead people started using 2/3 and called it the rule of thirds.

4. Great post. I only thought of Fibonacci numbers as retracements (in technical analysis of stock charts). It will be nice to try to apply this to photography

5. I’m using Lightroom 4, and couldn’t find the Golden Ratio or Spiral

6. Richard, using Lightroom it is Shift-O to rotate on a Mac.

7. Sorry I missed your reply on Friday Richard, it’s in Lightroom 4 on PC.

8. Reblogged this on fabioandroider.

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Richard Harrington is the founder of RHED Pixel, a visual communications company based in Washington, D.C. He is the Publisher of Photofocus as well as an author on Lynda.com. Rich has authored several books including From Still to Motion, Understanding Photoshop, Professional Web Video, and Creating DSLR Video.

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