Thoughts on Fibonacci Series Segmentation of Images

I made a photo of the Fens described previously. I called it “We are so small in the eye of God” as that is the thought that the image evoked in me.

I liked it enough to want to print it. It is a 55 x 165 mm negative taken on on my Fuji G617 camera. My largest enlarger is a 4x5 enlarger which can only accommodate 127 mm in length (5 in x 25.4 mm/in). It is also inconvenient to use this enlarger. I thus thought I should look at different ‘triptych’ forms that I can make using my 60 mm x 60 mm enlarger and print the overall image in segments. This can be quite effective.

I tried first for a proper Triptych (3 equal-sized segments) This fit in with my enlarger as 3 x 60mm is greater than 170mm on the negative. However the scene is neatly divided in thirds where the sun exactly straddles the left side division and the road and farm straddles the right side division. It looks messy.

Tryptych Mock-up

Next I opted to look at 4 segments (a quadriptych) and this works much better. Additionally each segment has an aspect ratio of 3:4 which fits exactly the 12” x 16” paper size. This would give me an image 48” across and 16” high. This got me very excited as the size would be substantial and the prototype of the layout works effectively I feel. I finally made this print and a frame a mount for it which I described in this post.
Quadritych Mock-up
Speaking to my wife she suggested I look at Fibonacci versions which I immediately latched on to as an interesting idea. The Fibonacci series is a an easy to compute number series that also forms the basis of the golden ratio 1.816:1. The series is computed by summing the the first two numbers (starting with 0 and 1) to make the third then proceeding in the same fashion. So 0+1=1 then 1+1=2, 1+2=3, 2+3=5, 3+5=8, 5+8=13, 8+13=21 etc to give the series of 0, 1, 1, 2, 3, 5, 8, 13, 21...

My first attempt was 1,2,3,5,8. This breaks the sun up and the largest segment is too big for my 6x6 enlarger. However I am intrigued by the diminishment of the image on the left edge.
1-2-3-5-8 Series Mock-up

I also tried 4 numbers. Again the largest segment is too big for my 6x6 enlarger. Though the breaks work nicely for this image.
2-3-5-8 Series Mock-up


I then tried a series of 3 numbers. One quickly realizes that mathematically the larger of the 3 segments is always half the image.  ( the two smaller numbers sum to the larger, image length = a+b+c where c=a+b so length = 2x c) Again this creates a practical problem in that my 6x6 enlarger I planned to use cannot make an image from half a 165mm negative. My 4x5 could however. The proportions are pleasing and they work with this image.

1-2-3 Mock-up
3-5-8 Mockup
5-8-13 Mockup
The 3-5-8 and 5-8-13 look useful though again I cannot print the right hand images on my 6x6 enlarger so would have to move to the ‘Beast’ 4x5 enlarger. They are nearly identical with the ratios of widths in each being similar. This image divides nicely this way.
3+5+8=16     3/16 = .188, 5/16 = .375,  8/16 = .5
5+8+13=26.  5/26 = .192, 8/26 = .308, 13/26 = .5

If I were to print this on 16x20” paper, given the right hand image has to fit on a sheet of paper, this would give about a 40” wide image. The left two images could be printed on a second sheet of the same size then cut to the dimensions.


2-5-3 Mockup with largest segment in the middle. 
The other observation about the 3 image motif is that if one puts the largest image in the middle then the two smaller images could be folded over the center image to cover it. Some religious Triptychs were arranged for the left and right images to be hinged so that they could be closed over the central image. (Indeed tych is Greek for ‘fold’.) This is always possible with this style of Triptych though it is asymmetrical.
This inspires a framing idea borrowed from the religious tradition of an asymmetric folding frame. Perhaps the back of the frame could reveal another photograph split into 2 images.
















Comments