Drawing and Painting the Landscape – What is the Proportion of the Rectangle?

Fibonacci Spiral

Lesson 29 is the first lesson in the chapter on Composition in Drawing and Painting the Landscape by Philip Tyler.

Philip starts the chapter by defining composition:

Composition is the art of arranging the various elements of the image into a whole, a balancing act with the shapes, colour, tonalities and mark making to create a visually interesting, exciting landscape.

Most of the lessons in the chapter are about mathematical concepts that can help with composition, but lesson 29 includes the important message:

Mathematics underpins many things but one shouldn’t be bogged down by it.

The lesson starts by describing the golden logarithmic spiral. Wikipedia has a good explanation with a nice animation (Wikipedia - Golden spiral).

Philip explains a technique for drawing a Fibonacci spiral - which is an approximation of the golden spiral. He suggests using a pencil and compass to draw the spiral - which I found impossible to do accurately - the diagrams in this post are drawn in PowerPoint. The technique results in an approximation of a spiral. We draw a sequence of circular arcs. As the resulting shape transitions from one arc to another, the distance of the curve from the centre jumps and the centre moves. In a true spiral the centre stays in the same place and the distance to the centre changes continuously and smoothly. 

Philip points out the ratios of a lot of off the shelf canvases: 1 x 1, 1 x 2, 2 x 3, 3 x 5 and 5 x 8 are based on adjacent numbers in the Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 65, 89, 144, 233, …) and the rectangles appear when drawing a Fibonacci spiral (the 5 x 8 rectangle is highlighted in the second diagram).

Fibonacci Spiral - 5 x 8  Rectangle

This leads into an exercise to explore alternative compositions for a scene by drawing it multiple times altering the format, scale, colour and placement. (I think Philip missed tone from this list).

Mousehole - Thumbnails
Watercolour Pencil
Stillman & Birn Alpha Series Sketchbook
30.5cm x 21.5cm (12" x 8.5")

I made some mistakes with this exercise. 

• The scene is too pretty and too detailed. It would be better to use an image that is simpler and less obviously attractive – something that needs some work to improve it
• The rectangles are too repetitive. I drew rectangles based on the ratios of watercolour paper blocks. It would be better to use fewer more varied rectangles
• Watercolour pencil is not the right medium
• The most fundamental mistake was not doing some monochrome tonal studies first

This was still a useful exercise. I’ve learnt a couple of things that will help if I paint the scene. 

My favourite of the thumbnails is top right. I prefer this to the one directly below it which is closer to the proportions of the original photo – this challenges my assumption that I don’t need to work on the size and placement of the scene - maybe I can improve things by zooming in.

Most importantly I realise the importance of creating a pleasing tonal pattern for this scene and my next step will be to draw some simpler monochrome thumbnails using 4 or 5 tones.