Most artists have heard of the golden ratio or rule of two-thirds, but not every artist know all the different variations let alone how to use such mathematical tools. In this article I will go over these various tools of Phi and my interpretation on how to and when to use them. Also for the digital artists I have included these files to be transparent PNGs that can easily be adjusted to the area of what ever size canvas you may be working on because when stretch or squashed it will keep the ratio in relation to your canvas, allowing for a quick compositional grid overlay.
The Golden Ratio
The golden ratio is is a grid divided into thirds, with the middle rows being half the size of one of the out rows but when the outer rows are added to the middle then the total length and width are attained in a balanced mathematical proportion with a ratio of 1.68. To use this grid in art, one simply needs to place the focal point of their composition on and around one or more of the intersections of the grid. Another option is to the columns for placement. If one used the center then one can create a power focus but such focus needed only when the subject is overwhelm the audience. For instance the statue of liberty or the Monolith from 2001 space Odyssey.
The Rule of Two-Thirds
This is the cousin of the Golden Ratio and it is used exactly the same way with just a little different placement as the area of the piece is divided equally into thirds.
The Golden Triangle
The Golden Triangle is a little different than the ratios and the point of using this tool is for directional line or for placement that breaks up the piece into thirds. If used for directional line the focal points line up and the intersection and spread out but for placing the images into thirds then one to two of the triangles will contain your focal points but it is best to do this on separate planes.
The Golden Spiral
The bottom one is the one with the transparency
The Golden Spiral is about placement and flow of the picture to help guide the eye of the viewer around the picture plane. This is a powerful grid and it is a form of fractal that can be found all through out nature. From studying various strong compositions and other articles about this tool I can tell you that it is the hardest one to follow, but I hope my understanding will make it clear you you all. The grid itself is based on the golden ratio but it can definitely spiral tighter and tighter and it keeps breaking down . Inside these sections you can place your main focal points of your composition as long as they remain for the most part of the inside track of the spiral that is formed from the cornered points. Secondary focal points can be created by placing them as an intersection along this spiral path which will create flow and guide the eye around your composition.
Down Below are examples of my artwork that show how these grids work for strong compositions.
Also it is important to note that you don't have to limit your self to just one of these tools or the multiple use of the same tool but with different orientation with the only proviso that you do not distort the ratios.
I have included one more transparent ratio grid and that is a master grid that gives all possible orientation, but I would advise starting off with these separately until you understand how they work before trying to use them all at once.
Lastly if you have any questions please feel to ask and I will answer them the best I can. Also I don't claim total knowledge in how the golden ratio can be used and I feel that there are many different methods in using it so if you know something I don't then please share with a comment.