Geometric Abstraction #1
We have chosen the most complex arrangement from our sketches to demonstrate a range of techniques that you can use to further develop your composition. The aim of most abstract art of this type is to find an arrangement of the components that reflects some kind of fundamental order.
In our first example we have reduced the components to a two dimensional network of positive and negative shapes. Wherever two black planes overlap they change to white and create a checkerboard pattern. There are, however, several areas in the composition where three planes overlap and these have been colored red to maintain the integrity of the design.
Geometric Abstraction #2
In this example we have continued using a two dimensional checkerboard pattern but have placed a greater emphasis on color.
Note that we have restricted the number of colors to four: the three primaries and black. If a complex pattern is shaded with too many colors the effect gets too complicated for the human eye to appreciate. Therefore, in order to 'reflect some kind of fundamental order' it is best to use as few colors as possible - four to be safe according to the Four Color Theorem  in mathematics.
Geometric Abstraction #3
In our third example we have assigned four transparent tones, one to each of the four planes of our component. The way we perceive the transparency of these overlapping planes creates a fluctuating form of ambiguous space.
Geometric Abstraction #4
In our next development we have translated the transparent monochrome tones of the previous example into color and outlined the drawing with black lines to create a vibrant stained glass effect.
Geometric Abstraction #5
This development switches to a more three dimensional interpretation of our drawing. The opaque planes of each component are arranged to form interlocking shapes that suggest a sculptural chain. The bold red background was added to contrast with the monochrome components and accentuate their form.
Geometric Abstraction #6
Our final study continues the three dimensional development of our image where each component is a different color in a sequence that progresses through the colors of the spectrum. The sequence both starts and ends with red to complete a visually satisfying sense of order.
The sketches above demonstrate the type of thought processes that artists follow when developing ideas for 'Geometric Abstraction'. There are variations that you can add to the process in the search for 'some kind of fundamental order'.