## Perspective as Geometric Abstraction

This lesson uses the perspective drawing of a cube as the main component in an abstract artwork. It is inspired by a style of art called 'Geometric Abstraction'. The aim of the lesson is to explore the effects of tone and color on the shape and form of an abstract composition.

'Geometric Abstraction' is a hard-edged style of abstract art that uses geometric shapes as the visual components of an artwork. It relates to several abstract art movements in the 20th century (Cubism, Suprematism, Constructivism, De Stijl, Op Art and Minimalism) but has historical roots in the classical idea of geometry as an expression of beauty.

## Perspective as Geometric Abstraction - Step 1

One Point Perspective

We begin this lesson by constructing a simple one-point perspective drawing of a wire-frame cube to use as a visual component in an abstract composition. We are going increase the visual possibilities of this component by repeating, rotating, composing and coloring it.

Note: You may draw any regular geometric form to use as your visual component.

## Perspective as Geometric Abstraction - Step 2

Trace, rotate and transfer your form.

Once you have drawn your cube (or any other regular form), make a tracing of it so that you can transfer its image several times, each rotated at a different angle. You should build up a group of about eight cubes to use as the components of your composition.

## Perspective as Geometric Abstraction - Step 3

Explore different arrangements of your form in a series of sketches.

The next stage is to create some sketches that explore the type of shapes that occur when you arrange and overlap your components.

## Perspective as Geometric Abstraction - Step 4

Experiment with tone and color in your sketches.

To complete your sketches you should apply various arrangements of tone and color to explore the different effects they have on your artwork. We have left the front and back planes of our components open to increase their interaction with the shapes and forms that you see through them.

Finally you should choose one arrangement to develop further. Some artists prefer simple arrangements, like the one on the top left of our illustration, where you can easily see the balance and relationship of its shapes; others prefer complex arrangements, like the one on the bottom right, where you can lose yourself in the complexity of the image.

## 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 [1] 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'.