Abstract Designs Based On A 4 x 4 Square Grid

Introduction:

I get quite a few short spans of available time (eg. while out waiting to come home on public transport, after some shopping) for doing some things that might be inspiring. I came up with a 'simple' scheme for producing a wide range of geometric abstract designs based on a 4 x 4 square grid. I have found that it is a good way of producing intellectual and creative abstract images, in short spans of time. The scheme sets some limits and 'defines the rules' for the development of the abstract designs.

Hand drawn abstract design based on a 4 x 4 square grid.

I usually have a small notebook and a biro with me, for writing notes, etc. The notebook has horizontal lines printed on each page for writing along. I found that I could use the space from 5 consecutive printed lines to draw a square (using two vertical lines), so that the square is divided by 4 equal horizontal regions (made by the printed horizontal lines).

Drawing a square, using 5 printed horizontal lines.

I then add 3 vertical lines to divide the square into 4 equal vertical regions. This forms a square, with a grid of 4 x 4 smaller squares.

Dividing up the square.

The overall square is now divided into halves, quarters, and 16ths. Some diagonals divide the overall square into halves and quarters in other ways.

Dividing up the square more.

Adding more diagonals divides the square into 8ths, and provides some interesting patterns. This is the basic scheme that I use for developing my hand-drawn designs. I also make use of diagonals that are drawn between points that are separate from each other by 2 units high by 1 unit wide, or 2 units wide by 1 unit high.

Back at home, I firstly developed some clean geometric versions of my hand-drawn designs using some programs I put together using the free software package, Processing 3. I found that I could define the points within the square using array coordinates. I could save the images created as PNG format images and SVG (Scalable Vector Graphics) files.

I now develop my clean geometric designs using InkScape (a freely available vector graphics package that is similar to Adobe Illustrator). From my programs developed using Processing 3, I created Scalable Vector Graphics (SVG) files that could be loaded into InkScape and that contained all of the dividing lines within my scheme's main square. It divides the main square into 3,584 smaller triangles that can be coloured either black or white. This means that the number of possible designs is enormous (3,584! or 3,584 factorial, or 3,584 x 3,583 x 3,582 x ... etc. ... x 2 x 1, or virtually infinite - please consider that 30! is approximately 2.65 x 10³², 50! is approximately 3.04 x 10⁶⁴, 300! is approximately 3.06 x 10⁶¹⁴ (that is approximately a "3" followed by 614 "zeros" - which is a huge number), so 3,500! would be absolutely enormous)! It may be worth mentioning that I have already developed about 450 designs based on the 4 x 4 square grid scheme using InkScape alone.

I now find that I can develop several designs in short spans of time using InkScape on my computer, as well as being able to produce several hand-drawn designs in my notebooks within short spans of time (which was an important consideration for this project)!

The philosophy behind my abstract images:

The vast majority of music we enjoy is similar to abstract art. We don’t expect to hear mainly recorded sounds of our everyday lives when we listen to music (as we might expect to see mainly recognisable real-world scenes within the visual art we see). We instead expect to hear an emotionally moving composition of relationships - abstract relationships.

For me, there are two basic intentions for creating abstract artwork. One is to explore and play with the relationships of abstract pictorial elements, such as line, colour, shape, direction, texture, tone, gradation, composition, balance, etc., to gain a better understanding of visual communication and emotional connections. The other is to use my understanding of visual elements to pro-actively express a particular idea or emotional situation.

What I am mainly looking for in this month's abstract explorations, are pleasing relationships of basic picture elements. These explorations are mostly trial and error sessions, deliberating on, and responding to the various combinations of elements that develop within the overall images. The feelings from my visual understanding and subconscious become important for determining what might “work”, or what might “not work”.

I have found computers to be marvellous tools for exploring abstract visual relationships. I can produce many designs quickly, and explore different combinations of elements using a medium that doesn't require additional physical materials such as paint, boards, brushes, etc. I can save multiple states of ideas and working, and easily compare and reflect on those saved states afterwards.

Hand Drawn Designs.

Designs Drawn Using Processing 3.

Designs Drawn Using InkScape, page 1.

Designs Drawn Using InkScape, page 2.