You now maybe some of the abstract geometric painters such as Piet Mondrian, Max Bill or Georges Vantangerloo. Recently, I saw an exhibition of the works of Verena Loewensberg. She too has made some very interesting geometric paintings. Just check them out on the net.

Especially interesting is a painting with a periodically repeating pattern of yellow discs and parts of varying size. The pattern is wound around like a spiral. I am using this as an inspiration for a computer graphic.

Instead of a periodic pattern I am using a quasiperiodic sequence. I do not use the quasiperiodic Fibonacci sequence, because it has only two different symbols and want more variety. Thus I made up a different method for generating a quasiperiodic sequence of an arbitrary number of symbols.

Here I used four symbols and I am explaining the method for this special case. We use the numbers 1, 2, 3 and 4 to denote the symbols. To grow a sequence we read the numbers from the beginning and append 4, 3 ,2 and 1 to the sequence if we have read the number 4. For a number 3 we append 4, 3, and 2. For 2 we append 4 and 3. Finally for a number 1 we only append a 4. If we start with a sequence that has only the number 4 we get first the sequence 44321, then 44321432, then 432143243 and so on. This sequence is similarly quasiperiodic as the quasiperiodic Fibonacci sequence.

Then I choose to represent the number 4 by a very narrow blue rectangle, 3 by a broader red rectangle, 2 by a nearly quadratic green rectangle and 1 by a yellow square. The drawing starts at the center with the blue rectangle, then it goes up to another blue rectangle, then to the right to a red rectangle, then down two steps (a green rectangle and a square), to the left (a blue and a red rectangle), then up and so on. Just see yourself:

Abstract geometric design based on a quasiperiodic sequence.

Clearly, the computer is very useful to create abstract geometric pictures. Should this be considered art ? Would you look differently at a work by Piet Mondrian if he had used a computer to generate it ?

One could make a copy of the image on the computer screen using oil on canvas. What would be more original ? The image on the screen, a photo of it, the oil painting, a photo of the oil painting or the computer program ?

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