Monday 15 August 2016

Constructive Method in Geometric Art

Take a look at this image

stripes

It is just 25 vertical stripes.

But I can apply a transformation to it -

stripes, twisted

I call this transformation "twist" (the name is arbitrary). If I call the first image "stripes", I can call this image "stripes, twisted".



I have another transformation that I call "four-up" (again, the name is arbitrary). This makes four copies of an image and tiles a square with the four copies, flipped so as to have matching edges.

stripes, twisted, four-up

Here we have four copies of the "stripes, twisted" image, so this one is called "stripes, twisted, four-up".

This process of constructing an image by transforming an existing image I call "constructive". Obviously, you need a stock of images to begin with, but once you have a stock of transformations to apply you can create many new images just by selectively composing them.

For example, we can twist "stripes, twisted, four-up" to get "stripes, twisted, four-up, twisted"

stripes, twisted, four-up, twisted

You can see more of this sequence, if you care to at http://systemsartblog.blogspot.co.uk/2016/03/pixels-vectors-mathematics-and-more.html .

Naming the image in the way I do is not unimportant, although the names can clearly get out of hand if you apply many transformations. The constructive method exemplified here is a derivative of functional programming, an established method of programming which is used in many specialised areas and supported by many programming languages.

New images are created by applying transformations to existing images to produce entirely new images without damaging the original image in any way. This is the key idea in functional programming. Nothing is ever altered, only new things are created. Hence - constructive.

The "name" of the constructed object is just the function (i.e. transformation) applied to the original. I just like to write the name of the function after the name of the image. Hence - "stripes, twisted" rather than "twisted stripes.

Of course, what you can do with still images you can also do with videos. Take a look at this example



It should probably be named, "stripes, twisting" rather than "stripes, twisted" because of its motion. Nevertheless, it's a constructed object, achieved by applying transformation to an existing object (video).

Here's another example



This time there is clearly more than one transformation in use. More about this later, when I write about the methods used to construct this example.