Fractals, Infinity or Both?

The Real Alcazar - or Royal Palace - in Seville, Spain has an area at one of the lower levels called "The Queen's Bath". It would have been a pretty large (and shallow) bathtub to use for one person and the most interesting feature of this room is actually the architecture surrounding the bath. The ribbed faults that support the roof over the bath create an almost hypnotic effect. We see ever more arches contained within the arches as our eye travels to the back of the space.

The Queen's Bath in the Real Alcazar, Seville, Spain

One way to think about this image is to think of it as suggesting infinity. Behind each arch in another arch, and behind that arch is yet another one, and so on and so on. We have to fool ourselves a little bit, because we obviously know very well that the space does not go on indefinitely.

Another way to think about the image is to consider the fact that the photograph contains smaller copies of itself. This is called self-similarity and is one way to create fractal images. In a perfect fractal there would indeed be infinitely many copies of the original image contained in the photograph. In this example we see a partial realization of such a self similar figure.

Below is a photograph of a fairly narrow hallway next to the Queen's Bath. We again see this illusion of infinity in a doorway that contains an image of another doorway, containing yet another image of a doorway, etc. There are at least 5 doorways in this image and one could imaging that there would be infinitely more behind them, thereby creating an infinitely long corridor with infinitely many doorways.

Narrow hallway next to the Queen's Bath

I wanted to complete this (short) gallery of photographs with this image from the Mezquita in Cordoba, Spain. In this photograph we yet again see this illusion of infinity. In this instance there is a suggestion of an infinite number of arches receding into the distance.

Arches in the Mezquita in Cordoba, Spain

Any student of art would interpret this as a case of linear perspective with the vanishing point located close to or at the center of the image of course.