The Fractal Perspective
Self-similarity
in Fractal Art
by Ken Keller
01/31/04

shadows of shadows
fall across eyes
within eyes.

Fractal art uses several effects that are not generally found in other art techniques. These unique effects, when skillfully used, produce images that are important advances in contemporary art. These effects can be used to explore fresh areas of human perception. 

Self-similarity is a well known property inherent in fractal imagery. What is perhaps not as generally appreciated is how this effect actually works in physical reality when viewing large fractal art prints. 

A very finely detailed and complex fractal when printed at a large print size may display many different image compositions, each image appearing as one moves closer to the print surface. Physically moving closer to the print is analogous to virtually zooming in on a fractal with a computer fractal program. The change depends on the scale of your viewpoint, on how far you are from the fractal print and the resolution of the print.  I call this self-similarity and its persistence over scale ranges the Fractal Perspective.

The fractal perspective can be illustrated as follows. Imagine a fractal printed at a size of 10 feet by 10 feet in an art gallery. When you walk into the gallery you see the fractal print on the far wall about 50 feet away. The fractal image will appear to be a cohesive shape or composition. As you approach the fractal this shape will appear to change. As the detail of the image becomes apparent, (your view is going into the fractal), the overall perception of the image changes. This image is very different than when viewed at 30 then 20 then 10 then 3 feet away from the surface of the image. This effect, which I call the fractal perspective effect, is a new type of aesthetic experience. 

For an example consider one of my Divine Symmetry series of fractals. These fractals are of high iteration, that is, that when you zoom within the fractal ever more defined detail is revealed. 

Click for larger image Click for larger image Click for larger image
50 feet away 20 feet away 3 feet away

The first image is what you would see if you were 50 feet away from a 10 foot by 10 foot printed image of Divine Symmetry II. The second image is from 20 feet away. The third is 3 feet away from the image. 

The fractal perspective effect occurs for an appropriately constructed fractal print on a gallery wall as it does for a fractal in the virtual reality of the computer zoom. If you are walking toward a print in a gallery or zooming in on a fractal with a computer the effect is essentially the same. Of course the physical print in a gallery will involve more of your senses and attention and depends on the size and resolution of the actual print. The effect is more visceral when seen in physical reality than in virtual reality and is a completely fascinating experience. 

The ideal situation to demonstrate the fractal perspective would be to display a fractal print large enough to exhibit large scale self-similarity. The image you would see at the greatest viewing distance would be the same image you would see at the closest viewing distance. 

This ideal situation is hard to achieve in practice for all but the most simple fractals. The degree that the work deviates from this ideal situation is the degree to which it is similar to a normal but very large and detailed geometric, non-fractal drawing. The degree of fractality involved in the different viewpoint images should also be considered. Fractality is a measure of the fractal's dimensional (scale) complexity. It can be a precisely defined value. It is determined by imposing ever smaller grids onto the an image. Fractality is another aspect of fractal art that will be discussed in the future.

 

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