Here are two circles with an eighth removed. As we can see, they can move together. What about adding more such broken circles? How densely can we slide them together?
Here is an example with three circles, each one sixth missing:
This is maybe a little bit remarkable: If you take two such broken circles and rotate them by 60º against each other, you can slide them along each other so that one end point of one circle moves on the other circle, and vice versa. The first question (which must have an easy answer, of course) is: why does this work for these angles?
As shown above, this allows us to pack three of these broken circles together, creating a mild form of prettiness.
Now let’s use four broken circles, with a quarter removed each, rotated by 90º, and colored appropriately:
Again, one can slide these circles along each other. Can you do this with six broken circles? Does this work with other angles?
Mona Hatoum’s impressive installation of this name was shown in the Diversity United exhibit in Berlin this year, and the catalogue speculates that what we see here are the ghost-like fragments of a house.
I saw these hanging concrete pieces as probes into space, an attempt to make visible what has disappeared.
In this reconstruction, I am using PoVRay to probe textured space. A texture in PoVRay is function of the three spatial coordinates whose values is used in a color map to determines the color value of an object at the point given by the three coordinates. Above the function is sqrt(x2+y2+z2), and the color map a simple grayscale gradient, so that spheres centered at the origin have the same color value. Objects placed into the scene appear to be carved out of this space.
Above is a more complete reconstruction of Haroum’s installation, using the same spatula texture with added reflection. And below are the same probes, using an entirely different texture based on the function sin(x)+sin(y)+sin(z).