Sculptures of Imagination

William Overington

I have devised a new genre of sculpture whereby sculptures are imagined, yet imagined with precision, by means of interpreting coded tiles that are set out upon a plane. The idea is that oblong tiles could be set out on a gallery floor, or set into the grass in a park, with coded markings upon them. A person skilled in the art of reading the virtual world creativity language that the system employs can then determine the shape and position in space of the sculpture. Just as, for example, one might read the word horse and know what sort of animal is meant without actually seeing a horse, so this visual spatial language allows one to understand the sculptural shape that is intended.

Consider, as an example, a set of twelve such tiles. They are oblong. The aspect ratio is not important. An aspect ratio of 1.5 might be used if paving slabs are used. An aspect ratio of 1.4142 might be used if pieces of A4 size paper are being used for experimentation. If tiles are being made specially from raw materials, the aspect ratio may be as desired. The construction point of a tile is the mid-point of one of the two shorter edges of the tile. Near the construction point are some symbols or some text. For this example I shall use the text option. The symbol option is so as to enable construction of tiles where there is no reference to the roman alphabet so as to be able to produce language independent sculptures. Two tiles have 1 upon them. Two tiles have 2 upon them. Two tiles have 3j2 upon them. Two tiles have 5 upon them. Two tiles have 6 upon them. Two tiles have 7j2 upon them. Consider the tiles in numerical order. Consider one of the tiles with 1 upon it. Up and out symmetrically from the construction point imagine a construction line at 45 degrees to the plane. Consider the other tile that has 1 upon it. Also for this tile, up and out symmetrically from the construction point imagine a construction line at 45 degrees to the plane. Where these construction lines meet, as they will if the tile layout is not in error, is a point in mid-air to be regarded as point 1. Having established the point in mid-air, please disregard the construction lines. Similarly establish point 2 as a point in mid-air. However, as 2 is one greater than 1, a line is imagined as being drawn from point 2 to point 1. Now establish point 3 as a point in mid-air. As 3 is one greater than 2 a line is imagined as being drawn from point 3 to point 2. In addition, the j2 part of 3j2 means that a line is to be drawn to point 1 as well. The target of point 1 is deduced from 3j2 by subtracting 2 from 3, as the 2 is a relative address. This use of a relative address is so that a whole sculpture can have a constant added to each index value without having to alter internal line drawing, this feature being useful when merging two sculptures together to form one whole total sculpture. There are no tiles with an index number of 4 in this particular sculpture. Now establish point 5 as a point in mid-air. There is no line to a point 4 as there is no point 4 in this particular sculpture. Now establish point 6 as a point in mid-air. There is a line to point 5 automatically. Now establish point 7 as a point in mid-air. There is a line to point 6 automatically and the j2 of 7j2 produces a line to point 5, as 7 minus 2 is 5.

The imagined sculpture thus consists of two triangles floating in mid-air. The size and orientation of the triangles in mid-air depends upon the placing of the tiles on the plane. For example, there could be two congruent triangles in parallel vertical planes. For example, there could be two interlinked triangles each in a vertical plane with each of the two said vertical planes being at right angles to the other. Moving the tiles around on the plane allows one to specify either of these examples and many others.

In order to fill the first triangle change the 3j2 tiles for 3j2f tiles. In order to fill the second triangle change the 7j2 tiles for 7j2f tiles. In order to fill the first triangle transparently use 3j2f0 tiles. The general colour of the fill is taken from the colour of the tiles. For example, the tiles for this example could be made with the first six tiles red and the second six tiles blue if desired.

I envisage that such sculptures might be a useful art feature for public parks, open areas in town squares, open areas in shopping malls and so on, as well as art galleries. They would be relatively inexpensive, interesting to stop a while and consider. They have the advantage that, while one is considering such a sculpture of imagination, the sculpture is precisely defined such that one can put one's hand out in mime style and decide exactly in space where the sculpture exists; yet from a distance there is nothing obstructing the view.

The language has features for circles, ellipses and spheres, for fills and for two types of rotation.

The first type of rotation is ordinary rotation, namely rotation of a line feature about an axis. In this type of rotation a line produces a cylindrical tube, or a disc with a hole in it or a flower pot wall type shape depending upon the relative orientations of the line that is rotated and the rotation axis. A circle thus rotated can be used to produce a torus. An ellipse thus rotated can produce various shapes depending upon original orientations of the ellipse and the rotation axis. Plane figures such as a triangle can also be rotated.

The second type of rotation is where an item is repeated in its entirety so that a stated number of occurrences are spaced out around a circle.

In each type of rotation, rotation need not be for the whole 360 degrees.

There are other features, such as the arctangent operator so that the construction line is not at 45 degrees but at another angle. For example, 9a2 would specify tiles where the construction line goes up at the angle whose tangent is 2 to the horizontal plane.

Readers might like to know that an overview of the system is in the lyrics of a song that I published in news://rec.music.makers.songwriting earlier today. The song is called Sculptures of Imagination.