dappled designs


image courtesy Edward Tufte

As sunlight passes through the crown of a tree, every small opening in the crown serves as the aperture of a pinhole camera that casts an image of the sun on the ground. These sun images vary in size and brightness and may overlap, forming shadows of intricate detail and rich intensity gradations.

Artists call this dappled light. As the sun makes its way across the sky, the shapes change relatively quickly (a property of the moiré phenomenon).

If we could carefully design a tree-shaped sculpture with precisely positioned twigs and leaves, we could make a sundial that marks the passage of times and seasons by casting intricately detailed transient shadow images. For example, a tree sculpture installation that casts shadow portraits of persons whose birthday it is on that day — every day of the year, at a specific time.


shadow sculpture


Shadow sculptures are interesting for at least two reasons:

First, the objects that cast the shadows don’t have to look as though they have anything in common with the shadows themselves. Such is this piece at the Museum of Fine Arts:

Tim Noble and Sue Webster, Real life is rubbish

Or in this advertisement:

Secondly, the meaning of the sculpture can change as the light source moves or changes. Such is this thesis project of an art student:

Time-lapse Shadow Verse

Both reasons are more mathematical than aesthetic, but the boundary is subtle. According to one definition, beauty is the sense of wonder, whereas art is the expression of that sense. Well, mathematics is all about wonder. Both of these examples are quite primitive from the mathematical point of view and an engineer with good geometrical skills could design something far more impressive. For some reason most engineers rarely give much thought to such projects. Could it be that engineers are less prone to respond to symbolism?

I actually like both pieces for their artistic value too. Shadows and the motion of the sun across the sky do convey a sense of the passing of time and the illusory nature of perception.

Any artists/mathematicians care to brainstorm a few ideas? For example, in the shadow sculpture above, it would not be too difficult to modify the pile of junk so that it casts for different meaningful shadows onto four different walls simultaneously, but that’s just the beginning.