Physics, Art, and Programming Ben Hoffman

Accurate Art:

Physics principles can help our artistic abilities as well as help us to understand the way things around us work. I think that it would be beneficial for artists to take some physics courses. To capture an idea effectively, one must portray the situation in a manner that is scientifically correct. I have seen many pieces of art that would look more real (not that realism is every artists goal) had the artist taken a crash course in optics.

The example that I was working with was that of a disturbance in water (a water drop perhaps). One could simply draw a rough sketch of what they think this situation looks like, but is there a more accurate and physically correct way to portray the situation?

When asking myself these questions I started to list things that I knew:

1. A disturbance in water produces mostly transverse waves because water is a much less compressible substance than air and much less likely to produce longitudinal or compression waves.

2. Transverse waves that are harmonic behave in a sinusoidal manner .

3. In the case of the water, the effects of the disturbance will be distributed (mostly) radially on the plain of the water’s surface (again because of water’s lower compressibility)

 

4. This would lead be to the conclusion that the intensity of the disturbance’s effect will fall off at 1/R (where R is the radius from the initial point of disturbance) because the total effect will be the same over any given circumference.

 

Looking at the above list, one can start to visualize a set of concentric circles that are been moved up and down (in the z direction) with great differences in height near the disturbance but less as the circles’ radii grow. This is much as we expected it to look based on just our common knowledge.

Now that we know that the disturbance is sinusoidal and falls off with 1/R we can start to build the proper father equations to graph the situation:

Z = sin(R)/R Y = Rsin(ø) X = Rcos(ø)

This is what the parent functions for the water drop situation would look like based on what we know. Some constants have to be added to make the situation appear on a human scale. Also the picture has to reflect a fraction of the changing z value in the vertical components of the graph or else the z values of each circle would be undetectable. If some if the z vector shows up in our vertical then some of the y vector disappears into the undetectable z direction. (In affect the three dimensional picture is being rotated.) What we end up with is something that obeys many more of the laws of physics than a rough sketch would:

We can easily alter the angle and add some artistic liberties......

Interesting note: You might have noticed a glitch in all of the circles on this page. In the center of the right side of these circles there is a line. This, I discovered, is because the program I am using has a π value that's slightly larger than actual π. I just thought that I'd let you know.

Cool.

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