Interaction

Let's discuss the role of interaction in general, for any of the projects: 2D, 3D, Physical. By "interaction", I mean the engagement of the human in the representation. Typical engagements can be done with the usual devices: mouse, keyboard, and tablet but others are certainly possible: microphone, webcam. And then, you get into programmable hardware devices (based on things like a BASIC STAMP microcontroller) driven by sensors (strain gauges, temperature, pressure, phototransistors...). So, interactivity can be achieved through many technologies.

What is the nature of the interaction?

Method 1: INTERACTION TO SUPPORT UNDERSTANDING THE REPRESENTATIONAL MAPPING
The basic sort described in the 2D project description is to use interaction to explore the mapping between source and target components (the complete mapping between source and target). This requires that the source and target be presented somehow in the work. They could be next to each other or one appears on top of the other (morphing), in in some other creative way. Pointing at a source component highlights or otherwise indicates the equivalent target component, and vice versa.
Method 2: INTERACTION TO CONTROL NATURAL BEHAVIORS ASSOCIATED WITH THE SOURCE + TARGET OBJECTS
Each source object is going to have a natural behavior. For example, an equation can be "solved" numerically or symbolically. This solving is dynamic and can be seen via interaction. IE: clicking on a node causes that node to "execute". Or perhaps, you will need a GUI of sorts to create the potential for interaction in support of behavior. Sometimes, you will have variables or constants - choosing these can be done through sliders, etc..
Method 3: INTERACTION FOR A META-LEVEL PRODUCTION IN WHICH THE OBJECTS ARE LOCATED
Interactivity and the source and target objects can be positioned in the piece as being elements of a "production". This production can have narrative or story. You may remember the example that I showed about the Spiral of Cornu laboratory with the bubbling sound. It was a very weak story because there were only 1 or 2 pieces of text " Believe me Friends...That is how the Spiral of Cornu was invented..." but this piece was very original at the time because no other student used narrative, or a story to place their piece inside the context of something bigger. Last year, one student did it by creating a Flash presentaton involving representation of a probabilistic model (you might remember this -- the simulated paper as a background looked like old parchment).