Making a color cube from color planes
Multiple 2D color planes
can be stacked next to each other like books on a shelf
to form a color cube. The following explanation walks you
through this process of transformation. The color cube at
the end will look like this:
Let's look at our plant growth example again. When the experiment is run with different rates of fertilizer application, we generate six 2D graphs, each with its own family of curves (Figure 3).
Figure 3 - Six graphs, showing the different plant growth as a result of varying rates in fertilizer application.
All of the 2D graphs are then converted into color planes as previously explained. These planes would then look like this:
Figure 7 - The six graphs from Figure 3 are converted to 2D color planes where plant growth is now represented by a color.
The color planes are then stacked next each other, like books on a shelf, to form a cube of color. The color planes are stacked in order and the third axis is formed from the variable that is ordered. In this example the new axis represents the rate of fertilizer application. Remember that the color represents plant growth.
Figure 8- Assembling the color planes.
On one axis would be the rate of water introduction, on the second axis the amount of sunlight, and on the third axis the rate of fertilizer application.
The movie shows the process of going from multiple color planes to a single 3D graph, with three independent variables and the dependent variable represented by color.
This movie requires Windows Media Player
We can slice the cube in three different ways. Each time we slice it, we can see how two of the variables change as one is fixed. If we take a slice where the sunlight is 10 hours per day, then we would get a single plane of color that shows how the plant growth changes with rate of water and fertilizer application, since we are holding sunlight fixed. The second way to slice the cube is keeping water fixed, which shows how plant growth is affected by the amount of sunlight and rate of fertilizer application. The third slice possible would be to hold the rate of fertilizer application fixed and view the effect of the amount of sun and the rate of water application on plant growth.
A cut where sun is held constant would yield the 2D color plane with the rate of fertilizer and water application on the axes of the slice.
A cut where water is held constant would yield the 2D color plane with rate of fertilizer application and amount of sunlight on the axes of the slice.
A cut where the rate of fertilizer application is held constant and one would see the 2D color plane with the rate of water application and amount of sunlight on the axes of the slice.
Copyright © 1998 Central Virginia Governor's School for Science and Technology Lynchburg, VA