Editing CLUViz Geometric Algebra Animation Software (section)

====Sliders====
Sliders at the bottom of the visualisation allow the user to interact with the module and change various elements to gain a better understanding of how it works. 
* Two sliders are used to alter the e1 and e2 elements of the initial message vector m, with the e3 element being automatically set to the highest value that ensures that m isn't greater than a unit vector in length.
* Two sliders are used to alter the rotation angle of Alice and Bob between 0 and 360 degrees. Naturally the initial rotation of each is considered to be a clockwise rotation, while the second is counter-clockwise.
* The final slider is used to alter the rotation speed of Alice's Rotation Axis to 1 of 8 different speeds. An option is also provided to halt the animation at any stage, allowing the user to take a closer look.

As mentioned, the animation is conducted through the movement of a single element- that being Alice's Rotation Axis. This movement, allows the user to accurately determine how the difference between the initial and final message vectors alters with the difference between Alice's and Bob's Rotation Axis. As you can see, at the exact point where Alice's Rotation Axis crosses over with Bob's Rotation Axis, the initial message vector crosses over with the final message vector, hence indicating that the four rotations commute. This is further demonstrated via the support diagrams shown to the sides of the main animation.
[[Image:4D_Screenshot.jpg|thumb|700px|right|A screenshot of the CLUViz visualization for 4D-Rotations]]