Editing CLUViz Geometric Algebra Animation Software (section)

==4D CLUViz Work==
The next step after programming the 3D rotations was to attempt to animate the rotations in 4 dimensions to help give us a better understanding of how they work and hopefully provide us with some conclusive information on whether the rotations could be utilised for secure encryption. In order to represent the 4 dimensional rotations, the previous 3D program was used as the foundation however with several additions.

An additional rotation axis was added for each Alice and Bob bringing the total number of rotation axes to four, as two rotation axes were needed to perform each rotation in 4 dimensions. As a result, two support diagrams were added to allow the user to alter the rotation angles of the new rotation axes. Also, as with the 3 dimensional visualisation, we wished to show the vector displacement between each pair of rotation axes during animation to show how it affects the difference in the initial and final message vectors. As a result, five more support diagrams were added to the right.

In order to depict the 4th dimension for the initial and final message vectors, two spheres were added as shown in red and magenta. The magnitude of each sphere represented the e4 component of each the initial and final message vectors, with the remaining (e1, e2, e3) elements being represented by the 3D vector as in the previous program. Hence, it was programmed that the initial and final message would only equal when the vectors overlapped and the two corresponding spheres were of equal magnitude. However, as known from our other 4D GA work, the conditions for which the two independent 4D rotations can commute are vastly more complicated than we had originally anticipated and as such we ran into difficulty in making these rotations viable, valid and consistent with the theories behind them. We got to the point with our theoretical work that forced us to start looking into higher dimensions and as a result, the 4D visualisation became obsolete.