As seen in Wolfram's book, "A New Kind of Science", one can visualize the evolution of a two-dimensional cellular automaton in three dimensions, by stacking up the two-dimensional states along a third spatial dimension.
The user interface of this program was implemented in the FastLight ToolKit (FlTk), GLUT and Open Inventor. The previous image shows the history of the cellular automaton with a cube placed at each voxel-on position.
The following image shows the spatial evolution of the same cellular automaton with the voxels represented as Lego-like bricks.
And the following image shows the same cellular automaton evolving in three dimensions by adding instances of the geometrical representation of the cubic cell designed for the Three-Dimensional Kinetic Cellular Automaton.
This program, at present, places the cubes at voxel addresses in 3-space without regard to the physical mechanism by which semi-autonomous cells would move when constrained to connection into the support matrix and movement against each other. For now, we can simply materialize the cells out of thin "air" (bytes -- in 3-D computer graphics).
The next step in this development is to begin to program the animation of how a structure such as a 3-D cellular automaton would behave as an entity constrained to exist physically.