Automaton3D Quantum

This application is the Quantum edition of the Automaton3D application, which is also freely available at the Atomic Concepts web site. The automata created in the quantum edition are identical to those created in the original 3D version. The only difference is that the process of constructing and displaying the automata happens immediately, without the need to wait until the final structure has been calculated and displayed. This is possible by pre-calculating the duration of time required, given the automaton's specification, for each of the automaton's points to complete one full cycle of movement (i.e. for each point to return to its initial position in space). Then the final form of the automaton can be immediately displayed. In order to understand how the final form is achieved, it is advisable to first experiment with the original Automaton3D application in order to see how the resulting automaton is created and to compare the two versions.

Other than the ability to pre-calculate and display the automaton, there a couple of subtle differences between the two versions of this application.


An automaton is any mechanism whose movement or operation follows automatically from its design or programmed instructions. Once set into motion, the automaton carries out its movement or action without need of additional instructions and without intervention from outside agents

The automata which are modeled in this application are composed of a set of spheres, each rolling upon the surface of one other sphere in a fully deterministic pattern in space and in time. Because an automaton must have a finite number of spheres, one of the spheres cannot be rolling along the surface of another and so that sphere is made to be stationary relative to the viewpoint. The paths through space taken by one or more points within each sphere can also be visualized as the automaton carries out is choreographed movements.

Spatially, each sphere has a set of child spheres which roll in circular paths on its surface, thus forming a hierarchy, or tree, of spheres. The size of each child sphere is relative to the size of the parent sphere. Each sphere has an axis of rotation about which it turns (as the earth turns around on its axis once each day) except the single stationary sphere in an automaton, which does not turn. Furthermore, the axis of each child sphere is relative to the axis of its parent sphere. Because the child sphere's axis of rotation must perpendicular (at right angles) to the circular path along which it rolls on its parent sphere, the child sphere's axis actually determines the child sphere's orbital path along the surface of its parent sphere. Please try to visualize.

The above statements do not yet describe a fully deterministic pattern of motion in space and time, as there has been no mention of time. Assume there are three spheres A, B, C. Assume that sphere B is rolling on the surface of sphere A, and that sphere C is rolling on the surface of sphere B. Now, because the duration of time that it takes for child sphere B to complete one full orbit, or revolution (not rotation), around its parent sphere A is completely independent from the duration of time that it takes child sphere C to complete one full revolution around its parent sphere B, it is evident that it will be necessary, in order to fully determine the motion of these three spheres in space and time, to define a relation between these two independent time frames. In fact, what is necessary is to create such a relationship for every pair of spheres, relating the duration in time required for one full revolution in the one pair of spheres to the duration in time required for one full revolution in another pair of spheres.

The combination of spatial relationships and temporal relationships described above constitute a fully deterministic pattern of movement in space and time for a finite set of spheres, and so I call these things automata. This application is a laboratory for the synthesis of the automata.

File menu controls

In addition to the standard File menu commands for creating new files, and for loading and saving files, the following commands are available in the File menu for creating and saving still images and movies of an automaton.

NOTE:   When a movie is created, the rendering is not done to the screen so you will not see the frames which are being captured. Furthermore, the application will become unresponsive until all of the frames for a movie have all been captured. Be patient. At this point a window should appear in which you can select the type of video compression to use when assembling the AVI movie from the individual frames. I recommend choosing ‘Microsoft Video 1’. The movie which is produced will be named ‘Automaton3D.avi’ in the ‘movie’ directory within the folder which contains the Automaton3D executable file.


Automaton viewing controls


Automaton construction and design controls

The controls for constructing and designing the automaton are all located on the right side of the application window. There are three main windows which are arranged vertically.


NOTE:   The last property page in the bottom-most window, the page whose tab is labeled 'View', is not specific to the sphere currently selected in the tree of spheres. This page contains additional controls affecting the overall view of the automaton.


Figure A   Sphere Hierarchy Window


Figure B   Sphere Hierarchy Construction Window


Figure C   Selected Sphere Properties Window


Sphere Hierarchy Construction Window

The 'Sphere Hierarchy Construction Window' contains 3 buttons used to add and remove spheres from the sphere tree, and to designate one of the existing spheres as a template for future additions to the sphere tree. The three buttons have the following actions.



NOTE: There is no undo command. So be cautious when deleting spheres


Selected Sphere Properties Window

The bottom-most window, called the 'Selected Sphere Properties Window', is acutally a set of pages (each of which can be accessed by clicking on its corresponding tab) which allow you to manipulate the various properties, or characteristics, of the sphere which is currently selected in the tree of spheres in 'Sphere Hierarchy Window'. When a sphere is the selected sphere, it's name will be high-lighted in blue or gray. Note that exactly one sphere is selected in the tree at all times. Therefore, in order to change any of the properties of a particular sphere, you must first select that sphere in the tree of spheres by clicking on its name. Then you can affect the properties of that sphere, changing its name, color, size, axis, etc, using the controls in the property pages in the 'Selected Sphere Properties Window'.

The individual pages of the 'Selected Sphere Properties Window' and the properties of the selected sphere which they control are described below in left-to-right order.