MULTIPLE SIMULTANEOUS PATHS 

       Approaching Complexity (Something You Cannot Predict)

Instead of viewing space as fixed, a passive arena (simple games, puzzles and mazes), the S3 network architecture uses space and geometry as active participants in the problem universe.

The S3 is a dynamic router, a system of programmable binary switches, a “flying junction” (an over-and-under junction of tunnels which weave past each other) housed within a cubical exoskeleton with multiple axes of rotation and alternative, manipulator-controlled ball trajectories, offering exit in all orientations.

In Cybernetic terms, the Sis about regulatory switching, a heuristic routing (ball or vector) system:  seeking best paths in an unfriendly (blocking) network / environment of switchable links; where dynamic programming is required to optimize incompletely understood and changing systems (using locally implemented full switching at all nodes, not a hierarchy of routing control centers).

In other words, the Sis a tangible, lucid demonstration of basic behaviors (consciousness) of the brain through mechanical concepts (switches); a cubical maze module offering a development of choices (control flow) to create linearly independent / dependent paths, using a ball, or symmetry in mathematics.




                                           (checkered paths allow exit)  


MULTIPLE PATH                            JUNCTION PATH

[paths cross within a single S3:       [two or more paths converge (Airball)]

0,  1,  2,  3,  4 (good luck!)]

AIR BALL                                       TUNNEL BALL

[passes through air]                        [passes through tunnels]

TRANSPARENT                             OPAQUE

[clear S3]                                         [“Black Box” (good luck!)]

OFFSET                                         FACE-TO-FACE

[irregular alignment]                        [square alignment]


[multiple paths within fewest S3s]


[“anything goes”]


[four paths begin / cross within a single S3]


               (checkered paths allow exit)

                         CHALLENGES / GAMES


1)  Law of Gravity

2)  Law of Lowest Exit

(Given that a ball must exit at the lowest Slevel and obey gravity.)


Multiple simultaneous paths, but no paths can share an input or output 

(with the exception of AIR BALL).


[Player has the option of hacking into 

or blocking opponent paths]


[Player has the further option of designating the elimination of specified S3s (routers)

in a fixed 3 x 3 x 3 array]


For Example 

Using the fewest S3s

Make two, or three, or four

Simultaneous paths which

Which begin from the SAME S3.

(remember that the ball must exit at the lowest Slevel and obey gravity.)

Make the most paths, or

Longest paths, or

Most multiple paths, etc.

(at least one path traverses all S3s)

Timed / not timed.




Position S3s in any way;

Connect tunnels in any way;

Make any combination of paths.

Chicken Little



Crisscross Dunk

AIR BALLS from two or more 

different paths

into shared tunnel.


Call the Spot

Using a given number of S3s, 

make the ball exit at a given spot(s).

Two-Color Game

Two players, Red and Blue, take turns connecting S3s,

Linking tunnels to gain strategic / tactical advantage, 

While blocking, or hacking into, the opponent’s paths.


                  (checkered paths allow exit)



                                  S3 VIRTUAL REALITY 

                                  (rotation /  calibration sensors / glowing paths)



Escape From The Labyrinth 

Levels of difficulty (accelerating rates of change and complexity).

Labyrinths:  Increasingly larger universe of S3s. 

S3 reorientations:  Increasing number  

(random / non-random -- time limited / time free).

Roller Coaster Loops 

Loop paths cross within a single S3

0,  1,  2,  3,  4 (good luck!)

Dueling Roller Coasters

Loops vs. Loops

Crisscross Dunk Circuits (Knots)

AIR BALLS from two or more 

path circuits by shared tunnel(s).


Double Back 

In a given cubical block of S3s:

Start at base and successively reorient S3s to 

make a fixed path up to top and back down and exit.

Start at top and successively reorient S3s to 

make a fixed path down to bottom and back up and exit.


© Michael S. Sommer, Ph.D. 2015