Glider-Guns in 3d Cellular Automata Discrete Dynamics Lab

k=6 Beehive-rule period=6

k=7 Spiral-rule period=8

Beehive-rule 3d glider-gun v=3 k=6 ijh=40x10x40 -- click panels to enlarge
kcode= 0022000220022001122200021210=(hex)0a0282816a0264 (v3k6x1.vco in DDLab)
"Glider dynamics in 3-value hexagonal cellular automata: the beehive rule", Int.J.Unconv.Comp, Vol.1, No.4, 2005, 375-398. (PREPRINT)
step 1. step 2. step 3. step 4. step 5. step 6.

Spiral-rule 3d glider gun v=3 k=7 ijh=40x10x40 -- click panels to enlarge
kcode=000200120021220221200222122022221210=(hex)020609a2982a68aa64 (v3k7w1.vco in DDLab)
"On spiral glider-guns in hexagonal cellular automata: activator-inhibitor paradigm" Int.J.Mod.Phys C, Vol. 17, No. 7,1009-1026, (PREPRINT)
step 1. step 2. step 3. step 4. step 5. step 6. step 7. step 8.

In these examples, imagine looking down into a shallow box 40 x 40, and 10 cells deep. Periodic boundaries have been suppressed so that the gliders fall out of the space so an not to interfere with the generating core.

The 3d glider-guns are periodic structures fixed in one location, which spontaneously emerged in the dynamics from random initial states. The CA rules are identical to the k-totalistic rules -- beehive and spiral, but apply to a 3d (nearest neighbour) cubic neighbourhood. Because k-totalistic rules are symmetric -- independent of the location of values in the neighbourhood -- the glider-guns exist in each chirality and in all possible orientations. Many other structures also emerge -- gliders, compound-gliders, and mobile glider-guns, but as yet no static structures analagous to 2d eaters in the 2d spiral rule. I discovered the 3d glider-gun in the beehive-rule in 2004, and in the spiral-rule in June 2009. The best way to search for these structures is to set a small random 3d block in DDLab, 2 or 3 cells in diameter, and observe the result. The core of the glider-gun can then be isolated (and saved) with other DDLab methods.

ijh=52x10x52 with periodic boundaries
beehive rule: step 31. The dynamics enters a cycle where this pattern repeats every 48 steps. spiral rule: step 165 -- gun core still preserved. spiral rule: step 202 -- gun core has just deconstructed.

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Last modified: June 2009