Discrete Dynamics Lab
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Spiral+Glider rule

The spiral+gliders rule-table (kcode)
showing all 56 possible mutations, and neighborhoods controling the basic spiral and glider
0002000220022001112200021110 (rule v3k6x2.vco in DDLab)

                24 22  18 15     87     10 -some important outputs
                 | |   |  |      ||     ||
      kcode = 0022000220022001122200021210 (v3k6x1 beehive)
      kcode = 0002000220022001112200021110 (v3k6x1 spiral+gliders)
                ^              ^       ^   3 differences from beehive
                    kcode index
        spiral     /  totals: 2s+1s+0s=k=6 
          freq    /  /         kcode        2=black 1=red 0=white
 basic      /    /  /         /             w-b-b-r-w-w-w-b-b-r-w--->
 glider    /    /  /         /  mutations   spiral wave 
 ------   /    / 2_1_0      /   2___1___0   -----------
backgr-> 9->  0: 0 0 6  -> 0    o   c   -   -white background->white
 head+-> 1    1: 0 1 5  -> 1    0   -   0   -red corner&tip moves forward
         7->  2: 0 2 4  -> 1    g   -   cg  -red edge moves forward 
         1    3: 0 3 3  -> 1 -+ S   -   S
 out4    1    4: 0 4 2  -> 2 -+ -   S   S
 out3    0    5: 0 5 1  -> 0 -+ S   S   -
 out1    0    6: 0 6 0  -> 0 -+ S   S   -
  side2->2..  7: 1 0 5  -> 0    c   c   -
  side1->1    8: 1 1 4  -> 2    -   c   c   -red lead tip->black
 side1+  1    9: 1 2 3  -> 2    -   c   c   -red 2nd tip->black
         1   10: 1 3 2  -> 1 -+ S   -   S
 out2    1   11: 1 4 1  -> 1 -+ S   -   S
 tail    0   12: 1 5 0  -> 1 -+ S   -   S
   head->5-> 13: 2 0 4  -> 0    c   c   -
         1   14: 2 1 3  -> 0    G   c   -
         6   15: 2 2 2  -> 2    -   c   c   -1st black edge moves forward
         1   16: 2 3 1  -> 2    -   cg  cg  -black inside tip->black
         1   17: 2 4 0  -> 0    S   S   -
         3.. 18: 3 0 3  -> 0    c   c   -
         1   19: 3 1 2  -> 2    -   c   cg 
         2.. 20: 3 2 1  -> 2    -   c   cg
         1   21: 3 3 0  -> 0    S   cg  -   -1st black in corner->black
         5-> 22: 4 0 2  -> 0    cg  c   -   -back black edge->white
 center->1   23: 4 1 1  -> 0    S   c   -
         5-> 24: 4 2 0  -> 2    -   cg  S   -2nd black edge moves forward
         1   25: 5 0 1  -> 0    S   c   -   -white inside corner->white
         1   26: 5 1 0  -> 0    S   cg  -    or black inside corner->white
         1   27: 6 0 0  -> 0    S   cg  -
key to mutations: 
wildcards -+ (spirals if outputs random) 
S=spirals, 
G=gliders, g=weak gliders, cg=chaos+gliders
c=chaos, o=order, 0=all 0s


 

histogram of frequency of
neighbourhoods. Top: kcode index 0

56 single mutations to the Spiral+Glider rule
28/56 are quasi-neutral, click to enlarge
index
0-6
0

1

2

3

4

5

6

index
7-13
7

8

9

10

11

12

13

index
14-20
14

15

16

17

18

19

20

index
21-27
21

22

23

24

25

26

27


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Last modified: Dec 2004