Pattern Inventory


     The complete inventory of worms comprises 411 patterns.  They are unique in that they have different sets of rules.  However, that does not mean that they necessarily appear unique.  The patterns may be generated in different order - something that can not be gleaned from post inspection of the finished product.  They may also recur in different orientations or reflections.

     Of the 411 patterns, 329 are “known finite”, 71 are clearly “infinite” due to their simple geometric shape and repetitive behaviour, leaving 11 indefinite patterns.  Some of the patterns in the latter category have been traced to more than 500 million units with no conclusive proof that they will eventually stop.

Summary of Patterns

DescriptionPatterns
Known Finite329
Chain19
Triangle12
Hexagon19
Regular shape12
Non-symmetrical9
Undetermined11
Total:411

     In the tables below are all the possible patterns listed in order of size.  The pattern ID is a unique ordinal pattern identifier numbered #1 to #411.

329 Known Finite Patterns – sorted by size

Sizes 1 to 100

SizeIDRules
9#3732 0 0
9#3962 4 4
12#3832 1 0 4
12#4062 5 1 0
12#4092 5 4 0
15#3742 0 1 0
15#3972 4 5 0
18#3852 1 4 4
18#4072 5 1 4
18#4102 5 4 4
21#3842 1 0 5
23#2041 4 2 1 2 2 1
23#2511 4 5 1 2 2 1
27#3812 0 1 4 2
27#4042 4 5 4 2
28#92 1 0 5 1
28#93 1 0 5 4
28#1501 2 1 5 5
29#31 1 0 1 5 2 1
29#1281 2 1 4 2 1
29#1941 4 2 1 0 1
29#2071 4 2 1 2 5 1
29#2111 4 2 1 4 1 2
29#2411 4 5 1 0 1
29#2541 4 5 1 2 5 1
29#2581 4 5 1 4 1 2
29#2751 5 0 1 1 5
29#3081 5 2 1 1 5
30#3752 0 1 4 0
30#3982 4 5 4 0
33#5 1 0 1 0 0 1
33#1401 2 1 5 1 0
33#1491 2 1 5 4 4
SizeIDRules
33#2011 4 2 1 2 1 1
33#2481 4 5 1 2 1 1
33#2661 5 0 0 1 5
33#2741 5 0 1 1 1
33#3071 5 2 1 1 1
34#1861 4 2 0 2 5
34#2331 4 5 0 2 5
35#2121 4 2 1 4 1 5
35#2591 4 5 1 4 1 5
37#3802 0 1 4 1 5
37#4032 4 5 4 1 5
39#1971 4 2 1 0 4 5
39#2441 4 5 1 0 4 5
42#1441 2 1 5 4 0 2
43#38 1 0 1 5 4 2 0
44#2171 4 2 5 5
44#2641 4 5 5 5
44#2781 5 0 1 4 1 5
45#1311 2 1 4 2 4 5
45#2721 5 0 0 4 5 5
45#3762 0 1 4 1 2
45#3992 4 5 4 1 2
46#78 1 0 4 4 0 0 5
46#2061 4 2 1 2 2 5
46#2531 4 5 1 2 2 5
48#17 1 0 1 0 4 1
48#24 1 0 1 5 0 1
48#39 1 0 1 5 4 2 1
48#42 1 0 1 5 4 5 1
48#1211 2 1 4 0 1
48#1361 2 1 4 4 1 2
48#1371 2 1 4 4 1 5
48#1421 2 1 5 1 4
SizeIDRules
48#1511 2 5 1
48#2151 4 2 5 1
48#2621 4 5 5 1
48#3461 5 4 1 1 2 1
48#3481 5 4 1 1 5 1
48#3942 1 4 5 2
50#1881 4 2 0 4 4 1
50#1951 4 2 1 0 4 1
50#2351 4 5 0 4 4 1
50#2421 4 5 1 0 4 1
50#2651 5 0 0 1 1
52#2081 4 2 1 2 5 4
52#2551 4 5 1 2 5 4
53#41 1 0 1 5 4 5 0
53#1451 2 1 5 4 0 5
54#44 1 0 4 0 0 1 0
55#2761 5 0 1 4 1 1
55#3021 5 0 5 5 1 5
57#53 1 0 4 0 1 5
57#1141 2 0 4 1 5
58#3491 5 4 1 1 5 5
61#13 1 0 1 0 2 5 5
62#1331 2 1 4 2 5 2
62#3001 5 0 5 5 1 1
63#3862 1 4 5 0
66#35 1 0 1 5 4 1 0
67#4 1 0 1 0 0 0 5
67#16 1 0 1 0 4 0 5
67#27 1 0 1 5 0 5 5
67#43 1 0 1 5 4 5 5
68#14 1 0 1 0 4 0 1
68#3932 1 4 5 1 5
69#2681 5 0 0 4 1 5
SizeIDRules
71#48 1 0 4 0 0 5 0
71#2771 5 0 1 4 1 2
73#91 1 0 4 4 2 5 5
73#1781 4 2 0 0 5 2
73#1981 4 2 1 0 5 1
73#2251 4 5 0 0 5 2
73#2451 4 5 1 0 5 1
77#1221 2 1 4 0 4 1
78#2711 5 0 0 4 5 1
79#2031 4 2 1 2 1 5
79#2501 4 5 1 2 1 5
81#1721 4 2 0 0 1 2
81#2191 4 5 0 0 1 2
83#22 1 0 1 5 0 0 2
83#1711 4 2 0 0 1 1
83#2181 4 5 0 0 1 1
85#21 1 0 1 5 0 0 1
86#9 1 0 1 0 2 0
86#1671 2 5 2 5 2 5
90#1771 4 2 0 0 5 1
90#1871 4 2 0 4 1
90#2241 4 5 0 0 5 1
90#2341 4 5 0 4 1
92#1131 2 0 4 1 4 5
93#34 1 0 1 5 2 5 5
94#1731 4 2 0 0 1 5
94#2201 4 5 0 0 1 5
96#23 1 0 1 5 0 0 5
97#51 1 0 4 0 1 0 2
99#10 1 0 1 0 2 1
99#20 1 0 1 0 4 5 5
99#1411 2 1 5 1 2

Sizes 101 to 1000

SizeIDRules
101#1641 2 5 2 5 0 5
102#49 1 0 4 0 0 5 2
105#3 1 0 1 0 0 0 2
105#1291 2 1 4 2 4 1
107#3431 5 4 1 0 5 2
110#52 1 0 4 0 1 0 5
110#94 1 2 0 0 1 2
112#2871 5 0 1 5 5 5
112#3201 5 2 1 5 5 5
113#2801 5 0 1 4 5 2
113#3121 5 2 1 4 2 5
114#1241 2 1 4 0 4 5
114#3471 5 4 1 1 2 5
118#65 1 0 4 2 1 1 5
119#2811 5 0 1 4 5 5
122#75 1 0 4 2 5 2 5
126#3291 5 2 5 4 1 5
130#71 1 0 4 2 5 0 2
130#3011 5 0 5 5 1 4
132#3141 5 2 1 4 5 5
134#1271 2 1 4 0 5 5
134#2861 5 0 1 5 5 1
136#3131 5 2 1 4 5 1
138#84 1 0 4 4 0 5 5
138#3711 5 4 4 5 5 5
140#2791 5 0 1 4 5 1
148#3091 5 2 1 4 1 1
151#1431 2 1 5 4 0 1
152#1341 2 1 4 2 5 5
152#3191 5 2 1 5 5 1
153#72 1 0 4 2 5 0 5
159#2701 5 0 0 4 2 5
162#1661 2 5 2 5 2 4
SizeIDRules
165#2851 5 0 1 5 2 5
173#1591 2 5 2 1 4 4
176#1111 2 0 4 1 4 1
176#3171 5 2 1 5 2 1
180#3411 5 4 1 0 1 5
181#97 1 2 0 0 1 4 5
194#3391 5 4 1 0 1 1
196#15 1 0 1 0 4 0 2
196#74 1 0 4 2 5 2 2
196#2671 5 0 0 4 1 1
201#1081 2 0 0 5 4 2
203#26 1 0 1 5 0 5 2
206#3041 5 0 5 5 5 4
212#81 1 0 4 4 0 1 5
219#2021 4 2 1 2 1 4
219#2491 4 5 1 2 1 4
235#7 1 0 1 0 0 5 2
236#1631 2 5 2 5 0 4
237#1091 2 0 0 5 4 5
242#3051 5 0 5 5 5 5
245#3541 5 4 1 5 5 1
247#95 1 2 0 0 1 4 1
247#3101 5 2 1 4 1 5
248#1621 2 5 2 5 0 1
248#1961 4 2 1 0 4 2
248#2431 4 5 1 0 4 2
262#3371 5 2 5 5 5 1
281#1321 2 1 4 2 5 1
284#1851 4 2 0 2 2 5
284#2321 4 5 0 2 2 5
285#1761 4 2 0 0 4 5
285#2231 4 5 0 0 4 5
286#3381 5 2 5 5 5 5
SizeIDRules
287#3261 5 2 5 1 5 5
289#50 1 0 4 0 1 0 1
294#3401 5 4 1 0 1 2
295#2 1 0 1 0 0 0 1
296#45 1 0 4 0 0 1 2
304#1041 2 0 0 5 2 1
306#2991 5 0 5 2 5 5
309#96 1 2 0 0 1 4 2
321#3551 5 4 1 5 5 5
327#11 1 0 1 0 2 5 1
330#82 1 0 4 4 0 5 1
338#3321 5 2 5 4 5 5
345#1011 2 0 0 4 2 4
347#89 1 0 4 4 2 5 1
354#1051 2 0 0 5 2 2
354#3421 5 4 1 0 5 1
356#3231 5 2 5 1 2 1
393#3111 5 2 1 4 2 1
398#69 1 0 4 2 1 5 5
411#3892 1 4 5 1 2 4
415#1151 2 0 4 4 1 2
419#2941 5 0 5 2 1 1
438#3872 1 4 5 1 2 1
438#3882 1 4 5 1 2 2
451#58 1 0 4 0 5 5 0
451#59 1 0 4 0 5 5 5
454#2981 5 0 5 2 5 1
475#12 1 0 1 0 2 5 2
496#1931 4 2 0 4 5 5
496#2401 4 5 0 4 5 5
512#3651 5 4 4 5 0 5
514#1681 2 5 2 5 4 1
533#3251 5 2 5 1 5 1
SizeIDRules
534#32 1 0 1 5 2 5 1
534#37 1 0 1 5 4 1 5
534#3211 5 2 5 1 1 1
553#1581 2 5 2 1 4 1
558#3601 5 4 4 1 5 1
561#1481 2 1 5 4 2 5
606#3241 5 2 5 1 2 5
609#1231 2 1 4 0 4 2
609#3772 0 1 4 1 4 1
609#4002 4 5 4 1 4 1
615#3792 0 1 4 1 4 4
615#4022 4 5 4 1 4 4
623#3151 5 2 1 5 1 1
631#64 1 0 4 2 1 1 0
631#1061 2 0 0 5 2 5
636#3031 5 0 5 5 5 1
663#3511 5 4 1 5 1 5
684#19 1 0 1 0 4 5 2
697#1791 4 2 0 0 5 5
697#2261 4 5 0 0 5 5
708#3441 5 4 1 0 5 5
711#99 1 2 0 0 4 1 4
731#1571 2 5 2 1 2 5
732#2691 5 0 0 4 2 1
735#1121 2 0 4 1 4 2
738#1701 2 5 2 5 4 5
747#67 1 0 4 2 1 2 2
839#1031 2 0 0 4 5 4
843#3361 5 2 5 5 2 5
897#1751 4 2 0 0 4 2
897#2221 4 5 0 0 4 2
970#47 1 0 4 0 0 2 2

Sizes over 1000

SizeIDRules
1020#56 1 0 4 0 5 2 1
1063#1651 2 5 2 5 2 1
1116#1691 2 5 2 5 4 4
1457#3681 5 4 4 5 1 5
1515#1021 2 0 0 4 5 2
1545#54 1 0 4 0 5 1 0
1550#70 1 0 4 2 5 0 1
1564#2951 5 0 5 2 1 5
1574#3341 5 2 5 5 1 5
1632#2901 5 0 5 1 4 1
1632#2911 5 0 5 1 4 5
1660#46 1 0 4 0 0 2 0
1672#2821 5 0 1 5 1 1
1688#1901 4 2 0 4 4 5
1688#2371 4 5 0 4 4 5
1742#3181 5 2 1 5 2 5
1831#18 1 0 1 0 4 5 1
1932#8 1 0 1 0 0 5 5
1978#2921 5 0 5 1 5 1
2056#66 1 0 4 2 1 2 0
2155#6 1 0 1 0 0 5 1
2373#3922 1 4 5 1 4 4
2377#3161 5 2 1 5 1 5
2478#3902 1 4 5 1 4 1
2526#1461 2 1 5 4 2 1
2565#1561 2 5 2 1 2 4
2578#1181 2 0 4 4 5 4
2578#1191 2 0 4 4 5 5
2754#73 1 0 4 2 5 2 1
2754#3271 5 2 5 4 1 1
2811#3501 5 4 1 5 1 1
2857#1471 2 1 5 4 2 2
3566#1921 4 2 0 4 5 2
3566#2391 4 5 0 4 5 2
SizeIDRules
3793#2051 4 2 1 2 2 4
3793#2521 4 5 1 2 2 4
3943#1071 2 0 0 5 4 1
4318#33 1 0 1 5 2 5 2
4371#2961 5 0 5 2 4 1
4419#1911 4 2 0 4 5 1
4419#2381 4 5 0 4 5 1
4432#40 1 0 1 5 4 2 5
4802#3691 5 4 4 5 5 1
5132#1001 2 0 0 4 2 2
5148#2931 5 0 5 1 5 5
5708#3301 5 2 5 4 5 1
5715#1991 4 2 1 0 5 2
5715#2461 4 5 1 0 5 2
5865#681 0 4 2 1 5 0
7143#2971 5 0 5 2 4 5
7275#3351 5 2 5 5 2 1
7524#251 0 1 5 0 5 1
7565#3621 5 4 4 1 5 5
7584#1531 2 5 2 1 0 4
7882#1301 2 1 4 2 4 2
9260#1541 2 5 2 1 0 5
10307#2831 5 0 1 5 1 5
10460#281 0 1 5 2 0 1
10795#571 0 4 0 5 2 4
17859#871 0 4 4 2 0 5
22847#1251 2 1 4 0 5 1
45477#3581 5 4 4 1 0 5
52549#2881 5 0 5 1 1 1
83618#3331 5 2 5 5 1 1
220142#1521 2 5 2 1 0 1
569804#551 0 4 0 5 1 2
918339#601 0 4 2 0 1 0

Infinite

Chain
CycleBaseAngleDistIDRules
100.0 (0)1#10
53120.0 (4)1#3822 0 1 5
500.0 (0)1#3952 1 5
560.0 (0)1#4052 4 5 5
51180.0 (3)1#4082 5 1 5
560.0 (0)1#4112 5 4 5
11660.0 (5)1#361 0 1 5 4 1 1
11120.0 (0)1#1351 2 1 4 4 1 1
11120.0 (0)1#2101 4 2 1 4 1 1
111180.0 (3)1#2571 4 5 1 4 1 1
1100.0 (0)1#3451 5 4 1 1 1
28412150.0 (0,1)1.73#981 2 0 0 4 1 2
28415330.0 (3,4)1.73#1741 4 2 0 0 4 1
28415150.0 (0,1)1.73#2211 4 5 0 0 4 1
71240253.9 (1,2,2,2)3.61#3281 5 2 5 4 1 2
711761133.9 (3,4,4,4)3.61#3311 5 2 5 4 5 2
1482195300.0 (1)4#3521 5 4 1 5 2 1
1481200160.0 (5)4#3531 5 4 1 5 2 5
????#2891 5 0 5 1 1 5
Triangle
IDRules
#1201 2 0 4 5
#1261 2 1 4 0 5 2
#1391 2 1 4 4 5
#1601 2 5 2 1 4 5
#2001 4 2 1 0 5 5
#2091 4 2 1 2 5 5
#2141 4 2 1 4 5
#2471 4 5 1 0 5 5
#2561 4 5 1 2 5 5
#2611 4 5 1 4 5
#2841 5 0 1 5 2 1
#3721 5 4 5
Hexagon
IDRules
#291 0 1 5 2 0 2
#301 0 1 5 2 0 5
#631 0 4 2 0 5
#761 0 4 4 0 0 1
#851 0 4 4 2 0 1
#1101 2 0 2
#1161 2 0 4 4 1 4
#1611 2 5 2 2
#1801 4 2 0 2 1 1
#1811 4 2 0 2 1 4
#1821 4 2 0 2 1 5
#2161 4 2 5 2
#2271 4 5 0 2 1 1
#2281 4 5 0 2 1 4
#2291 4 5 0 2 1 5
#2631 4 5 5 2
#3061 5 2 0
#3561 5 4 4 1 0 1
#3631 5 4 4 5 0 1
Symmetric
IDRules
#771 0 4 4 0 0 2
#901 0 4 4 2 5 2
#1381 2 1 4 4 4
#1891 4 2 0 4 4 2
#2131 4 2 1 4 4
#2361 4 5 0 4 4 2
#2601 4 5 1 4 4
#2731 5 0 0 5
#3591 5 4 4 1 1
#3611 5 4 4 1 5 2
#3671 5 4 4 5 1 2
#3701 5 4 4 5 5 2
Non-symmetric
IDRules
#791 0 4 4 0 1 1
#801 0 4 4 0 1 2
#831 0 4 4 0 5 2
#861 0 4 4 2 0 2
#881 0 4 4 2 1
#1171 2 0 4 4 2
#3571 5 4 4 1 0 2
#3641 5 4 4 5 0 2
#3661 5 4 4 5 1 1

Infinite ???

IDRulesShownComments¼ scale
#611 0 4 2 0 1 5 31,847,646Irregular blob, frighteningly random.320,749,428
#621 0 4 2 0 2 18,435,606Grows by contours297,492,480
#1551 2 5 2 1 2 1 23,100,569(>800M) Could be chain.264,759,447
#1831 4 2 0 2 2 1 N/A(>15M) Rounded hexagon 
#1841 4 2 0 2 2 4 13,906,381(>300M)296,955,694
#2311 4 5 0 2 2 4 13,907,633(>420M) 
#2301 4 5 0 2 2 1 N/A(>20M) Giant hexagon 
#3221 5 2 5 1 1 5 23,874,479(>370M)371,625,962
#3782 0 1 4 1 4 2 N/A(>10M) 
#3912 1 4 5 1 4 2 16,445,543(>20M) 
#4012 4 5 4 1 4 2 13,640,475(>30M) 

     The above patterns are scaled down quite a bit to be able to represent very large populations.  Segments take only 0.1 screen pixels horizontally.  Every 1,000,000 units the color changes.  They are cycled in the following sequence: Red, Green, Blue, Cyan, Magenta, Yellow.  The bracketed amount is the number of millions of units to which the pattern has been traced.

The ¼ scale column shows pattern populations when the size was reduced by a factor of four.


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