n-Cell Thick Patterns (2)

In this post, I resume the study of the minimum length of an n-cell thick pattern that exhibits infinite growth.

Details on 4-cell thick patterns were pending.  Find out about them here.

4-cell thick

There are thirty-one minimum-length 4-cell thick patterns that exhibit infinite growth. They fit inside a 4 x 7 rectangle.

• Pattern #1 #3 #30 (15, 15, and 14 alive cells, respectively)

Pattern #1 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
5b2o$2b5o$2o2bobo$obob2o!

Pattern#3 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
5b2o$ob5o$bo2bobo$obob2o!

Pattern#30 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
o2b2obo$2bo3bo$bo3b2o$o2b4o!

They produce a block-laying switch engine, and achieve stability at generation 2780:

The final population includes eleven gliders.

• Pattern #2 #5 #6 #7 #8 #9 #10 #11 #15 #16 #18 #28 #29 (14, 14, 15, 14, 15, 14, 15, 13, 14, 15, 14, 16, and 16 alive cells, respectively)

Pattern #2 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
5b2o$o2b2obo$2bo2bo$6o!

Pattern #5 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
4b3o$bo2bobo$2bo2bo$6o!

Pattern #6 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
4b3o$bo2b3o$2bo3bo$6o!

Pattern #7 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
4b3o$b2obobo$5bo$6o!

Pattern #8 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
4b3o$b2ob3o$6bo$6o!

Pattern #9 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
4b3o$obobobo$5bo$6o!

Pattern #10 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
4b3o$obob3o$6bo$6o!

Pattern #11 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
3bo2bo$bobo2bo$o2bob2o$ob2obo!

Pattern #15 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
2bob3o$bo2bobo$5bo$6o!

Pattern #16 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
2bob3o$bo2b3o$6bo$6o!

Pattern #18 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
2b2obo$2obob2o$b2o3bo$obo3bo!

Pattern #28 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
b6o$o$2o2bobo$3obobo!

Pattern #29 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
b6o$o3bo$2o2bobo$3o3bo!

They produce a block-laying switch engine, and achieve stability at generation 656, (658 for pattern #11, #18):

The final population includes two gliders.

• Pattern #4 (13 alive cells)

Pattern #4 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
4b3o$bo2bo$2o3b2o$obob2o!

It produces a glider-making switch engine, and achieves stability at generation 825:

• Pattern #12 (17 alive cells)

Pattern #12 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
3bo2bo$4ob2o$2b2o2bo$4ob2o!

It produces a block-laying switch engine, and achieves stability at generation 514:

The final population includes one glider.

• Pattern #13 (14 alive cells)

Pattern #13 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
3b2o$o2bob2o$ob2obo$3o3bo!

It produces a block-laying switch engine, and achieves stability at generation 2089:

The final population includes six gliders.

• Pattern #14 #17 (11, and 11 alive cells, respectively)

Pattern #14 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
2bo2bo$o2bobo$o2bobo$o4b2o!

Pattern #17 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
2b2obo$o4bo$o2bobo$o4b2o!

It produces a block-laying switch engine, and achieves stability at generation 428:

There are no gliders in the final population.

• Pattern #19 #20 (15, and 15 alive cells, respectively)

Pattern #19 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
2b3obo$b2o2b2o$3ob2o$o4bo!

Pattern #20 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
bo4bo$b2ob3o$2o2bo$ob3obo!

They produce a block-laying switch engine, and achieve stability at generation 5534:

The final population includes sixteen gliders.

• Pattern #21 #27 (15, and 12 alive cells, respectively)

Pattern #21 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
bo3bo$b4obo$2bo2b2o$2ob2obo!

Pattern #27 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
b2o3bo$bobo2bo$o5bo$obob2o!

It produces a block-laying switch engine, and achieves stability at generation 2914 (2913 for pattern #27):

The final population includes four gliders.

• Pattern #22 #23 #24 (14, 14, and 13 alive cells, respectively)

Pattern #22 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
bo3bo$o2b4o$o3bo$3o2b2o!

Pattern #23 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
bo3bo$o2b4o$o3b2o$3o3bo!

Pattern #24 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
bo3b2o$o2b3o$o3bo$3o2bo!

They produce a block-laying switch engine, and achieve stability at generation 915:

The final population includes five gliders.

• Pattern #25 (16 alive cells)

Pattern #25 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
bobobo$2bo2bo$4o2bo$3ob3o!

It produces a block-laying switch engine, and achieves stability at generation 4697:

The final population includes eighteen gliders.

• Pattern #26 (15 alive cells)

Pattern #26 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
bob3o$b2o3bo$bo3b2o$obob3o!

It produces a glider-making switch engine, and achieves stability at generation 1291:

• Pattern #31 (16 alive cells)

Pattern #31 (RLE)

#CXRLE Pos=0,0
x = 7, y = 4, rule = B3/S23
obo2b2o$b3o2bo$4bobo$3ob3o!

It produces a block-laying switch engine, and achieves stability at generation 3799:

The final population includes eight gliders.