Decompositions [GAME]

[OCAfan55]

So we all know syntheses, but what about decompositions?
To "decompose" something (in this game) is when you take a stable object like so

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x = 3, y = 4, rule = B3/S23
bo$obo$obo$bo!

and place any amount of the same object to turn it into gliders (more than one glider is accepted and supported)

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x = 11, y = 11, rule = B3/S23
b2o$o2bo$b2o$6bo$2bo2bobo$bobobobo$bobo2bo$2bo6bo$8bobo$8bobo$9bo!

The starting pattern is

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x = 6, y = 6, rule = B3/S23
4bo$3bobo$2bo2bo$bob2o$bo$2o!

[PK22]

This does sort of ruin the fun, but I hacked together a script to do it automatically:

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import lifelib
sess = lifelib.load_rules('b3s23')
lt = sess.lifetree(n_layers = 1, memory = 1000)
transformations = ['identity', 'rot270', 'rot180', 'rot90', 'flip_x', 'flip_y', 'swap_xy', 'swap_xy_flip']
import random
def addpt(pt):
    pt += basept(random.choice(transformations))(random.randint(-placearea, placearea), random.randint(-placearea, placearea))[random.randint(0, period-1)]
    return pt
rle = input('Enter headerless RLE of pattern.\n>')
objs = int(input('How many objects do you want to place?\n>'))
basept = lt.pattern(rle)
bbox = basept.bounding_box
placearea = round(max(bbox[2], bbox[3]) * 2.2)
period = basept.period
componentnums = [len(basept[x].components()) for x in range(period)]
min_components = objs * min(componentnums)
max_components = objs * max(componentnums)
for n in range(1000000):
    if (n+1)%1000 == 0:
        print(str(n+1)+'/1000000 solutions tested.')
    pt = lt.pattern('b!')
    for x in range(objs):
        pt = addpt(pt)
    if len(pt.components()) >= min_components and len(pt.components()) <= max_components:
        if pt[200].population == 5:
            if pt[200].wechsler in ['153', '163']:
                print('#C Solution found:')
                print(pt.rle_string())
                break

An example solution using three copies:

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#CLL state-numbering golly
x = 12, y = 16, rule = B3/S23
2b2o$bo2bo$2bobo$3bo$4b3o3bo$6bo2bobo$8bo2bo$7bob2o$7bo$6b2o$4bo$
3bobo$2bo2bo$bob2o$bo$2o!

It is quite slow, but it gets there in the end for small objects:

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x = 15, y = 15, rule = B3/S23
3b2o$3bobo$5bo$b4o$o$obo3b2o$b2o2bo2bo$5bob2o$2b2obo6b2o$2bo2bo6bobo$
3b2o9bo$10b4o$9bo$9bobo$10b2o!

[I6_I6]

3 objects:

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x = 20, y = 8, rule = B3/S23
18bo$17bobo$4bo4b2o5bo2bo$3bobo2bo2bo3bob2o$2bo2bo2bobo4bo$bob2o4bo4b
2o$bo4b3o$2o4bo!

Next:

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x = 7, y = 3, rule = B3/S23
5b2o$ob2o2bo$2ob2o!

[I6_I6]

I just did it myself:

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x = 11, y = 24, rule = B3/S23
4b2o$4bo$5bo$4b2o$4bo$6bo$5b2o11$9b2o$4bob2o2bo$4b2ob2o2$5b2o$ob2o2bo
$2ob2o!

Next:

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x = 5, y = 7, rule = B3/S23
2bo$bobo$bobo$2ob2o$bobo$bobo$2bo!

[b-engine]

8 because I'm doing it manually:

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x = 54, y = 21, rule = B3/S23
17b2o$5b2o10bo$ob2o2bo12bo$2ob2o13b2o$18bo$19bo12b2o$18b2o7bob2o2bo15b
2ob2o$27b2ob2o9b2o4bo2b2obo$7b2o27bob2o2bo4b2o$7bo17b2o9b2ob2o$8bo11b
ob2o2bo$7b2o11b2ob2o$7bo$9bo$8b2o32b2o$42bo$43bo$42b2o$42bo$44bo$43b2o
!

Next:

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x = 9, y = 7, rule = B3/S23
2b2o$2bo$3b3ob2o$5bobo$b3obobo$o2bob2o$2o!

[OCAfan55]

4 for I6_I6's pick (2 gliders!)

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x = 12, y = 18, rule = B3/S23
3bo$b5o$o5bo$b5o$3bo$8bo$6b5o$5bo5bo$3bo2b5o$2bobo3bo$2bobo$b2ob2o3bo
$2bobo3bobo$2bobo3bobo$3bo3b2ob2o$8bobo$8bobo$9bo!

4 for b-engine's pick (also 2 gliders!)

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x = 25, y = 26, rule = B3/S23
10b2o$10bo$11b3ob2o$13bobo$9b3obobo$8bo2bob2o$8b2o6b2o$16bo2bob2o$17b
3obobo$6b2o13bobo$6bo12b3ob2o$7b3ob2o5bo$9bobo6b2o$5b3obobo$4bo2bob2o
$4b2o2$2bo$2b3o$5bo$2b4o$2bo$obob2o$2o2bo$4bobo$5b2o!

Next:

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x = 9, y = 10, rule = B3/S23
7b2o$8bo$5b3o$4bo$4b2o2$2b2o$3bo$3o$o!

[yyh_baboon]

4 for 3 gliders!

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 x = 39, y = 25, rule = B3/S23
2o$obo$2bo$2bobo$3b2o$6b2o$6bobo2bo$8bo2b3o$8b2o4bo$13b2o2$15b2o$15bo
$16b3o5b2o$19bo5bo$18b2o2b3o5b2o$21bo8bo$21b2o8b3o$34bo$19b2o12b2o$20b
o$17b3o15b2o$17bo17bo$36b3o$38bo!

Next:

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 x = 8, y = 6, rule = B3/S23
7bo$5b3o$b2obo$2bobob2o$obobo2bo$2o3b2o!

[OCAfan55]

Simple 3 object solution for one glider

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x = 24, y = 32, rule = B3/S23
19b2ob2o$18bobobo$18bo3bo$19b3o2$19b3o$18bo2bo$18b2o14$9b2o$9bo2bo$10b
3o2$10b3o$7bobo3bo$5b3obobobo$b2obo5b2ob2o$2bobob2o$obobo2bo$2o3b2o!

Next:

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x = 7, y = 8, rule = B3/S23
3bo$2bobo$3bo2$b5o$o5bo$obobobo$b2ob2o!