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Close life variants

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Close life variants

Postby A for awesome » October 4th, 2014, 3:23 pm

This thread is for posting patterns from rules that very closely resemble Life, yet differ in subtle ways. Here is one:
@RULE SubtlyNotLife
@TABLE
n_states:3
neighborhood:Moore
symmetries:rotate4reflect
var a={0,1,2}
var aa={a}
var ab={a}
var ac={a}
var b={1,2}
var ba={b}
var bb={b}
var bc={b}
var bd={b}
var be={b}
var bf={b}
var bg={b}
0,b,ba,bb,0,0,0,0,0,1
0,b,ba,0,bb,0,0,0,0,1
0,b,ba,0,0,bb,0,0,0,1
0,b,ba,0,0,0,bb,0,0,1
0,b,ba,0,0,0,0,bb,0,1
0,b,ba,0,0,0,0,0,bb,1
0,b,0,ba,0,bb,0,0,0,1
0,b,0,ba,0,0,bb,0,0,1
0,b,0,0,ba,0,bb,0,0,1
0,0,b,0,1,0,ba,0,0,2
b,a,0,0,0,0,0,0,0,0
b,0,a,0,0,0,0,0,0,0
b,ba,bb,bc,bd,a,aa,ab,ac,0
b,ba,bb,bc,a,bd,aa,ab,ac,0
b,ba,bb,bc,a,aa,bd,ab,ac,0
b,ba,bb,a,bc,bd,aa,ab,ac,0
b,ba,bb,a,bc,aa,bd,ab,ac,0
b,ba,bb,a,bc,aa,ab,bd,ac,0
b,ba,bb,a,bc,aa,ab,ac,bd,0
b,ba,bb,a,aa,bc,bd,ab,ac,0
b,ba,bb,a,aa,bc,ab,bd,ac,0
b,ba,bb,a,aa,bc,ab,ac,bd,0
b,ba,bb,a,aa,ab,bc,bd,ac,0
b,ba,bb,a,aa,ab,bc,ac,bd,0
b,ba,a,bb,aa,bc,ab,bd,ac,0
b,a,ba,aa,bb,ab,bc,ac,bd,0
@COLORS
0 30 30 30
1 255 0 0
2 200 0 0

This rule is almost exactly the same as Life, but, for instance, the R pentomino doesn't last as long. The pi is also slightly different, stabilizing at 173 gens. Also, the diehard, in this rule, does not actually die:
x = 8, y = 3, rule = SubtlyNotLife
.A$6.A$3A3.2A!

Here is a precursor made of normal cells of a still life that does not work in normal Life:
x = 9, y = 9, rule = SubtlyNotLife
6.A$.2A.A$5.A2.A$A.2A.2A$A.A.A2.A$5.A$4.2A.A$7.A$4.2A!
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

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Re: Close life variants

Postby c0b0p0 » October 22nd, 2014, 11:10 pm

The rule below is two-state and differs from life in only one transition.
@RULE alife


@TABLE

n_states:2
neighborhood:Moore
symmetries:rotate8reflect

var a={0,1}
var b={a}
var c={a}
var d={a}
var e={a}
0,1,1,1,0,0,0,0,0,1
0,1,0,1,1,0,0,0,0,1
0,0,0,1,1,0,0,1,0,1
0,0,1,0,0,1,0,0,1,1
0,1,0,1,0,0,0,1,0,1
1,0,0,0,0,0,0,0,0,0
1,1,0,0,0,0,0,0,0,0
1,1,a,1,b,1,c,1,d,0
1,1,a,1,b,1,c,d,1,0
1,1,1,1,a,1,b,c,d,0
1,a,1,1,1,b,c,1,d,0
1,1,1,1,1,a,b,c,d,0
1,a,1,1,b,1,c,d,1,0
1,1,1,a,b,1,1,c,d,0

@COLORS

# colors from
# http://necsi.org/postdocs/sayama/sdsr/java/loops.java
# Color.black,Color.blue,Color.red,Color.green,
# Color.yellow,Color.magenta,Color.white,Color.cyan,Color.orange
1    0    0  255
2  255    0    0
3    0  255    0

In spite of that, the rule is very different from Life in behavior. For example, the preloaf (in Life) shown below is a p4.
x = 3, y = 3, rule = alife
b2o$2o$o!


The rule has a much greater variety of ships, with three naturally occurring ships. The bookend develops into the c/42 diagonal glide-reflective ship shown below, which produces an extraneous block and then deletes it.
x = 10, y = 5, rule = alife
7b3o$6bo2$2o4b3o$bo!

The property can be used to eat other ships. An example of this is shown below.
x = 50, y = 10, rule = alife
bo$2o4$47b3o$bobo42bo$bo2bo$bo2bo35b2o4b3o$4bo36bo!


There is also a 2c/7 diagonal ship, shown below.
x = 5, y = 5, rule = alife
3o$3bo$4bo$o3bo$bo2bo!
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Re: Close life variants

Postby A for awesome » December 9th, 2014, 6:50 pm

I found another interesting variant of Life. Here is the rule table:
@RULE 2diagonal
@TABLE
n_states:2
neighborhood:Moore
symmetries:rotate4reflect
0,1,1,1,0,0,0,0,0,1
0,1,1,0,1,0,0,0,0,1
0,1,1,0,0,1,0,0,0,1
0,1,1,0,0,0,1,0,0,1
0,1,1,0,0,0,0,1,0,1
0,1,1,0,0,0,0,0,1,1
0,1,0,1,0,1,0,0,0,1
0,1,0,1,0,0,1,0,0,1
0,1,0,0,1,0,1,0,0,1
0,0,1,0,1,0,1,0,0,1
0,0,1,0,0,0,1,0,0,1
1,0,0,0,0,0,0,0,0,0
1,1,0,0,0,0,0,0,0,0
1,0,1,0,0,0,0,0,0,0
1,1,1,0,0,0,0,0,0,1
1,1,0,1,0,0,0,0,0,1
1,1,0,0,1,0,0,0,0,1
1,1,0,0,0,1,0,0,0,1
1,0,1,0,1,0,0,0,0,1
1,0,1,0,0,0,1,0,0,1
1,1,1,1,0,0,0,0,0,1
1,1,1,0,1,0,0,0,0,1
1,1,1,0,0,1,0,0,0,1
1,1,1,0,0,0,1,0,0,1
1,1,1,0,0,0,0,1,0,1
1,1,1,0,0,0,0,0,1,1
1,1,0,1,0,1,0,0,0,1
1,1,0,1,0,0,1,0,0,1
1,1,0,0,1,0,1,0,0,1
1,0,1,0,1,0,1,0,0,1
1,1,1,1,1,0,0,0,0,0
1,1,1,1,0,1,0,0,0,0
1,1,1,1,0,0,1,0,0,0
1,1,1,0,1,1,0,0,0,0
1,1,1,0,1,0,1,0,0,0
1,1,1,0,1,0,0,1,0,0
1,1,1,0,1,0,0,0,1,0
1,1,1,0,0,1,1,0,0,0
1,1,1,0,0,1,0,1,0,0
1,1,1,0,0,1,0,0,1,0
1,1,1,0,0,0,1,1,0,0
1,1,0,1,0,1,0,1,0,0
1,0,1,0,1,0,1,0,1,0
1,0,0,0,1,1,1,1,1,0
1,0,0,1,0,1,1,1,1,0
1,0,0,1,1,0,1,1,1,0
1,0,0,1,1,1,0,1,1,0
1,0,0,1,1,1,1,0,1,0
1,0,0,1,1,1,1,1,0,0
1,0,1,0,1,0,1,1,1,0
1,0,1,0,1,1,0,1,1,0
1,0,1,1,0,1,0,1,1,0
1,1,0,1,0,1,0,1,1,0
1,0,0,1,1,1,1,1,1,0
1,0,1,0,1,1,1,1,1,0
1,0,1,1,0,1,1,1,1,0
1,0,1,1,1,0,1,1,1,0
1,1,0,1,0,1,1,1,1,0
1,1,0,1,1,1,0,1,1,0
1,0,1,1,1,1,1,1,1,0
1,1,0,1,1,1,1,1,1,0
1,1,1,1,1,1,1,1,1,0

It is exactly the same as GoL, except for a cell is born also if it has two diagonally opposite neighbors. Here are two oscillators:
x = 5, y = 5, rule = 2diagonal
3b2o$3b2o$2bo$2o$2o!

x = 11, y = 11, rule = 2diagonal
4b2o$3bobo2$bo3bo$o$2obo3bob2o$10bo$5bo3bo2$5bobo$5b2o!

The last one is extensible, I think in both directions.
This rule is technically exploding in character, but seems to be just as engineerable as Life. A boat can eat a glider, as shown:
x = 7, y = 6, rule = 2diagonal
2bo$obo$b2o$5bo$4bobo$5b2o!

It can also act as a memory device, via the previous and following reactions:
x = 4, y = 7, rule = 2diagonal
bo$bobo$b2o2$bo$obo$b2o!

Unfortunately, much of Life's technology does not work in this rule, for example the Gosper glider gun and the twin bees shuttle.
And finally, a pattern that produces two temporary long long long long canoes (and four temporary aircraft carriers):
x = 8, y = 8, rule = 2diagonal
5bo$4b3o$5b3o$6bo$bo$3o$b3o$2bo!

I suspect that canoe variants are much more common in this rule, because of the extra transition impacting patterns with a diagonal axis of symmetry.
Edit: And long ships. I have yet to find a common predecessor, however.
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

Aidan F. Pierce
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Re: Close life variants

Postby A for awesome » December 28th, 2014, 11:14 am

A small period 4 oscillator in 2diagonal:
x = 6, y = 6, rule = 2diagonal
3b2o$2bo2bo$5bo$4bo$o$2o!

And another, larger one:
x = 11, y = 11, rule = 2diagonal
9b2o$10bo$6bo2$5b2obo$4bobo$2bob2o2$4bo$o$2o!
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

Aidan F. Pierce
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Re: Close life variants

Postby A for awesome » January 8th, 2015, 3:13 pm

A wick based on a previous oscillator:
x = 35, y = 35, rule = 2diagonal
33b2o$34bo$30bo2$29b2obo$28bobo$26bob2o2$24bo3bo2$23b2obo$22bobo$20bob
2o2$18bo3bo2$17b2obo$16bobo$14bob2o2$12bo3bo2$11b2obo$10bobo$8bob2o2$
6bo3bo2$5b2obo$4bobo$2bob2o2$4bo$o$2o!
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

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Re: Close life variants

Postby A for awesome » January 9th, 2015, 2:47 pm

The first puffer in this rule (that is, the first puffer whose debris doesn't explode):
x = 41, y = 27, rule = 2diagonal
9b3o17b3o$9bo2bo15bo2bo$9bo6b3o3b3o6bo$9bo5bo2bo3bo2bo5bo$10bobo2b2obo
3bob2o2bobo5$18b2ob2o$17bobobobo$4bo11b2o5b2o11bo$3b3o11b2o3b2o11b3o$
2b2obo29bob2o$2b3o31b3o$3b2o13b2ob2o13b2o$14b2o2b2ob2o2b2o$14b2o9b2o$b
o37bo$3o35b3o$ob2o33b2obo$b3o33b3o$b3o12b2o5b2o12b3o$b3o9bobobo5bobobo
9b3o$b2o9bo3b2o5b2o3bo9b2o$12b5o7b5o$13b3o9b3o!

Edit: Another puffer:
x = 52, y = 50, rule = 2diagonal
15bo19bo$14b3o17b3o$13b2obo5bo5bo5bob2o$13b3o5b3o3b3o5b3o$14b2o5bob2ob
2obo5b2o4$23b2ob2o2$19b4obobob4o$19b4obobob4o$8b3o12bo3bo12b3o$7bo2bo
8b2ob3ob3ob2o8bo2bo$10bo8b2o3bobo3b2o8bo$10bo8b3ob2ob2ob3o8bo$7bobo10b
3o5b3o10bobo$15b2o5b3ob3o5b2o$14bo2bo4b3ob3o4bo2bo$5b3o8bo17bo8b3o$5bo
2bo3bo2bo19bo2bo3bo2bo$5bo6b3o8bo3bo8b3o6bo$5bo3bo12bobobobo12bo3bo$5b
o3bo31bo3bo$5bo16b3ob3o16bo$6bobo33bobo8$4bo41bo$3b3o14b2o7b2o14b3o$3b
ob2o13b3o5b3o13b2obo$4b3o14b3o3b3o14b3o$4b3o7bo21bo7b3o$4b3o6bobo19bob
o6b3o$4b2o6b2ob2o17b2ob2o6b2o$15bobo15bobo$16b3o13b3o$19bo11bo$17b2o
13b2o$17bo15bo!
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

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Re: Close life variants

Postby A for awesome » March 27th, 2015, 1:08 pm

An agar based on a failed replicator:
x = 452, y = 452, rule = 2diagonal
226bo$225bobo$224bo3bo$223bo3bo$224bobo$225bo2$219bo13bo$218bobo11bobo
$217bo3bo9bo3bo$216bo3bo9bo3bo$217bobo11bobo$218bo13bo2$226bo$225bobo$
224bo3bo$223bo3bo$208bo15bobo17bo$207bobo15bo17bobo$206bo3bo31bo3bo$
205bo3bo31bo3bo$206bobo33bobo$207bo35bo2$201bo13bo21bo13bo$200bobo11bo
bo19bobo11bobo$199bo3bo9bo3bo17bo3bo9bo3bo$198bo3bo9bo3bo17bo3bo9bo3bo
$199bobo11bobo19bobo11bobo$200bo13bo21bo13bo2$208bo35bo$207bobo33bobo$
206bo3bo31bo3bo$205bo3bo31bo3bo$190bo15bobo17bo15bobo17bo$189bobo15bo
17bobo15bo17bobo$188bo3bo31bo3bo31bo3bo$187bo3bo31bo3bo31bo3bo$188bobo
33bobo33bobo$189bo35bo35bo2$183bo13bo21bo13bo21bo13bo$182bobo11bobo19b
obo11bobo19bobo11bobo$181bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$180bo3b
o9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$181bobo11bobo19bobo11bobo19bobo11bob
o$182bo13bo21bo13bo21bo13bo2$190bo35bo35bo$189bobo33bobo33bobo$188bo3b
o31bo3bo31bo3bo$187bo3bo31bo3bo31bo3bo$172bo15bobo17bo15bobo17bo15bobo
17bo$171bobo15bo17bobo15bo17bobo15bo17bobo$170bo3bo31bo3bo31bo3bo31bo
3bo$169bo3bo31bo3bo31bo3bo31bo3bo$170bobo33bobo33bobo33bobo$171bo35bo
35bo35bo2$165bo13bo21bo13bo21bo13bo21bo13bo$164bobo11bobo19bobo11bobo
19bobo11bobo19bobo11bobo$163bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo
3bo9bo3bo$162bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$163bob
o11bobo19bobo11bobo19bobo11bobo19bobo11bobo$164bo13bo21bo13bo21bo13bo
21bo13bo2$172bo35bo35bo35bo$171bobo33bobo33bobo33bobo$170bo3bo31bo3bo
31bo3bo31bo3bo$169bo3bo31bo3bo31bo3bo31bo3bo$154bo15bobo17bo15bobo17bo
15bobo17bo15bobo17bo$153bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo$
152bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$151bo3bo31bo3bo31bo3bo31bo3bo31bo
3bo$152bobo33bobo33bobo33bobo33bobo$153bo35bo35bo35bo35bo2$147bo13bo
21bo13bo21bo13bo21bo13bo21bo13bo$146bobo11bobo19bobo11bobo19bobo11bobo
19bobo11bobo19bobo11bobo$145bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo
3bo9bo3bo17bo3bo9bo3bo$144bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo
9bo3bo17bo3bo9bo3bo$145bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo
19bobo11bobo$146bo13bo21bo13bo21bo13bo21bo13bo21bo13bo2$154bo35bo35bo
35bo35bo$153bobo33bobo33bobo33bobo33bobo$152bo3bo31bo3bo31bo3bo31bo3bo
31bo3bo$151bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$136bo15bobo17bo15bobo17bo
15bobo17bo15bobo17bo15bobo17bo$135bobo15bo17bobo15bo17bobo15bo17bobo
15bo17bobo15bo17bobo$134bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$133bo
3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$134bobo33bobo33bobo33bobo33bobo
33bobo$135bo35bo35bo35bo35bo35bo2$129bo13bo21bo13bo21bo13bo21bo13bo21b
o13bo21bo13bo$128bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo
11bobo19bobo11bobo$127bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo
3bo17bo3bo9bo3bo17bo3bo9bo3bo$126bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo
17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$127bobo11bobo19bobo11bobo19bob
o11bobo19bobo11bobo19bobo11bobo19bobo11bobo$128bo13bo21bo13bo21bo13bo
21bo13bo21bo13bo21bo13bo2$136bo35bo35bo35bo35bo35bo$135bobo33bobo33bob
o33bobo33bobo33bobo$134bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$133bo
3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$118bo15bobo17bo15bobo17bo15bobo
17bo15bobo17bo15bobo17bo15bobo17bo$117bobo15bo17bobo15bo17bobo15bo17bo
bo15bo17bobo15bo17bobo15bo17bobo$116bo3bo31bo3bo31bo3bo31bo3bo31bo3bo
31bo3bo31bo3bo$115bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$116b
obo33bobo33bobo33bobo33bobo33bobo33bobo$117bo35bo35bo35bo35bo35bo35bo
2$111bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo$110bobo11b
obo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo
11bobo$109bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo
3bo17bo3bo9bo3bo17bo3bo9bo3bo$108bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo
17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$109bobo11bobo19bo
bo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo$
110bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo2$118bo35bo
35bo35bo35bo35bo35bo$117bobo33bobo33bobo33bobo33bobo33bobo33bobo$116bo
3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$115bo3bo31bo3bo31bo3bo
31bo3bo31bo3bo31bo3bo31bo3bo$100bo15bobo17bo15bobo17bo15bobo17bo15bobo
17bo15bobo17bo15bobo17bo15bobo17bo$99bobo15bo17bobo15bo17bobo15bo17bob
o15bo17bobo15bo17bobo15bo17bobo15bo17bobo$98bo3bo31bo3bo31bo3bo31bo3bo
31bo3bo31bo3bo31bo3bo31bo3bo$97bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3b
o31bo3bo31bo3bo$98bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo$99bo
35bo35bo35bo35bo35bo35bo35bo2$93bo13bo21bo13bo21bo13bo21bo13bo21bo13bo
21bo13bo21bo13bo21bo13bo$92bobo11bobo19bobo11bobo19bobo11bobo19bobo11b
obo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo$91bo3bo9bo3bo17bo
3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9b
o3bo17bo3bo9bo3bo$90bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo
17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$91bobo11bobo19bob
o11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19b
obo11bobo$92bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo
13bo2$100bo35bo35bo35bo35bo35bo35bo35bo$99bobo33bobo33bobo33bobo33bobo
33bobo33bobo33bobo$98bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo
31bo3bo$97bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$82bo
15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo
15bobo17bo$81bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo15b
o17bobo15bo17bobo15bo17bobo$80bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo
31bo3bo31bo3bo31bo3bo$79bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3b
o31bo3bo31bo3bo$80bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo
$81bo35bo35bo35bo35bo35bo35bo35bo35bo2$75bo13bo21bo13bo21bo13bo21bo13b
o21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo$74bobo11bobo19bobo11bobo19bo
bo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo
19bobo11bobo$73bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo
3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$72bo3bo
9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3b
o17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$73bobo11bobo19bobo11bobo19bob
o11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19b
obo11bobo$74bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo
13bo21bo13bo2$82bo35bo35bo35bo35bo35bo35bo35bo35bo$81bobo33bobo33bobo
33bobo33bobo33bobo33bobo33bobo33bobo$80bo3bo31bo3bo31bo3bo31bo3bo31bo
3bo31bo3bo31bo3bo31bo3bo31bo3bo$79bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31b
o3bo31bo3bo31bo3bo31bo3bo$64bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo
15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo$63bobo15bo17bobo15b
o17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo15b
o17bobo$62bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3b
o31bo3bo$61bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo
3bo31bo3bo$62bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bob
o$63bo35bo35bo35bo35bo35bo35bo35bo35bo35bo2$57bo13bo21bo13bo21bo13bo
21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo$56bobo11bobo
19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bo
bo19bobo11bobo19bobo11bobo19bobo11bobo$55bo3bo9bo3bo17bo3bo9bo3bo17bo
3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9b
o3bo17bo3bo9bo3bo17bo3bo9bo3bo$54bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo
17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo
3bo9bo3bo17bo3bo9bo3bo$55bobo11bobo19bobo11bobo19bobo11bobo19bobo11bob
o19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11b
obo$56bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo
21bo13bo21bo13bo2$64bo35bo35bo35bo35bo35bo35bo35bo35bo35bo$63bobo33bob
o33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo$62bo3bo31bo3bo31bo3b
o31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$61bo3bo31bo3bo31bo
3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$46bo15bobo17bo15b
obo17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo15b
obo17bo15bobo17bo$45bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo
17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo$44bo3bo31bo3b
o31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$43bo
3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo
3bo$44bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo
$45bo35bo35bo35bo35bo35bo35bo35bo35bo35bo35bo2$39bo13bo21bo13bo21bo13b
o21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo$38bo
bo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo
19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo$37bo3bo9b
o3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo
17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$36bo
3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9b
o3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$
37bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bo
bo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo$38bo13b
o21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo
13bo21bo13bo2$46bo35bo35bo35bo35bo35bo35bo35bo35bo35bo35bo$45bobo33bob
o33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo$44bo3bo31bo3bo
31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$43bo3b
o31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3b
o$28bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bo
bo17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo$27bobo15bo17bobo15bo17b
obo15bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo17b
obo15bo17bobo15bo17bobo$26bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo
3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$25bo3bo31bo3bo31bo3bo31bo3bo31b
o3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$26bobo33bobo33bo
bo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo$27bo35bo35bo
35bo35bo35bo35bo35bo35bo35bo35bo35bo2$21bo13bo21bo13bo21bo13bo21bo13bo
21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo$20bob
o11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19b
obo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo$
19bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo
3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9b
o3bo17bo3bo9bo3bo$18bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo
17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo
3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$19bobo11bobo19bobo11bobo19bobo11bo
bo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo
11bobo19bobo11bobo19bobo11bobo19bobo11bobo$20bo13bo21bo13bo21bo13bo21b
o13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo
2$28bo35bo35bo35bo35bo35bo35bo35bo35bo35bo35bo35bo$27bobo33bobo33bobo
33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo$26bo3bo31bo3bo
31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo
$25bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3b
o31bo3bo31bo3bo$10bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo
15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo
$9bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo
17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo$8bo3bo31bo3bo
31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo
31bo3bo$7bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo
31bo3bo31bo3bo31bo3bo31bo3bo$8bobo33bobo33bobo33bobo33bobo33bobo33bobo
33bobo33bobo33bobo33bobo33bobo33bobo$9bo35bo35bo35bo35bo35bo35bo35bo
35bo35bo35bo35bo35bo2$3bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo
21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo$2bobo11bobo
19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bo
bo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo
11bobo$bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo
17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo
3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$o3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo
3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo
17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$bobo
11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bo
bo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo
19bobo11bobo$2bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo
21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo2$10bo35bo35bo35bo35bo
35bo35bo35bo35bo35bo35bo35bo35bo$9bobo33bobo33bobo33bobo33bobo33bobo
33bobo33bobo33bobo33bobo33bobo33bobo33bobo$8bo3bo31bo3bo31bo3bo31bo3bo
31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$7bo3bo
31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo
31bo3bo31bo3bo$8bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo
17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo
$9bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo
15bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo$26bo3bo31bo3bo
31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo
$25bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3b
o31bo3bo31bo3bo$26bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo
33bobo33bobo33bobo$27bo35bo35bo35bo35bo35bo35bo35bo35bo35bo35bo35bo2$
21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo
13bo21bo13bo21bo13bo21bo13bo$20bobo11bobo19bobo11bobo19bobo11bobo19bob
o11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19b
obo11bobo19bobo11bobo19bobo11bobo$19bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo
3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo
17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$18bo3bo9bo3bo17bo
3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9b
o3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$
19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bo
bo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo
11bobo$20bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13b
o21bo13bo21bo13bo21bo13bo21bo13bo2$28bo35bo35bo35bo35bo35bo35bo35bo35b
o35bo35bo35bo$27bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo
33bobo33bobo33bobo$26bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo
31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$25bo3bo31bo3bo31bo3bo31bo3bo31bo3b
o31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$26bobo17bo15bobo17b
o15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo17b
o15bobo17bo15bobo17bo15bobo$27bo17bobo15bo17bobo15bo17bobo15bo17bobo
15bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo
15bo$44bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo
31bo3bo31bo3bo$43bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3b
o31bo3bo31bo3bo31bo3bo$44bobo33bobo33bobo33bobo33bobo33bobo33bobo33bob
o33bobo33bobo33bobo$45bo35bo35bo35bo35bo35bo35bo35bo35bo35bo35bo2$39bo
13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo
21bo13bo21bo13bo$38bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bob
o11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19b
obo11bobo$37bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo
9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3b
o17bo3bo9bo3bo$36bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17b
o3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo
9bo3bo17bo3bo9bo3bo$37bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo
19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bo
bo19bobo11bobo$38bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13b
o21bo13bo21bo13bo21bo13bo21bo13bo2$46bo35bo35bo35bo35bo35bo35bo35bo35b
o35bo35bo$45bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo
33bobo$44bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo
31bo3bo31bo3bo$43bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3b
o31bo3bo31bo3bo31bo3bo$44bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo
17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo$45bo17bob
o15bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bob
o15bo17bobo15bo17bobo15bo$62bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo
31bo3bo31bo3bo31bo3bo31bo3bo$61bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3b
o31bo3bo31bo3bo31bo3bo31bo3bo$62bobo33bobo33bobo33bobo33bobo33bobo33bo
bo33bobo33bobo33bobo$63bo35bo35bo35bo35bo35bo35bo35bo35bo35bo2$57bo13b
o21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo
13bo$56bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bob
o11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo$55bo3bo9bo3bo
17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo
3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$54bo3bo9bo3bo17bo3bo
9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3b
o17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$55bobo11bobo19bobo11bobo19bob
o11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19b
obo11bobo19bobo11bobo$56bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo
21bo13bo21bo13bo21bo13bo21bo13bo2$64bo35bo35bo35bo35bo35bo35bo35bo35bo
35bo$63bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo$62bo
3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$61b
o3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$
62bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo
15bobo17bo15bobo17bo15bobo$63bo17bobo15bo17bobo15bo17bobo15bo17bobo15b
o17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo$80bo3bo31bo3bo31bo
3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$79bo3bo31bo3bo31bo3bo31b
o3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$80bobo33bobo33bobo33bobo33bobo
33bobo33bobo33bobo33bobo$81bo35bo35bo35bo35bo35bo35bo35bo35bo2$75bo13b
o21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo$74bo
bo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo
19bobo11bobo19bobo11bobo19bobo11bobo$73bo3bo9bo3bo17bo3bo9bo3bo17bo3bo
9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3b
o17bo3bo9bo3bo$72bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17b
o3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$73bobo
11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bo
bo11bobo19bobo11bobo19bobo11bobo$74bo13bo21bo13bo21bo13bo21bo13bo21bo
13bo21bo13bo21bo13bo21bo13bo21bo13bo2$82bo35bo35bo35bo35bo35bo35bo35bo
35bo$81bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo$80bo3bo31b
o3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$79bo3bo31bo3bo
31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$80bobo17bo15bobo17bo
15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo$81b
o17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo15b
o17bobo15bo$98bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$
97bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$98bobo33bobo
33bobo33bobo33bobo33bobo33bobo33bobo$99bo35bo35bo35bo35bo35bo35bo35bo
2$93bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo$92b
obo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo
19bobo11bobo19bobo11bobo$91bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3b
o9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$90bo3bo9bo
3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo
17bo3bo9bo3bo17bo3bo9bo3bo$91bobo11bobo19bobo11bobo19bobo11bobo19bobo
11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo$92bo13bo21bo13b
o21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo2$100bo35bo35bo35bo
35bo35bo35bo35bo$99bobo33bobo33bobo33bobo33bobo33bobo33bobo33bobo$98bo
3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$97bo3bo31bo3bo31b
o3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$98bobo17bo15bobo17bo15bobo17bo
15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo$99bo17bobo15bo17bobo15b
o17bobo15bo17bobo15bo17bobo15bo17bobo15bo17bobo15bo$116bo3bo31bo3bo31b
o3bo31bo3bo31bo3bo31bo3bo31bo3bo$115bo3bo31bo3bo31bo3bo31bo3bo31bo3bo
31bo3bo31bo3bo$116bobo33bobo33bobo33bobo33bobo33bobo33bobo$117bo35bo
35bo35bo35bo35bo35bo2$111bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13b
o21bo13bo$110bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bob
o19bobo11bobo19bobo11bobo$109bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo
3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$108bo3bo9bo3bo17bo3bo
9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3b
o$109bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo
11bobo19bobo11bobo$110bo13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo
21bo13bo2$118bo35bo35bo35bo35bo35bo35bo$117bobo33bobo33bobo33bobo33bob
o33bobo33bobo$116bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$115bo
3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$116bobo17bo15bobo17bo15b
obo17bo15bobo17bo15bobo17bo15bobo17bo15bobo$117bo17bobo15bo17bobo15bo
17bobo15bo17bobo15bo17bobo15bo17bobo15bo$134bo3bo31bo3bo31bo3bo31bo3bo
31bo3bo31bo3bo$133bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$134bobo33bo
bo33bobo33bobo33bobo33bobo$135bo35bo35bo35bo35bo35bo2$129bo13bo21bo13b
o21bo13bo21bo13bo21bo13bo21bo13bo$128bobo11bobo19bobo11bobo19bobo11bob
o19bobo11bobo19bobo11bobo19bobo11bobo$127bo3bo9bo3bo17bo3bo9bo3bo17bo
3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$126bo3bo9bo3bo17bo3bo
9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$127bobo11bo
bo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo$128bo
13bo21bo13bo21bo13bo21bo13bo21bo13bo21bo13bo2$136bo35bo35bo35bo35bo35b
o$135bobo33bobo33bobo33bobo33bobo33bobo$134bo3bo31bo3bo31bo3bo31bo3bo
31bo3bo31bo3bo$133bo3bo31bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$134bobo17bo
15bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo$135bo17bobo15bo17bobo
15bo17bobo15bo17bobo15bo17bobo15bo$152bo3bo31bo3bo31bo3bo31bo3bo31bo3b
o$151bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$152bobo33bobo33bobo33bobo33bobo
$153bo35bo35bo35bo35bo2$147bo13bo21bo13bo21bo13bo21bo13bo21bo13bo$146b
obo11bobo19bobo11bobo19bobo11bobo19bobo11bobo19bobo11bobo$145bo3bo9bo
3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$144bo3bo9bo3bo
17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$145bobo11bobo19bo
bo11bobo19bobo11bobo19bobo11bobo19bobo11bobo$146bo13bo21bo13bo21bo13bo
21bo13bo21bo13bo2$154bo35bo35bo35bo35bo$153bobo33bobo33bobo33bobo33bob
o$152bo3bo31bo3bo31bo3bo31bo3bo31bo3bo$151bo3bo31bo3bo31bo3bo31bo3bo
31bo3bo$152bobo17bo15bobo17bo15bobo17bo15bobo17bo15bobo$153bo17bobo15b
o17bobo15bo17bobo15bo17bobo15bo$170bo3bo31bo3bo31bo3bo31bo3bo$169bo3bo
31bo3bo31bo3bo31bo3bo$170bobo33bobo33bobo33bobo$171bo35bo35bo35bo2$
165bo13bo21bo13bo21bo13bo21bo13bo$164bobo11bobo19bobo11bobo19bobo11bob
o19bobo11bobo$163bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$
162bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$163bobo11bobo19b
obo11bobo19bobo11bobo19bobo11bobo$164bo13bo21bo13bo21bo13bo21bo13bo2$
172bo35bo35bo35bo$171bobo33bobo33bobo33bobo$170bo3bo31bo3bo31bo3bo31bo
3bo$169bo3bo31bo3bo31bo3bo31bo3bo$170bobo17bo15bobo17bo15bobo17bo15bob
o$171bo17bobo15bo17bobo15bo17bobo15bo$188bo3bo31bo3bo31bo3bo$187bo3bo
31bo3bo31bo3bo$188bobo33bobo33bobo$189bo35bo35bo2$183bo13bo21bo13bo21b
o13bo$182bobo11bobo19bobo11bobo19bobo11bobo$181bo3bo9bo3bo17bo3bo9bo3b
o17bo3bo9bo3bo$180bo3bo9bo3bo17bo3bo9bo3bo17bo3bo9bo3bo$181bobo11bobo
19bobo11bobo19bobo11bobo$182bo13bo21bo13bo21bo13bo2$190bo35bo35bo$189b
obo33bobo33bobo$188bo3bo31bo3bo31bo3bo$187bo3bo31bo3bo31bo3bo$188bobo
17bo15bobo17bo15bobo$189bo17bobo15bo17bobo15bo$206bo3bo31bo3bo$205bo3b
o31bo3bo$206bobo33bobo$207bo35bo2$201bo13bo21bo13bo$200bobo11bobo19bob
o11bobo$199bo3bo9bo3bo17bo3bo9bo3bo$198bo3bo9bo3bo17bo3bo9bo3bo$199bob
o11bobo19bobo11bobo$200bo13bo21bo13bo2$208bo35bo$207bobo33bobo$206bo3b
o31bo3bo$205bo3bo31bo3bo$206bobo17bo15bobo$207bo17bobo15bo$224bo3bo$
223bo3bo$224bobo$225bo2$219bo13bo$218bobo11bobo$217bo3bo9bo3bo$216bo3b
o9bo3bo$217bobo11bobo$218bo13bo2$226bo$225bobo$224bo3bo$223bo3bo$224bo
bo$225bo!
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

Aidan F. Pierce
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A for awesome
 
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Re: Close life variants

Postby A for awesome » September 6th, 2015, 5:18 pm

A 8c/16 ship in a close variant of Life:
x = 18, y = 17, rule = klife
9b3o$3o5bo2bo$o2bo8bo$o6bo3b2o$o3bob2o3bo$o3bo2bobo$o7bo$bobo4bo$7bo$
11bo$8bo6bo$9b2o3b3o$14bob2o$15b3o$15b3o$15b3o$15b2o!

Here is the rule:
@RULE klife
@TABLE
n_states:2
neighborhood:Moore
symmetries:rotate4reflect
0,1,1,1,0,0,0,0,0,1
0,1,1,0,1,0,0,0,0,1
0,1,1,0,0,1,0,0,0,1
0,1,1,0,0,0,1,0,0,1
0,1,1,0,0,0,0,1,0,1
0,1,1,0,0,0,0,0,1,1
0,1,0,1,0,1,0,0,0,1
0,1,0,1,0,0,1,0,0,1
0,1,0,0,1,0,1,0,0,1
0,0,1,0,1,0,1,0,0,1
0,1,1,0,1,0,0,0,1,1
1,0,0,0,0,0,0,0,0,0
1,1,0,0,0,0,0,0,0,0
1,0,1,0,0,0,0,0,0,0
1,1,1,0,0,0,0,0,0,1
1,1,0,1,0,0,0,0,0,1
1,1,0,0,1,0,0,0,0,1
1,1,0,0,0,1,0,0,0,1
1,0,1,0,1,0,0,0,0,1
1,0,1,0,0,0,1,0,0,1
1,1,1,1,0,0,0,0,0,1
1,1,1,0,1,0,0,0,0,1
1,1,1,0,0,1,0,0,0,1
1,1,1,0,0,0,1,0,0,1
1,1,1,0,0,0,0,1,0,1
1,1,1,0,0,0,0,0,1,1
1,1,0,1,0,1,0,0,0,1
1,1,0,1,0,0,1,0,0,1
1,1,0,0,1,0,1,0,0,1
1,0,1,0,1,0,1,0,0,1
1,1,1,1,1,0,0,0,0,0
1,1,1,1,0,1,0,0,0,0
1,1,1,1,0,0,1,0,0,0
1,1,1,0,1,1,0,0,0,0
1,1,1,0,1,0,1,0,0,0
1,1,1,0,1,0,0,1,0,0
1,1,1,0,1,0,0,0,1,0
1,1,1,0,0,1,1,0,0,0
1,1,1,0,0,1,0,1,0,0
1,1,1,0,0,1,0,0,1,0
1,1,1,0,0,0,1,1,0,0
1,1,0,1,0,1,0,1,0,0
1,0,1,0,1,0,1,0,1,0
1,0,0,0,1,1,1,1,1,0
1,0,0,1,0,1,1,1,1,0
1,0,0,1,1,0,1,1,1,0
1,0,0,1,1,1,0,1,1,0
1,0,0,1,1,1,1,0,1,0
1,0,0,1,1,1,1,1,0,0
1,0,1,0,1,0,1,1,1,0
1,0,1,0,1,1,0,1,1,0
1,0,1,1,0,1,0,1,1,0
1,1,0,1,0,1,0,1,1,0
1,0,0,1,1,1,1,1,1,0
1,0,1,0,1,1,1,1,1,0
1,0,1,1,0,1,1,1,1,0
1,0,1,1,1,0,1,1,1,0
1,1,0,1,0,1,1,1,1,0
1,1,0,1,1,1,0,1,1,0
1,0,1,1,1,1,1,1,1,0
1,1,0,1,1,1,1,1,1,0
1,1,1,1,1,1,1,1,1,0
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

Aidan F. Pierce
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Re: Close life variants

Postby M. I. Wright » September 10th, 2015, 12:07 am

This rule differs from life in two transitions, but for the life of me I can't remember which two. I'll let this example speak for itself:
x = 116, y = 54, rule = tlife
78bo$77bo24b2o$77b3o22b3o$102b2o$113bobo$96b2o14bo2bo$71b3o21bo2bo14bo
bo$72bo22bo2bo$96b2o4$79bo$71b3o3b2o$72bo5b2o4$33bo$12bo19bo15bo53bo$
11bo20b3o12bo53bobo7bo$11b3o33b3o51b2o7b2o$111bo2$79bo$72b3o4bobo$49b
3o21bo5b2o$15b3o31bo$15bo16b2o16bo$16bo15bobo$32bo3$79bo$77b2o$11bo66b
2o$10bo61bo$10b3o$71bobo$72bo$72bo$46b2o$30bo14bo2bo$14bo14b3o13b4o$
13b2o17bo$13bobo15bo5$b2o$o$b2o4b3o$2b2o4bo!
@RULE tlife
@TABLE
n_states:2
neighborhood:Moore
symmetries:rotate4reflect
0,1,1,1,0,0,0,0,0,1
0,1,1,0,1,0,0,0,0,1
0,1,1,0,0,1,0,0,0,1
0,1,1,0,0,0,1,0,0,1
0,1,1,0,0,0,0,1,0,1
0,1,1,0,0,0,0,0,1,1
0,1,0,1,0,1,0,0,0,1
0,1,0,1,0,0,1,0,0,1
0,1,0,0,1,0,1,0,0,1
0,0,1,0,1,0,1,0,0,1
1,0,0,0,0,0,0,0,0,0
1,1,0,0,0,0,0,0,0,0
1,0,1,0,0,0,0,0,0,0
1,1,1,0,0,0,0,0,0,1
1,1,0,1,0,0,0,0,0,1
1,1,0,0,1,0,0,0,0,1
1,1,0,0,0,1,0,0,0,0
1,0,1,0,1,0,0,0,0,1
1,0,1,0,0,0,1,0,0,1
1,1,1,1,0,0,0,0,0,1
1,1,1,0,1,0,0,0,0,1
1,1,1,0,0,1,0,0,0,1
1,1,1,0,0,0,1,0,0,1
1,1,1,0,0,0,0,1,0,1
1,1,1,0,0,0,0,0,1,1
1,1,0,1,0,1,0,0,0,1
1,1,0,1,0,0,1,0,0,1
1,1,0,0,1,0,1,0,0,1
1,0,1,0,1,0,1,0,0,1
1,1,1,1,1,0,0,0,0,0
1,1,1,1,0,1,0,0,0,0
1,1,1,1,0,0,1,0,0,1
1,1,1,0,1,1,0,0,0,0
1,1,1,0,1,0,1,0,0,0
1,1,1,0,1,0,0,1,0,0
1,1,1,0,1,0,0,0,1,0
1,1,1,0,0,1,1,0,0,0
1,1,1,0,0,1,0,1,0,0
1,1,1,0,0,1,0,0,1,0
1,1,1,0,0,0,1,1,0,0
1,1,0,1,0,1,0,1,0,0
1,0,1,0,1,0,1,0,1,0
1,0,0,0,1,1,1,1,1,0
1,0,0,1,0,1,1,1,1,0
1,0,0,1,1,0,1,1,1,0
1,0,0,1,1,1,0,1,1,0
1,0,0,1,1,1,1,0,1,0
1,0,0,1,1,1,1,1,0,0
1,0,1,0,1,0,1,1,1,0
1,0,1,0,1,1,0,1,1,0
1,0,1,1,0,1,0,1,1,0
1,1,0,1,0,1,0,1,1,0
1,0,0,1,1,1,1,1,1,0
1,0,1,0,1,1,1,1,1,0
1,0,1,1,0,1,1,1,1,0
1,0,1,1,1,0,1,1,1,0
1,1,0,1,0,1,1,1,1,0
1,1,0,1,1,1,0,1,1,0
1,0,1,1,1,1,1,1,1,0
1,1,0,1,1,1,1,1,1,0
1,1,1,1,1,1,1,1,1,0
Life/Syntheses/two-glider-collisions.rle is definitely worth checking out in all of these Life variants.

This particular one has, from left to right, a c/5 orthogonal spaceship (the T-tetromino), which because of its simplicity has several two-glider syntheses; a c/4 diagonal glide-reflective ship which isn't the 'standard' glider; a sparky p160 (40*4) rotating oscillator with a two-glider-synthesis; a p4 oscillator (the cap) with a 2-glider synthesis; and various interesting T-tetromino ship/standard glider collisions.
edit: starting to look for interesting stuff with the alternative c/4d glider. Here's a potential sawtooth base if backrakes are ever constructed in this rule:
x = 72, y = 68, rule = tlife
69b2o$68bo$69b2o$70b2o4$62b2o$61bo$62b2o$63b2o4$55b2o$54bo$55b2o$56b2o
4$48b2o$47bo$48b2o$49b2o4$41b2o$40bo$41b2o$42b2o4$34b2o$33bo$34b2o$35b
2o4$27b2o$26bo$27b2o$28b2o4$20b2o$19bo$20b2o$21b2o4$13b2o$12bo$13b2o$
14b2o6$2o$obo$bo!

its shape is simple enough to be eaten by a block:
x = 4, y = 9, rule = tlife
o$2obo$bobo$2bo4$2o$2o!

Eaters 1 and 2 function as normal. The loaf-flipping reaction works, but the rest of the Eater 3's stator needs some reimagining... the Eater 4 self-destructs, and eater 5 (twit) works as a still-life, but both of its glider-eating reactions cause it to self-destruct. The boat-bit reaction almost works, but the pre-boat instead evolves into a pond, destroying whatever still-life triggered the reaction.

None of the 'standard' life methuselahs work in this rule; the R-pentomino is a mango predecessor, the pi is a beehive predecessor, the B works for a bit but never gets to the Herschel stage, and the Herschel dies out in 17 generations.

EDIT: Okay, did not expect that.
x = 6, y = 7, rule = tlife
2o$2o$3b2o$3b3o$3b2o$2o$2o!
gamer54657 wrote:God save us all.
God save humanity.

hgkhjfgh

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Re: Close life variants

Postby BlinkerSpawn » September 10th, 2015, 5:24 pm

The two transitions are:
110
110
001 is survival, and

010
010
010 is death.

EDIT: Interesting way to place blocks anywhere in eleven gliders:
x = 165, y = 71, rule = tlife
162bo$162bobo$162b2o2$2bo$obo$b2o34$29bobo$30b2o$30bo2$134bo$133bo$
133b3o$46bo67bo$26bo20bo65bo$27bo17b3o65b3o$25b3o2$106bo$51bo54bobo$
52bo53b2o$50b3o9$92bo$92bobo$92b2o2$37bo$38bo$36b3o!

5G synth of the other c/4 diagonal:
x = 44, y = 40, rule = tlife
24bo$24bobo$24b2o5$2bo$3bo$b3o3$b2o$obo$2bo11$23b3o$23bo$24bo10$41b3o$
41bo$42bo!

And syntheses of bun-on-bun and honeycomb discovered while searching for the above one-glider cleanup:
x = 144, y = 62, rule = tlife
26bo$27bo$25b3o5$70bo21bo17bo$71bo18bobo17bobo$69b3o19b2o17b2o3$78bo$
77bobo$77bo2bo$78b2o19b2ob2o$98bobobobo$98bobobobo$41bo57bo3bo34bo3bo$
40bobo94bobobobo$39b2o96bobobobo$40bo97b2ob2o$99bo3bo$98bobobobo$98bob
obobo28bo$99b2ob2o29b2o$132bobo$31bo$30b3o$33bo$32bo29$3o$2bo$bo!
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

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Re: Close life variants

Postby M. I. Wright » September 10th, 2015, 8:36 pm

I started this post before your edits; you've covered some of the things I've written, but I'll leave it as it's still relevant.
First, though, the alternative c/4 can be made in four gliders from two directions:
#C the last two gliders can come in at any time after the pre-beehive forms,
#C and there are multiple placements for the rightmost glider (the synthesis works if it's
#C not there, but leaves some junk behind)
x = 16, y = 18, rule = tlife
3bo$3bobo$3b2o8bo$13bobo$13b2o2$2bo$bo$b3o7$bo$2o$obo!

And the arbitrarily-distant-block thing is really neat - was the placement of the two blocks for the c/2 synthesis just a lucky find? It takes only nine gliders, by the way.
x = 111, y = 31, rule = tlife
6bobo$7b2o$7bo$109bo$108bo$108b3o2$bo21bo67bo$2bo21bo65bo$3o19b3o65b3o
3$83bo$28bo54bobo$29bo53b2o$27b3o9$69bo$69bobo$69b2o2$14bo$15bo$13b3o!
What defines 'glider', though? It's entirely possible that there may be a gun for the 'alternative' glider (or, even more likely, for the T-tetromino) and not the 'regular' one.

The original post:
Thanks- I should've figured that out on my own, actually (blinker doesn't work and the pre-boat evolves into a pre-pond)

The fleet is the only one of Life's familiar fours that works here, but this honeyfarm predecessor becomes a different group of four (technically two) still-lives:
x = 7, y = 4, rule = tlife
3bo$b2ob2o2$o5bo!

The pattern is actually a failed 2D replicator - at generation 5, two copies of the pattern (both rotated 90 degrees) are visible, but they share the same sparks. At generation 10 four partial copies can be seen, and it evolves into its final form (two pairs of inducting buns) at generation 15.

As can be seen in the queen bee ship (although the word 'queen bee' is meaningless since it doesn't lay beehives...) the idea behind the xWSS and B-heptomino's forward growth still works - and the B-heptomino still travels a reasonable distance, in addition to plenty of modified Bs with varying reach - which leads me to believe that B conduits could be constructed in this rule, although Life's conduits obviously wouldn't work.

Lots of uncommon Life still-lifes are fairly common here: first off, since the R pentomino is a mango predecessor, the mango appears in almost every soup. There's also the 'super beehive', which the common triangle/phi spark evolves into (I've heard it called a "honeycomb", which makes no sense because it's bigger than a beehive, whereas in real life a honeycomb is part of and therefore smaller than a beehive... I'd call it a 'wasp nest' or something to do with those huge Cicada killers), and this extension of it:
x = 6, y = 6, rule = tlife
2b2o$bo2bo$ob2obo$ob2obo$bo2bo$2b2o!


lastly, demotion from 'alt' glider to 'regular' glider:
x = 5, y = 11, rule = tlife
o$2o$o5$2bo$bobo$bob2o$4bo!

It doesn't even miss a beat - the shape keeps on moving throughout the conversion!

I think one of the c/4d gliders should be named the 'ant' (in a Numberphile video, Conway said that he'd wishes he'd given that name to his glider); should the T be named or just called the 'T' or 'T glider'?

EDIT: I could've sworn that I'd seen some periodic TL factories in Life (as in, ones that create a T-tetromino and, if it's cleared out of the way before the next cycle, create another one in the same spot) - if I'm not misremembering, there might be a chance that a T gun could be made.
Last edited by M. I. Wright on September 10th, 2015, 9:11 pm, edited 1 time in total.
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Re: Close life variants

Postby BlinkerSpawn » September 10th, 2015, 8:58 pm

Better honeycomb synth:
x = 17, y = 30, rule = tlife
10bobo$10b2o$bo9bo$o$3o5$2b3o$2bo$3bo16$14b2o$14bobo$14bo!

And loaf siamese loaf from bun-on-bun:
x = 51, y = 23, rule = tlife
48bobo$48b2o$49bo17$obo4bo3bo$b2o3bobobobo$bo4bobobobo$7b2ob2o!
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Re: Close life variants

Postby M. I. Wright » September 10th, 2015, 9:23 pm

That honeycomb synthesis is clever - I'd noticed the relationship between it and the oscillator, but I didn't think it could lead to anything.

Another demotion, this time with the p160 oscillator:
x = 15, y = 10, rule = tlife
2bo$b3o$o$bo3$13bo$12bobo$11b2obo$11bo!


I wanted to see what could be done with the alt glider, so a DEC3 (easy/trivial; it can shift a block 3 spaces orthogonally), a clunky INC1 and a possible lead for a FIRE salvo:
x = 99, y = 40, rule = tlife
2o16b2o44b2o$2o16b2o44b2o4$31b2o44b2o$30b2o44b2o$29bo45bo$30b2o44b2o2$
10b2o14b2o44b2o$9b2o14b2o44b2o$8bo15bo10bo34bo$9b2o14b2o6b2obo34b2o$
33b2o$16bo16b2o$15bobo$14b2obo$14bo2$88b2o$87b2o$86bo$87b2o4$43b3o$43b
3o$42bo$43bo3$56b2o$55b2o40b2o$54bo41b2o$55b2o5b2o31bo$61b2o33b2o$60bo
$61b2o!


And you only need one glider to destroy a bun-on-bun.

3G synth of alife's bookend ship:
x = 41, y = 44, rule = alife
39bo$38bo$38b3o29$2bo$bo$b3o8$2o$obo$o!
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Re: Close life variants

Postby A for awesome » September 10th, 2015, 10:30 pm

Another alt-glider eater:
x = 10, y = 14, rule = tlife
4bo$bob2o3b2o$bobo3bobo$2bo5bo3$b2o$obo$2o2$3b2o$3bo$4b3o$6bo!

There's a BTS-based almost-eater, too:
x = 13, y = 13, rule = tlife
9bo$8bobo$8bobo$6b2obo$3bo3bo$ob2o3bo$obo2bob2o$bo3b2o2bo$8bobobo$5b3o
bob2o$6bo2bo$4bo3b2o$4b2o!

The BTS stator has to be heavily modified to work in this rule; it also loses most of its other functionality. Here's an actual eating reaction involving it:
x = 11, y = 13, rule = tlife
7bo$6bobo$o5bobo$o3b2obo$bo3bo$2o3bo$o2bob2o$3b2o2bo$6bobobo$3b3obob2o
$4bo2bo$2bo3b2o$2b2o!

Nothing that a simple boat can't do, anyway. I think the BTS is pretty much useless in this rule.
Edit: A normal glider reflects a c/5:
x = 6, y = 8, rule = tlife
bo$obo2$3o2$3b3o$3bo$4bo!

One-time 45-degree reflector:
x = 6, y = 8, rule = tlife
4bo$3bobo$3b2o2$2bo$bobo$2obo$o!
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

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Re: Close life variants

Postby gmc_nxtman » September 11th, 2015, 10:32 am

P8 wick in tlife:

x = 3, y = 37, rule = tlife
bo$3o4$3o$bo4$bo$3o4$3o$bo4$bo$3o4$3o$bo4$bo$3o4$3o$bo!


2-glider synth of mango:

x = 3, y = 7, rule = tlife
bo$o$3o2$bo$2o$obo!


Can someone make a rule where cells die on 2 opposing neighbors, and cells survive in the following configuration?

1,1,0,1,1,1,0,0,0,1


Every time I do it, it ends up not working.... There's probably something really simple that I'm missing..

@RULE hlife
@TABLE

n_states:2
neighborhood:Moore
symmetries:rotate8reflect
#Death on 0 Neighbors
1,0,0,0,0,0,0,0,0,0
#Death on 1 Neighbor
1,1,0,0,0,0,0,0,0,0
1,0,1,0,0,0,0,0,0,0
#Death on 2 Neighbors
0,0,0,0,1,1,0,0,0,0
#Death on 4 neighbors
1,1,1,1,0,0,0,1,0,0
1,1,0,1,0,0,1,0,1,0
1,0,1,0,1,1,0,1,0,0
1,1,1,1,0,0,1,0,0,0
1,1,1,0,0,0,0,1,1,0
1,1,1,0,0,1,0,0,1,0
1,1,1,0,0,1,0,1,0,0
1,1,1,1,0,1,0,0,0,0
1,1,1,0,1,1,0,0,0,0
1,1,1,0,0,1,1,0,0,0
1,0,1,1,0,1,1,0,0,0
#Death on 5 neighbors
1,1,1,1,1,0,0,1,0,0
1,0,1,1,1,1,0,0,0,0
1,1,1,1,1,0,1,0,0,0
1,0,1,1,1,0,1,0,1,0
1,1,1,0,1,1,0,1,0,0
1,1,1,1,1,0,0,0,1,0
1,0,1,0,1,1,1,0,1,0
1,1,1,0,1,0,1,1,0,0
1,0,1,1,0,0,1,1,1,0
#Death on 6 Neighbors
1,0,1,1,1,1,1,1,0,0
1,1,1,1,1,1,0,1,0,0
1,1,1,1,1,0,1,0,1,0
1,1,1,0,1,1,1,0,1,0
1,1,1,1,1,1,1,0,0,0
1,1,1,1,0,0,1,1,1,0
#Death on 7 Neighbors
1,1,1,1,1,1,1,0,1,0
1,1,1,1,1,1,1,1,0,0
#Death on 8 Neighbors
1,1,1,1,1,1,1,1,1,0
#Birth on 3 Neighbors
0,1,1,1,0,0,0,0,0,1
0,0,1,0,1,0,0,0,1,1
0,0,1,0,1,1,0,0,0,1
0,1,0,0,1,0,0,1,0,1
0,1,0,1,0,0,0,0,1,1
0,1,0,1,0,0,0,1,0,1
0,1,1,0,1,0,0,0,0,1
0,0,0,0,1,0,1,0,1,1
0,1,0,0,1,1,0,0,0,1
0,1,0,0,1,0,0,0,1,1
#Birth on 8 Neighbors
1,1,1,1,1,1,1,1,1,1

@COLORS
0  48  48  48
1 255 255   0
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Re: Close life variants

Postby M. I. Wright » September 11th, 2015, 10:58 pm

This works, right? (the extra transitions were just awkwardly tacked onto c0b0p0's alife rule, so it's not optimal)

@RULE hlife2
@TABLE

n_states:2
neighborhood:Moore
symmetries:rotate8reflect

var a={0,1}
var b={a}
var c={a}
var d={a}
var e={a}
0,1,1,1,0,0,0,0,0,1
0,1,0,1,1,0,0,0,0,1
0,0,0,1,1,0,0,1,0,1
0,0,1,0,0,1,0,0,1,1
0,1,0,1,0,0,0,1,0,1
1,0,0,0,0,0,0,0,0,0
1,1,0,0,0,0,0,0,0,0
1,1,0,0,0,1,0,0,0,0
1,1,0,1,1,1,0,0,0,1
1,0,1,1,0,1,1,0,0,0
1,1,a,1,b,1,c,1,d,0
1,1,a,1,b,1,c,d,1,0
1,1,1,1,a,1,b,c,d,0
1,a,1,1,1,b,c,1,d,0
1,1,1,1,1,a,b,c,d,0
1,a,1,1,b,1,c,d,1,0
1,1,1,a,b,1,1,c,d,0


It loses the cool LoM almost-replicator in your rule, unfortunately, AND it's explosive - but two-glider-syntheses.rle is still pretty interesting. For starters, it has two kickback-like reactions, one of which is a heisenburp:
x = 20, y = 12, rule = hlife2
18bo$bo15bo$o16b3o$3o5$15bo$4b3o7b2o$4bo9bobo$5bo!

It also has the c/5 t-tetromino glider, and the queen bee's blocks are pretty common to see (two blocks spaced 3 cells apart orthogonally); the R-pentomino becomes a pi which in turn evolves into said blocks, meaning that the pair has multiple 2-glider-syntheses. Unlike in tlife, though, hitting it with a T makes a p10 flipper instead of a spaceship:
x = 7, y = 8, rule = hlife2
2b3o$3bo5$2o3b2o$2o3b2o!


it also has this interesting infinitely-extensible glider arrangement:
x = 27, y = 39, rule = hlife2
o$b2o$2o4$4bo$5b2o$4b2o$bobo$2b2o$2bo3$12bo$13b2o$12b2o$9bobo$9b3o$7b
2obo$8b2o$7b2o$4bobo$5b2o17bo$5bo19b2o$24b2o$21bobo$21b3o$19b2obo$20b
2o$19b2o$16bobo$16b3o$14b2obo$15b2o$14b2o$11bobo$12b2o$12bo!
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Re: Close life variants

Postby gmc_nxtman » September 11th, 2015, 11:02 pm

It's nice, although it doesn't work the way I supposed it to.

x = 3, y = 2, rule = B3/S23
3o$obo!


The center cell should survive there.

Anyways,

2-glider synthesis of a ship:

x = 8, y = 14, rule = hlife2
6bo$5bo$5b3o9$2o$b2o$o!


I think that the following rule has some interest: (B2o3/S2!o3)

@RULE olife
@TABLE

n_states:2
neighborhood:Moore
symmetries:rotate8

var s={0,1}
var t={0,1}
var u={0,1}
var v={0,1}
var w={0,1}
var x={0,1}
var y={0,1}
var z={0,1}


1,1,1,1,0,0,0,0,0,1
1,1,1,0,1,0,0,0,0,1
1,1,1,0,0,1,0,0,0,1
1,1,1,0,0,0,1,0,0,1
1,1,1,0,0,0,0,1,0,1
1,1,0,1,0,1,0,0,0,1
1,1,0,1,0,0,1,0,0,1

1,1,1,0,0,0,0,0,0,1
1,1,0,1,0,0,0,0,0,1
1,1,0,0,1,0,0,0,0,1

0,1,0,0,0,1,0,0,0,1
0,1,1,1,0,0,0,0,0,1
0,1,1,0,1,0,0,0,0,1
0,1,1,0,0,1,0,0,0,1
0,1,1,0,0,0,1,0,0,1
0,1,1,0,0,0,0,1,0,1
0,1,0,1,0,1,0,0,0,1
0,1,0,1,0,0,1,0,0,1

1,s,t,u,v,w,x,y,z,0

@COLORS
0   0   0   0 black
1 255 255 255 white


x = 41, y = 15, rule = olife
12bo15bo$11bo15bo11bo$11b3o13b3o8bo$38b3o5$3o$2bo$bo$17b2o$16bobo13b2o
$18bo14b2o$32bo!


I'm sure this rule could be explored even more.

By the way, why isn't b5 happening in this rule?

@RULE FalseB5
@TABLE

n_states:2
neighborhood:Moore
symmetries:rotate8reflect
0,1,1,1,0,0,0,0,0,1
0,1,0,1,0,0,0,1,0,1
0,1,0,1,0,0,1,0,0,1
0,0,0,1,0,1,0,1,0,1
0,1,1,0,0,0,0,1,0,1
0,1,1,0,0,0,1,0,0,1
0,1,1,1,0,0,0,0,0,1
0,0,1,1,0,0,1,0,0,1
0,0,1,0,1,1,1,0,1,1
1,0,0,0,0,0,0,0,0,0
1,1,0,0,0,0,0,0,0,0
1,0,1,0,0,0,0,0,0,0
1,1,1,1,0,1,0,0,0,0
1,1,1,0,1,1,0,0,0,0
1,1,1,1,0,0,0,1,0,0
1,0,1,1,1,0,1,0,0,0
1,0,1,0,1,1,1,0,0,0
1,0,1,0,1,0,1,0,1,0
1,0,0,1,1,0,1,1,0,0
1,0,0,0,1,1,1,0,1,0
1,0,0,1,1,1,1,0,0,0
1,0,1,0,1,1,0,1,0,0
1,1,0,1,0,0,1,0,1,0
1,1,0,1,1,0,1,0,0,0
1,1,1,0,1,1,1,0,0,0
1,1,1,0,1,0,1,0,1,0
1,1,1,1,1,0,1,0,0,0
1,0,1,1,1,0,1,0,1,0
1,0,1,0,1,1,1,1,0,0
1,1,1,0,1,1,0,0,1,0
1,0,1,1,1,0,0,1,1,0
1,1,1,1,1,1,0,0,0,0
1,1,0,1,1,1,0,0,1,0
1,1,0,1,1,0,1,0,1,0
1,0,1,1,1,1,1,1,0,0
1,1,1,1,0,0,1,1,1,0
1,1,1,1,1,1,1,0,0,0
1,1,1,0,1,1,1,0,1,0
1,1,1,1,1,0,1,0,1,0
1,1,1,1,1,1,0,1,0,0
1,1,1,1,1,1,1,1,0,0
1,1,1,1,1,1,1,0,1,0

@COLORS
0  48  48  48
1   0 255   0


EDIT: A small pattern that emits a LWSS in klife:

x = 8, y = 6, rule = klife
5bo$5bobo$bo3bo$obo$3o$2o!


By the way, I just want a rule where the hat is a c/3 spaceship. (B5 in certain positions would be sufficient)
Last edited by gmc_nxtman on September 11th, 2015, 11:40 pm, edited 1 time in total.
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Re: Close life variants

Postby M. I. Wright » September 11th, 2015, 11:33 pm

Hm, olife seems a bit bland to me... here are a few things, though:
x = 29, y = 10, rule = olife
11b2o$11b2o$2b2o23b2o$2b2o11bo10bobo$2o12b3o9b2o$2o3$24bo$23b3o!


as for b5: it is happening - you just didn't account for every possible arrangement of 5 neighbors.
x = 18, y = 11, rule = FalseB5
2o3bobo$obo2bo$bo3bobo6$2o3b3o2b2o3b2o$o9bo4bobo$b2o3b2o2bobo2bo!


--

here are some syntheses in tlife. The first one wouldn't work from infinity, but it shouldn't be hard to put the oscillator predecessor there some other way:
x = 205, y = 49, rule = tlife
168bo$123bo44bobo$122bo45b2o$122b3o9$38bo3b2o$38b2ob2o$37bobo3bo11bobo
$56b2o$46bo9bo80bo$46bo91bo22bo$45b3o8b2o78b3o20b2o$55bobo102b2o$57bo$
48bo$48b3o106bo$48bo106b2o$85bo70b2o$86bo22bo37bobo$84b3o20b2o39b2o$
108b2o38bo2$34b2o$33bobo69bo$35bo67b2o$104b2o$95bobo$96b2o$96bo5$o3bo
3bo3bo3bo2bobobo7bo4bobobo5bo3bo3bo3bo3bo2bobobo23bobo3bo45bobo4bo3bo
2bobobo2bobobo2bobobo2bobo4bobobo2bo5bo3bo$184bo$o3bo3bo3bo3bo2bo10bob
o5bo7bo3bo3bo3bo3bo2bo26bo6bo45bo3bo2bo3bo4bo6bo4bo6bo6bo6bo5bo3bo$
184bo$obobo3bo3bo3bo2bobobo5bo3bo4bo7bobobo3bo3bo3bo2bobobo23bobo3bo
45bobo4bo3bo4bo6bo4bobobo2bobo4bobobo2bo7bo2$o3bo3bo4bobo3bo9bobobo4bo
7bo3bo3bo4bobo3bo30bo2bo45bo3bo2bo3bo4bo6bo4bo6bo2bo3bo6bo7bo2$o3bo3bo
5bo4bobobo5bo3bo4bo7bo3bo3bo5bo4bobobo23bobo3bobobo41bobo5bobo5bo6bo4b
obobo2bo3bo2bo6bobobo3bo!

The third one is interesting because, first off, the teardrop pattern dies out in tlife. The butterfly, however, evolves into a later generation of the teardrop and ends up creating the teardrop's beehives; this synthesis in turn evolves into a later generation of the butterfly, eventually creating the butterfly's beehives!

And some interesting reactions -
x = 51, y = 24, rule = tlife
42b3o3b3o$43bo5bo9$2o3b2o2$o5bo$b2ob2o$2b3o$19b3o3b3o14b3o3b3o$20bo5bo
16bo5bo5$bo3bo14b2o3b2o16b2o3b2o$obobobo12bo2bobo2bo15b2o3b2o$bo3bo14b
2o3b2o!

From left to right: c/2 eater (any equivalent SL works, of course), two-T salvo pushing two beehives one cell, and two slow two-T salvos pulling two blocks by two cells, creating long hook-on-long hook in the process.

Lastly, a two-stage 'double glider' eater in hlife2:
x = 17, y = 19, rule = hlife2
3bo$4b2o$3b2o$obo$b2o$bo6$14bo$15b2o$14b2o$11bobo$12b2o$12bo$15b2o$15b
2o!


EDIT: can you draw the three phases of the hat spaceship? I'm having trouble visualizing it.
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Re: Close life variants

Postby M. I. Wright » September 11th, 2015, 11:57 pm

Oh, I see what you meant by '1,1,0,1,1,1,0,0,0,1' - the problem with it is that the numbers go like this:
0,1,2,3,4,5,6,7,8,9

8,1,2
7,0,3
6,5,4

and not
0,1,2,3,4,5,6,7,8,9

1,2,3,
8,0,4
7,6,5

so 1,1,0,1,1,1,0,0,0,1 means that a cell survives on
1,0,1
0,1,1
0,0,1

The correct transition would be 1,0,1,1,0,0,0,1,1,1. Here's the correct ruletable (right?):
@RULE hlife3
@TABLE

n_states:2
neighborhood:Moore
symmetries:rotate8reflect

var a={0,1}
var b={a}
var c={a}
var d={a}
var e={a}
0,1,1,1,0,0,0,0,0,1
0,1,0,1,1,0,0,0,0,1
0,0,0,1,1,0,0,1,0,1
0,0,1,0,0,1,0,0,1,1
0,1,0,1,0,0,0,1,0,1
1,0,0,0,0,0,0,0,0,0
1,1,0,0,0,0,0,0,0,0
1,1,0,0,0,1,0,0,0,0
1,0,1,1,0,0,0,1,1,1
1,0,1,1,0,1,1,0,0,0
1,1,a,1,b,1,c,1,d,0
1,1,a,1,b,1,c,d,1,0
1,1,1,1,a,1,b,c,d,0
1,a,1,1,1,b,c,1,d,0
1,1,1,1,1,a,b,c,d,0
1,a,1,1,b,1,c,d,1,0
1,1,1,a,b,1,1,c,d,0

It's not explosive, still has the c/5o glider, and check out what the R-pentomino does:
x = 3, y = 3, rule = hlife3
bo$2o$b2o!
Last edited by M. I. Wright on September 11th, 2015, 11:59 pm, edited 1 time in total.
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Re: Close life variants

Postby gmc_nxtman » September 11th, 2015, 11:58 pm

Here's a p10 oscillator that may have been posted before:

x = 7, y = 4, rule = olife
2o3b2o$2b3o$2bobo$3bo!


Here's the hat spaceship:

x = 4, y = 5, rule = hlife3
3bo$2obo$o$2obo$3bo!


So I guess the R-pentomino is a c/14 diagonal glider?

x = 3, y = 3, rule = hlife3
2bo$3o$bo!
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Re: Close life variants

Postby M. I. Wright » September 12th, 2015, 12:02 am

That was the flipper I mentioned earlier. Is hlife3 correct?

It also seems a bit bland, although the R glider is all sorts of cool.
x = 21, y = 11, rule = hlife3
13b2o$13bobo$2bo11bo4b2o$2b2o14bobo$2bo16bo5$2o$2o!


edit: ohh, I see what you meant by the hat spaceship - but didn't you want a c/3 ship?
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Re: Close life variants

Postby gmc_nxtman » September 12th, 2015, 12:04 am

The "capped p4" works, and a small p4 flipper:

x = 12, y = 5, rule = hlife3
2b3o3bo2bo$3b2o3bo2bo$2o2bo3bo2bo$2bo6b2o$2bo!


An alternate p4:

x = 5, y = 5, rule = hlife3
2bo$2bo$2b3o$2o$2o!


EDIT: There's probably a grammar for these small p4's:

x = 5, y = 5, rule = hlife3
2b3o$2b3o$2ob2o$3o$3o!


Small wasp nest predecessor:

x = 4, y = 6, rule = hlife3
o$2bo$2bo$2b2o$2bo$bo!


2G synth of the R-ship:

x = 5, y = 7, rule = hlife3
2bo$2bobo$2b2o2$bo$b2o$obo!


And yes, I did want a c/3 one, although hlife3 is still pretty cool :wink:
Last edited by gmc_nxtman on October 28th, 2015, 9:05 pm, edited 5 times in total.
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Re: Close life variants

Postby BlinkerSpawn » September 12th, 2015, 12:04 am

M. I. Wright wrote:here are some syntheses in tlife. The first one wouldn't work from infinity, but it shouldn't be hard to put the oscillator predecessor there some other way:
RLE


Save yourself at least five gliders by not dealing with oscillators:
x = 13, y = 13, rule = tlife
6bo$4bobo4bo$5b2o3bo$10b3o$bo$2bo$3o4$2b2o$bobo$3bo!
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

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Re: Close life variants

Postby M. I. Wright » September 12th, 2015, 12:09 am

M. I. Wright wrote:It also seems a bit bland,

I retract that, this rule is neat. How would the c/3 ship have worked?

(that synthesis should've been obvious, BlinkerSpawn; thanks ;))

here's an interesting rule (I feel like we should give them more creative names...)
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Re: Close life variants

Postby BlinkerSpawn » September 12th, 2015, 10:41 pm

Well...
x = 5, y = 17, rule = tlife
2bo$2b2o$obo$bo10$3bo$2bobo$b2o$2bo!
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