## Live Free or Die

For discussion of other cellular automata.
fsrm
Posts: 135
Joined: February 22nd, 2016, 6:23 am

### Re: Live Free or Die

An interesting collision:

Code: Select all

x = 33, y = 5, rule = B2/S0
32bo$o30bo$bo29bo$bo30bo$o!


blah
Posts: 249
Joined: April 9th, 2016, 7:22 pm

### Re: Live Free or Die

Sorry if this isn't noteworthy: another one-time collision that results in 180 rotation. This one returns the moon on its original lane.

Code: Select all

x = 8, y = 7, rule = B2/S0
5bo3$o6bo$bo$bo$o4bo!

it's a stabilisation of the more obvious partial involving only one dot:

Code: Select all

x = 6, y = 4, rule = B2/S0
o$bo$bo$o4bo!  succ Naszvadi Posts: 543 Joined: May 7th, 2016, 8:53 am Contact: ### Re: Live Free or Die Just for being tracked: http://conwaylife.com/forums/viewtopic.php?f=11&t=2190 Who are the first discoverers to be included in lfod wiki? wildmyron Posts: 1371 Joined: August 9th, 2013, 12:45 am ### Re: Live Free or Die I have a backlog of results for LFoD which I hope to get around to posting some day, but one avenue of exploration which I had on the back-burner for some time has finally borne fruit: a surprisingly small p5 gun for the moon. Code: Select all #N Quintuple Pump #C A double barreled p5 gun for the moon in Live Free or Die #O Arie Paap, 9 Aug 2016 x = 19, y = 46, rule = B2/S0 7bo3bo$6b3ob3o$2bo2bo7bo2bo2$bo5bo3bo5bo$2o2bo2bobobo2bo2b2o$3bo4b3o4b
o$bobo4bobo4bobo$4bo9bo2$o17bo$2bo13bo$3b2o3bobo3b2o$4bo9bo$2bo2bo7bo 2bo$b2o4b5o4b2o$2b3o9b3o2$7b5o$9bo2$4bo4bo4bo$3bo4b3o4bo$3bo4b3o4bo$4b o4bo4bo2$9bo$7b5o2$2b3o9b3o$b2o4b5o4b2o$2bo2bo7bo2bo$4bo9bo$3b2o3bobo
3b2o$2bo13bo$o17bo2$4bo9bo$bobo4bobo4bobo$3bo4b3o4bo$2o2bo2bobobo2bo2b
2o$bo5bo3bo5bo2$2bo2bo7bo2bo$6b3ob3o$7bo3bo!
The stabilisation for the central mechanism actually comes from something I found while exploring supports for a p5 wick. I had been trying to extend wider partials to support the gun for quite some time when one of my searches came across a possible connection to the wick and then the connection jumped out at me.

Code: Select all

x = 101, y = 19, rule = B2/S0
5bo4bo32bo13bo32bo4bo$4b2obo7bo26b3o11b3o26bo7bob2o$2bo8bo2b3o14bo10bo
bo5bo5bobo10bo14b3o2bo8bo$6b2o4bo3bo11bo8bo4b3o4b3o4b3o4bo8bo11bo3bo4b 2o$5bo2bo3b2o2bo19b2o5bo5bobo5bo5b2o19bo2b2o3bo2bo$2bo11bo13bo7b2o11b 3o11b2o7bo13bo11bo$bo25b3o5b2o13bo13b2o5b3o25bo$2o2b2o9bo2bo5bo3bo5b2o 29b2o5bo3bo5bo2bo9b2o2b2o$bo4b2o4bo2bo2bo5bo4bobobobo29bobobobo4bo5bo
2bo2bo4b2o4bo$5b2o8bo2b2obob2obo11bo23bo11bob2obob2o2bo8b2o$bo4b2o4bo
2bo2bo5bo4bobobobo29bobobobo4bo5bo2bo2bo4b2o4bo$2o2b2o9bo2bo5bo3bo5b2o 29b2o5bo3bo5bo2bo9b2o2b2o$bo25b3o5b2o13bo13b2o5b3o25bo$2bo11bo13bo7b2o 11b3o11b2o7bo13bo11bo$5bo2bo3b2o2bo19b2o5bo5bobo5bo5b2o19bo2b2o3bo2bo$6b2o4bo3bo11bo8bo4b3o4b3o4b3o4bo8bo11bo3bo4b2o$2bo8bo2b3o14bo10bobo5bo
5bobo10bo14b3o2bo8bo$4b2obo7bo26b3o11b3o26bo7bob2o$5bo4bo32bo13bo32bo
4bo!
This suggests a nice p5 oscillator I called Bow Tie, though the name's probably a bit generic.

Code: Select all

x = 43, y = 19, rule = B2/S0
10bo21bo$3bo3bo2b2o19b2o2bo3bo$2b3o3bo3b2o3bo7bo3b2o3bo3b3o$5bo2bo25bo 2bo$11bo2bo2bo7bo2bo2bo$bo10bo2bo11bo2bo10bo$3b3o8b2o11b2o8b3o$7bo6bob 2obo3bob2obo6bo$2bo9bo7bobo7bo9bo$3o5bo2b3o6b3o6b3o2bo5b3o$2bo9bo7bobo
7bo9bo$7bo6bob2obo3bob2obo6bo$3b3o8b2o11b2o8b3o$bo10bo2bo11bo2bo10bo$
11bo2bo2bo7bo2bo2bo$5bo2bo25bo2bo$2b3o3bo3b2o3bo7bo3b2o3bo3b3o$3bo3bo 2b2o19b2o2bo3bo$10bo21bo!
====
fsrm wrote:I found a 12c/12 sideways free ship rake:

Code: Select all

rle
That's quite a neat mechanism. One ship converts the dot to a checker and also contributes to the conversion from checker to freeship pair.
fsrm wrote:An interesting collision:

Code: Select all

x = 33, y = 5, rule = B2/S0
32bo$o30bo$bo29bo$bo30bo$o!

This reaction is in the LFoD Collection
blah wrote:Sorry if this isn't noteworthy: another one-time collision that results in 180 rotation. This one returns the moon on its original lane.

Code: Select all

x = 8, y = 7, rule = B2/S0
5bo3$o6bo$bo$bo$o4bo!

I think this is an interesting area of exploration. When the challenge to find a reflector was announced I did some searching in this area. Here's my collection of non-exploding moon + dot reactions:

Code: Select all

x = 131, y = 132, rule = B2/S0
3bo3bo3$o5bo$bo$bo$o5bo3bo3$3bo3$7bo3$4bo15$3bo3bo55bo3$o5bo53bo5bo3bo$bo59bo$bo59bo$o5bo3bo49bo5bo3$3bo59bo3bo21$3bo2bo3bo52bo59bo6bo$69bo 2$o6bo52bo59bo$bo8bo50bo59bo5bo2bo$bo59bo2bo56bo2bo$o6bo52bo9bo49bo$
130bo$10bo$4bo59bo2bo55bo21$3bo5bo54bo5bo$6bo60bo55bo2bo2bo2$o60bo58bo$bo5bo2bo51bo5bo52bo5bo2bo$bo60bo58bobo$o60bo58bo$8bo60bo57bo$124bo$5b o60bo$71bo55bo17$66bo3bo3$3bo5bo54bo5bo$6bo60bo2$o60bo$bo5bo54bo5bo2bo$bo60bo$o60bo$8bo60bo2$5bo60bo$71bo$63bo! The latest version of the 5S Project contains over 226,000 spaceships. There is also a GitHub mirror of the collection. Tabulated pages up to period 160 (out of date) are available on the LifeWiki. drc Posts: 1664 Joined: December 3rd, 2015, 4:11 pm Location: creating useless things in OCA ### Re: Live Free or Die Nice p5 gun! That's the second gun ever, and it's a new period. \100\97\110\105 testitemqlstudop Posts: 1336 Joined: July 21st, 2016, 11:45 am Location: in catagolue Contact: ### Re: Live Free or Die How many patterns evolve into a spacefiller/quad-growth pattern???? Code: Select all #CXRLE Pos=-73,-53 x = 20, y = 20, rule = B2/S0 8bo2bo$9b2o7$o18bo$bo16bo$bo16bo$o18bo7$9b2o$8bo2bo!

Posts: 1954
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

### Re: Live Free or Die

testitemqlstudop wrote:How many patterns evolve into a spacefiller/quad-growth pattern????

Code: Select all

#CXRLE Pos=-73,-53
x = 20, y = 20, rule = B2/S0
8bo2bo$9b2o7$o18bo$bo16bo$bo16bo$o18bo7$9b2o$8bo2bo! Almost all of them. LifeWiki: Like Wikipedia but with more spaceships. [citation needed] testitemqlstudop Posts: 1336 Joined: July 21st, 2016, 11:45 am Location: in catagolue Contact: ### Re: Live Free or Die I guess why that LFoD is an explosive rule wildmyron Posts: 1371 Joined: August 9th, 2013, 12:45 am ### Re: Live Free or Die Here's a smaller relative of the c/4 diagonal giraffe (same frontend, same backend, glide reflect symmetry, but different middle) - lets call it the short necked giraffe: Code: Select all x = 50, y = 51, rule = B2/S0 14bo$13bo$12bo$11bo2bo$15bo3$12bob2obo2$11bo$bobo6b2o3bo$o3bo11bo$10bo
7b2o$o16b4o$bo2bo5bo4bo2b2o$5bo12bo2b2o$9bo4b3o4bo$15bo4b3o2bo$10bobo
6bo$16b2o6bo6bobo$24bo$14b2o17bo$15b2o5bo9b2o$16bo10bo$25bo2bo3bo$17bo 2bo7bo$22bo9b2o$28b2obo$23bo4bo$23bo9bo$20bo20bo$23bo5b2o9bobo$22b2o9b
2o11bo$28bo3bob4o3bob3o$20bobo12bobo9bo$46b3o$36b2o3bobo4b2o$32bo6bo9b o$31b2o4bo2bo8bo$30b2obobo2b2o$29b2o14b3o$30bobo5bo7bo2$35bo$39bo$36bo
b3o$33bo3bo2bo$40bo2$36b3o$37bo!
The backend supports a number of extensible tagalongs:

Code: Select all

x = 56, y = 178, rule = B2/S0
11bo$9bobobo$10b3o$8b3o6bo$10bo6b2o$9bo7bo2$13b3o4bo$14bo4bo$18bo$3bo 13bo2bo$2bobo16bo$bob2o$2bo2bo$4b3o11bob2obo$3bo2bo$2b2o2bo10bo$3b5obo
6b2o3bo$6bo3bo11bo$16bo7b2o$6bo16b4o$7bo2bo5bo4bo2b2o$11bo12bo2b2o$15b
o4b3o4bo$21bo4b3o2bo$16bobo6bo$22b2o6bo6bobo$30bo$20b2o17bo$21b2o5bo9b
2o$22bo10bo$31bo2bo3bo$23bo2bo7bo$28bo9b2o$34b2obo$29bo4bo$29bo9bo$26b
o20bo$29bo5b2o9bobo$28b2o9b2o11bo$34bo3bob4o3bob3o$26bobo12bobo9bo$52b 3o$42b2o3bobo4b2o$38bo6bo9bo$37b2o4bo2bo8bo$36b2obobo2b2o$35b2o14b3o$36bobo5bo7bo2$41bo$45bo$42bob3o$39bo3bo2bo$46bo2$42b3o$43bo6$13bo$12bo
$11bo$10bo2bo$14bo5bo$19bo$18bo$3bobo11bo2bo$2bo3bo14bo2$2bo$3bo2bo11b ob2obo2$17bo$7bobo6b2o3bo$6bo3bo11bo$16bo7b2o$6bo16b4o$7bo2bo5bo4bo2b 2o$11bo12bo2b2o$15bo4b3o4bo$21bo4b3o2bo$16bobo6bo$22b2o6bo6bobo$30bo$
20b2o17bo$21b2o5bo9b2o$22bo10bo$31bo2bo3bo$23bo2bo7bo$28bo9b2o$34b2obo
$29bo4bo$29bo9bo$26bo20bo$29bo5b2o9bobo$28b2o9b2o11bo$34bo3bob4o3bob3o
$26bobo12bobo9bo$52b3o$42b2o3bobo4b2o$38bo6bo9bo$37b2o4bo2bo8bo$36b2ob
obo2b2o$35b2o14b3o$36bobo5bo7bo2$41bo$45bo$42bob3o$39bo3bo2bo$46bo2$
42b3o$43bo4$14bo$13bo$12bo$11bo2bo$15bo2$20bo$19bo$18bo$17bo2bo$bobo 17bo$o3bo2$o17bob2obo$bo2bo$17bo$7bobo6b2o3bo$6bo3bo11bo$16bo7b2o$6bo 16b4o$7bo2bo5bo4bo2b2o$11bo12bo2b2o$15bo4b3o4bo$21bo4b3o2bo$16bobo6bo$22b2o6bo6bobo$30bo$20b2o17bo$21b2o5bo9b2o$22bo10bo$31bo2bo3bo$23bo2bo 7bo$28bo9b2o$34b2obo$29bo4bo$29bo9bo$26bo20bo$29bo5b2o9bobo$28b2o9b2o
11bo$34bo3bob4o3bob3o$26bobo12bobo9bo$52b3o$42b2o3bobo4b2o$38bo6bo9bo$
37b2o4bo2bo8bo$36b2obobo2b2o$35b2o14b3o$36bobo5bo7bo2$41bo$45bo$42bob
3o$39bo3bo2bo$46bo2$42b3o$43bo!

Edit 2: another tagalong:

Code: Select all

x = 54, y = 55, rule = B2/S0
3bobo5bo$10bo$9bo$2b2o4bo2bo$12bo5bo$17bo$16bo$bobo11bo2bo$o3bo14bo2$o$bo2bo11bob2obo2$15bo$5bobo6b2o3bo$4bo3bo11bo$14bo7b2o$4bo16b4o$5bo2bo
5bo4bo2b2o$9bo12bo2b2o$13bo4b3o4bo$19bo4b3o2bo$14bobo6bo$20b2o6bo6bobo$28bo$18b2o17bo$19b2o5bo9b2o$20bo10bo$29bo2bo3bo$21bo2bo7bo$26bo9b2o$32b2obo$27bo4bo$27bo9bo$24bo20bo$27bo5b2o9bobo$26b2o9b2o11bo$32bo3bob 4o3bob3o$24bobo12bobo9bo$50b3o$40b2o3bobo4b2o$36bo6bo9bo$35b2o4bo2bo8b
o$34b2obobo2b2o$33b2o14b3o$34bobo5bo7bo2$39bo$43bo$40bob3o$37bo3bo2bo$
44bo2$40b3o$41bo!
The latest version of the 5S Project contains over 226,000 spaceships. There is also a GitHub mirror of the collection. Tabulated pages up to period 160 (out of date) are available on the LifeWiki.

A for awesome
Posts: 1997
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1
Contact:

### Re: Live Free or Die

Extensible c/4 diagonal pseudo-pushalong:

Code: Select all

x = 118, y = 102, rule = B2/S0
3b3o$4bo$4b2o2bo$o2bo20bo4bo$3o4bo13bo3b4o$obo4bo5bobo13bo$22bo2bo$4b 2o9bo5bo2bo5bobo$2bo5b2o4b2o3bobo2bo2bo5bo$8b2o11bo10b2o2bo$12bobo18bo
b3o$25bo8bo2bo$10bo9bo4b2o10bo$5bo13b2o4bo$8bobo9b2o11b3o$5bob2o12b3o 11b2o$32b2o$31b2o2bo$32b2obo4bobo$37bo$34bo7bo$41b2o$31bo$35b2o2bobo$
33bo$33bobo$34b2o$31bo2bobo2$45bo4bo4bo$36bo$35bo2bo3bo2bo$45bo6b2o5bo$40bobobo2bobo5b4o$37bob2o7b2obo$48bo14bo$49bo8bo4b2o$46bob3o6b2o4bo$47bo2bo7b2o$50bo8b3o2$46b3o$47bo13bo2$57b3o5bo3bo$58bo3bo$59bobo5bobo$
57b3o4bob2o$61bo$60bo$61bo2$59bo$57bob2o$59b2o14bo4bo$72bo3b4o$60bo3bo
bo13bo$61bo11bo2bo$66bo5bo2bo5bobo$65b2o3bobo2bo2bo5bo$72bo10b2o2bo$63bobo18bob3o$76bo8bo2bo$71bo4b2o10bo$70b2o4bo$71b2o11b3o$72b3o10bo3$74bo10bo4bo4bo2$70b3o5bo3bo2bo$71bo3bo9bo6b2o5bo$72bobo5bobobo2bobo5b
4o$70b3o4bob2o7b2obo$74bo13bo14bo$73bo15bo8bo4b2o$74bo11bob3o6b2o4bo$87bo2bo7b2o$72bo17bo8b3o$70bob2o$72b2o12b3o$88b2o$73bo3bobo5b2o17bo4bo
$74bo9b2o2bo12bo3b4o$79bo5b2obo4bobo13bo$78b2o10bo11bo2bo$87bo7bo5bo2b
o5bobo$76bobo15b2o3bobo2bo2bo5bo$84bo16bo10b2o2bo$88b2o2bobo18bob3o$
86bo18bo8bo2bo$86bobo11bo4b2o10bo$87b2o10b2o4bo$84bo2bobo10b2o11b3o$
101b3o10bo2$89bo$88bo2bo3bo2$93bobo$90bob2o!

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

A for awesome
Posts: 1997
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1
Contact:

### Re: Live Free or Die

5-dot seed for infinite growth:

Code: Select all

x = 10, y = 9, rule = B2/S0
8bo2$3bo$6bo$9bo$3bo2$b2o$o2bo!


Code: Select all

x = 16, y = 63, rule = B2/S0
bo2$6bo$3bo10bo$o$6bo2bo$12bo$15bo$9bo$bo2$6bo$3bo10bo$o$6bo2bo$12bo$
15bo$9bo4$14bo2$9bo$12bo$15bo$9bo2$7b2o$6bo2bo7$9bo$15bo$12bo$9bo2$14b o4$9bo$15bo$12bo$6bo2bo$o$3bo10bo$6bo2$bo$9bo$15bo$12bo$6bo2bo$o$3bo 10bo$6bo2$bo!  EDIT: (2,1)c/5 frontend: Code: Select all x = 15, y = 18, rule = B2/S0 bo$o$4b3o$o$3bobo$5bo$2bo2bo$7bobobo$bo$5bo3bob2o$o6b3o2bobo$6bo$bo6bo$o6bo$3b2obo4bo2bo$3bo2bo6bo$obo5bo3bo$o2bobo3bo2bo!

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

77topaz
Posts: 1472
Joined: January 12th, 2018, 9:19 pm

### Re: Live Free or Die

A for awesome wrote:

Code: Select all

x = 16, y = 63, rule = B2/S0
bo2$6bo$3bo10bo$o$6bo2bo$12bo$15bo$9bo$bo2$6bo$3bo10bo$o$6bo2bo$12bo$
15bo$9bo4$14bo2$9bo$12bo$15bo$9bo2$7b2o$6bo2bo7$9bo$15bo$12bo$9bo2$14b o4$9bo$15bo$12bo$6bo2bo$o$3bo10bo$6bo2$bo$9bo$15bo$12bo$6bo2bo$o$3bo 10bo$6bo2$bo!  Hmm... if you could find a puffer that outputs that precise seed pattern of dots, then you'd be able to have a t*sqrt(t) growth rate. wildmyron Posts: 1371 Joined: August 9th, 2013, 12:45 am ### Re: Live Free or Die A for awesome wrote:5-dot seed for infinite growth: Code: Select all x = 10, y = 9, rule = B2/S0 8bo2$3bo$6bo$9bo$3bo2$b2o$o2bo! That's a nice reaction, I don't remember seeing it when I surveyed Moon + dot reactions, I think I was focussed on the reflector search and filtered out anything that grew. 77topaz wrote: A for awesome wrote: Code: Select all x = 16, y = 63, rule = B2/S0 bo2$6bo$3bo10bo$o$6bo2bo$12bo$15bo$9bo$bo2$6bo$3bo10bo$o$6bo2bo$12bo$15bo$9bo4$14bo2$9bo$12bo$15bo$9bo2$7b2o$6bo2bo7$9bo$15bo$12bo$9bo2$14b
o4$9bo$15bo$12bo$6bo2bo$o$3bo10bo$6bo2$bo$9bo$15bo$12bo$6bo2bo$o$3bo
10bo$6bo2$bo!

Hmm... if you could find a puffer that outputs that precise seed pattern of dots, then you'd be able to have a t*sqrt(t) growth rate.
Doing this at p9 would be very difficult, and it doesn't quite fit at p8, but at p12 there are lots of versatile puffers and reactions which would make this possible.
A for awesome wrote:EDIT: (2,1)c/5 frontend:

Code: Select all

x = 15, y = 18, rule = B2/S0
bo$o$4b3o$o$3bobo$5bo$2bo2bo$7bobobo$bo$5bo3bob2o$o6b3o2bobo$6bo$bo6bo
$o6bo$3b2obo4bo2bo$3bo2bo6bo$obo5bo3bo$o2bobo3bo2bo!  That looks very interesting, though I imagine it will be difficult to complete. The latest version of the 5S Project contains over 226,000 spaceships. There is also a GitHub mirror of the collection. Tabulated pages up to period 160 (out of date) are available on the LifeWiki. A for awesome Posts: 1997 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 Contact: ### Re: Live Free or Die A potentially new p4 c ship with a single well-isolated plus spark: Code: Select all x = 16, y = 14, rule = B2/S0 2b2o$bo$4bo5b2o$5bo3bo2bo$3bo2bo$2bo4bobobobo$bo12bo$o14bo6$10bobo! 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 CoolCreeper39 Posts: 58 Joined: June 19th, 2019, 12:18 pm ### Re: Live Free or Die Smallest spaceships of a certain speed by minimum bounding box area (If two have the same minimum bounding box, the one with a smaller minimum population is shown): c/1 orthogonal: 8-cell bounding box, 4 cells: Code: Select all x = 2, y = 4, rule = B2/S0 o$bo$bo$o!

c/2 orthogonal: 180-cell bounding box, 36 cells:

Code: Select all

x = 15, y = 12, rule = B2/S0
7bo3bo$6bo4bobo$5bo5bo2bo$10bo$bo7bo$12bobo$o4bo3b5o$bobo3bo4bo$12b2o$4bob2obobobo$12bo$4bobo2bo! 2c/5 orthogonal: 2,380-cell bounding box, 268 cells: Code: Select all x = 85, y = 28, rule = B2/S0 22bo2$26bo2bo$22b3o9b3o$32bo2bo21bo3bo$23bo3bo5b2o2bo2bo26bo$23bo2bo4b
o4bo3bo2bo5bo7bo8bo6bo$8bo14bo8bo3bo15bo8bo4bo2bo$13bo3bo2b2o15b2o20bo
bo8b2o5bo$12bo6b2o9b5obo2b2o3b3o2bo5bobob3o2bo6bo3b2o$5bo5bo4bo3bo3bo
8bo4bo13bo5bo2bo7b2o3bo4bo$o10bo2bo6bobobo4bobo7bo2bo2bo11b4o5bo4bo10b o$15bo9bo3b3o7bo3bo10bo4bobo2bo13b2obob2o$2bo5bo15bobo8bobo3bo2b2o9bob o18bo7bo$2bo5bo15bobo8bobo3bo2b2o9bobo18bo7bo$15bo9bo3b3o7bo3bo10bo4bo bo2bo13b2obob2o$o10bo2bo6bobobo4bobo7bo2bo2bo11b4o5bo4bo10bo$5bo5bo4bo 3bo3bo8bo4bo13bo5bo2bo7b2o3bo4bo$12bo6b2o9b5obo2b2o3b3o2bo5bobob3o2bo
6bo3b2o$13bo3bo2b2o15b2o20bobo8b2o5bo$8bo14bo8bo3bo15bo8bo4bo2bo$23bo 2bo4bo4bo3bo2bo5bo7bo8bo6bo$23bo3bo5b2o2bo2bo26bo$32bo2bo21bo3bo$22b3o
9b3o$26bo2bo2$22bo!
c/3 orthogonal: 2,929-cell bounding box, 475 cells:

Code: Select all

x = 101, y = 29, rule = B2/S0
22bo36bo32bo$21bo45bo$22b3o39bo6bo14bo2bo2bo$14bobobo4b2obo39bo11bo4bo 5bo2bo$2bo10b4obobo3b2obo34bobo3b4o3bo3bo11b2o3bob2o$b2obo5bo3b2o2b2ob o4bobo15bobo5bobo17bo2bo3bo12b2o5b2o$2b2o13bo5bo3bo23bo8bo6bo9bo9b2o2b
o2b2o4bo$4b2obo4b2o14b2o11bo4bo3b2o28bo2bob2o11b2o$bo5b2o2b3o2b4o3bo5b
o10bo5b2o7bo2bobo6bo2bo2bobobobo3b3o12b3o$o3bo4b5o16bob2o5bo4bo7b3o2bo 7b3o3bo6b2o5bo2bo4bo6bo$8bobo17bobo14bo5bo6b3o4bo2bo2bobo5bo11bobo2bo
2bo$9bo9b4o4b5o3bo38b3o5bo2b3o3b4o$17bo10bob2o19bo11bo3bo3bo5b2o2bo6bo
2bo4bo$31b2obob2o8bo10b2o4bobo6b2o8b3o4bo2bo$13bo16b3o10b2o5bo6b4o2b3o
11bo4bo7b3o$31b2obob2o8bo10b2o4bobo6b2o8b3o4bo2bo$17bo10bob2o19bo11bo
3bo3bo5b2o2bo6bo2bo4bo$9bo9b4o4b5o3bo38b3o5bo2b3o3b4o$8bobo17bobo14bo
5bo6b3o4bo2bo2bobo5bo11bobo2bo2bo$o3bo4b5o16bob2o5bo4bo7b3o2bo7b3o3bo 6b2o5bo2bo4bo6bo$bo5b2o2b3o2b4o3bo5bo10bo5b2o7bo2bobo6bo2bo2bobobobo3b
3o12b3o$4b2obo4b2o14b2o11bo4bo3b2o28bo2bob2o11b2o$2b2o13bo5bo3bo23bo8b
o6bo9bo9b2o2bo2b2o4bo$b2obo5bo3b2o2b2obo4bobo15bobo5bobo17bo2bo3bo12b 2o5b2o$2bo10b4obobo3b2obo34bobo3b4o3bo3bo11b2o3bob2o$14bobobo4b2obo39b o11bo4bo5bo2bo$22b3o39bo6bo14bo2bo2bo$21bo45bo$22bo36bo32bo!

c/4 orthogonal: 3,024-cell bounding box, 458 cells:

Code: Select all

x = 84, y = 36, rule = B2/S0
57bo$3bo16bo7bo7bo$13bo15bo5b2o7bo9bo4bo$6bobo13bo6bobo4b2o19bo2bo$bo
14bobo3bo2bo2b3o4bo10bo24bo$o6bo4bo13b3o7bobo7bo2bo2bo$3bo6b6o8bo4b2o
19b3o3bob4o6bo4bo4bo$2bo5bo5b3o4bo2bo8b4o3bo3bo3bo3b2ob2o3bo12bo3bo$2b
obo4bo4b2obo4bo11bo5bo4bo2bo5bo9b2obobo10bo$3bo3bo7b2obo5bo3b2o21b2obo 5bobob2o5bo3b2o2b2obo$b2obo9b2o7b2o13bo2bo9b2o6b3o4bo4bo8b2o$2b4o8bo 21bobobobo6b3o6bobo8bo4bo$3bo20bo4b2o7bo7bobo2b2o3bobo14bo3bobo2bo$39b obob2ob2obo2bobo20bo7bo$39bo5bo23bobo3bo$31bo7bo10bobo6bo8b2o8bo3bo$
28bobo2bo4b2o7bo4bo3bo5bo4b4o2b3obo$32bo4bobo2b2o2bo5bobo2bobobo4bobo 5bo4bo$32bo4bobo2b2o2bo5bobo2bobobo4bobo5bo4bo$28bobo2bo4b2o7bo4bo3bo 5bo4b4o2b3obo$31bo7bo10bobo6bo8b2o8bo3bo$39bo5bo23bobo3bo$39bobob2ob2o
bo2bobo20bo7bo$3bo20bo4b2o7bo7bobo2b2o3bobo14bo3bobo2bo$2b4o8bo21bobob
obo6b3o6bobo8bo4bo$b2obo9b2o7b2o13bo2bo9b2o6b3o4bo4bo8b2o$3bo3bo7b2obo
5bo3b2o21b2obo5bobob2o5bo3b2o2b2obo$2bobo4bo4b2obo4bo11bo5bo4bo2bo5bo 9b2obobo10bo$2bo5bo5b3o4bo2bo8b4o3bo3bo3bo3b2ob2o3bo12bo3bo$3bo6b6o8bo 4b2o19b3o3bob4o6bo4bo4bo$o6bo4bo13b3o7bobo7bo2bo2bo$bo14bobo3bo2bo2b3o 4bo10bo24bo$6bobo13bo6bobo4b2o19bo2bo$13bo15bo5b2o7bo9bo4bo$3bo16bo7bo
7bo$57bo! c/5 orthogonal: 864-cell bounding box, 116 cells: Code: Select all x = 48, y = 18, rule = B2/S0 34bo$35bo$22bo4bo3bo15bo$4bo10bo30bo$9bo17bo5b3o$10bo7bobo3b2obobo16bo
$4bo5b2o3bobo6bo3bo4bo9b3o$o2bo3b2ob5o6b2o5bo7b2o6bo2bo$o22b3o3bo4bo6b o3b2o$o22b3o3bo4bo6bo3b2o$o2bo3b2ob5o6b2o5bo7b2o6bo2bo$4bo5b2o3bobo6bo
3bo4bo9b3o$10bo7bobo3b2obobo16bo$9bo17bo5b3o$4bo10bo30bo$22bo4bo3bo15b
o$35bo$34bo!

c/4 diagonal: 256-cell bounding box, 37 cells:

Code: Select all

x = 16, y = 16, rule = B2/S0
5bob2o$8bobo$5bo$10bo2$12bobo$8b2o$2bo5b2o4b2o$4b2o9bo2$obo4bo5bobo$3o 4bo$o2bo$4b2o2bo$4bo$3b3o!  Last edited by CoolCreeper39 on August 6th, 2019, 2:42 pm, edited 1 time in total. Gamedziner Posts: 796 Joined: May 30th, 2016, 8:47 pm Location: Milky Way Galaxy: Planet Earth ### Re: Live Free or Die CoolCreeper39 wrote:c/2.5 Since speed represents cells per generation, it is always represented with positive integers. "c/2.5" is written as 2c/5. Code: Select all x = 81, y = 96, rule = LifeHistory 58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27.
A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A
$4.2A18$4.2A$4.2A2.2A$8.2A!


CoolCreeper39
Posts: 58
Joined: June 19th, 2019, 12:18 pm

### Re: Live Free or Die

Methuselahs in Live Free or Die (Non record-breakers are not shown):

1-cell bounding box: 1G

Code: Select all

x = 1, y = 1, rule = B2/S0
o!
2-cell bounding box: 12G

Code: Select all

x = 1, y = 2, rule = B2/S0
o$o! 8-cell bounding box: 20G Code: Select all x = 1, y = 8, rule = B2/S0 o3$o$o3$o!
11-cell bounding box: 24G

Code: Select all

x = 1, y = 11, rule = B2/S0
o3$o3$o$o3$o!

The smallest infinite growth pattern is this, with a 4-cell bounding box:

Code: Select all

x = 2, y = 2, rule = B2/S0
bo$2o! Compare that with Life’s smallest infinite growth pattern, with a 24-cell bounding box: Code: Select all x = 12, y = 2, rule = B3/S23 ob4ob2o2bo$o2b2ob6o!

A for awesome
Posts: 1997
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1
Contact:

### Re: Live Free or Die

April 30th, 2015, 9:20 pm
Nice! On the subject of almost-rakes, here's one I found back in the day:

Code: Select all

x = 11, y = 14, rule = B2/S0
7bo$2bo5bo$3bo5bo$4bo5bo$o9bo$3bo5bo$3bo$3bo$3bo5bo$o9bo$4bo5bo$3bo5bo$2bo5bo$7bo! Completed, 4 whole years later: Code: Select all x = 34, y = 32, rule = B2/S0 24bo2bo2bo$31bo$27b3o3bo$27b3o3bo$31bo$24bo2bo2bo4$23bo5bo$30bo$31bo$
32bo$21bobob2o5bo$bo22bo4bobo$o$o$bo22bo4bobo$21bobob2o5bo$32bo$31bo$30bo$23bo5bo4$24bo2bo2bo$31bo$27b3o3bo$27b3o3bo$31bo$24bo2bo2bo!
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