## Challenges

A forum where anything goes. Introduce yourselves to other members of the forums, discuss how your name evolves when written out in the Game of Life, or just tell us how you found it. This is the forum for "non-academic" content.
A for awesome
Posts: 1901
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1
Contact:

### Challenges

For challenges of any type related to cellular automata.

I'll give two to start off:

1. Who can find the non-totalistic rule with the most speeds exhibited by spaceships with <=10 cells in any phase?

[nevermind]2. Find a non-explosive B1e rule.[/nevermind]
This one has been solved by @gmc_nxtman. Feel free to come up with other examples, though.
Last edited by A for awesome on February 18th, 2017, 6:07 pm, edited 1 time in total.
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

gameoflifeboy
Posts: 474
Joined: January 15th, 2015, 2:08 am

### Re: Challenges

A for awesome wrote:2. Find a non-explosive B1e rule.
B1e/S12 has natural infinite growth in the form of one-cell-thick ladders, but I wouldn't call it explosive.

In fact, I think that any survival conditions can be added to the rulestring and patterns still won't explode.

A for awesome
Posts: 1901
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1
Contact:

### Re: Challenges

gameoflifeboy wrote:B1e/S12 has natural infinite growth in the form of one-cell-thick ladders, but I wouldn't call it explosive.

In fact, I think that any survival conditions can be added to the rulestring and patterns still won't explode.
That's probably true. Congratulations on solving my challenge, even though that's really not what I was imagining at all. The second statement I would call incorrect, however:

Code: Select all

x = 113, y = 82, rule = B1e/S012
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10b2o$85bo41bo$79bo4bo43bo4bo$81b2o47b2o! That might not be good enough to prevent boring solutions, though -- e.g., there might be a way to hit something like a block with an extensible spaceship, and wind up with a block. Probably simpler to allow only one representative of each class of extensible spaceships. B. Same question as (A), but now only glider-constructible spaceships are allowed. The initial pattern starts out with four glider salvos in the four quadrants of the pattern, but all-but-optionally-one of the gliders has to build a spaceship at some point. And as before, no two of the constructed spaceships can have the same apgcode, and only one member of each class of extensible spaceship is allowed. For (B) I guess it's not a requirement that all the constructed spaceships have to exist simultaneously at some particular generation of the pattern, though maybe it would be nice if that were an option. A for awesome Posts: 1901 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 Contact: ### Re: Challenges dvgrn wrote:I put together Life/Miscellaneous/Cambrian-Explosion.rle a decade ago, as a representative sample of the amazing things that had been invented up to 2006. But the pattern kind of gets boring after you run it for a while -- it just keeps expanding and gets awkward to look at. So -- what about a pattern that goes the other way? This is somewhat unrelated, but I think a subpattern like one of these might have a place in that pattern: Code: Select all x = 90, y = 103, rule = B3/S23 70bobo$73bo$69bo3bo$69bo3bo$73bo$70bo2bo$71b3o6$64b6o$63bo6bo$27bo$25b 3o$22bobo5b2o$25b3o3bo$18bo4b2o2bo2bo29bo12bo$19b4o2bobobo31b12o$24b2o
bob4o$25bobo5bo$24bo3bob3o$16b7o2b4obo27b18o$15bo7b2o32bo18bo$25bob2ob o$22bob2obob4o$25bobo5bo$22bobo3bob3o$25b4obo$12bo10b2o29bo24bo$13b10o 2bob2obo24b24o$24b2obob4o$25bobo5bo$24bo3bob3o$10b13o2b4obo21b30o$9bo
13b2o26bo30bo$25bob2obo$22bob2obob4o$25bobo5bo$22bobo3bob3o$25b4obo$6b
o16b2o23bo36bo$7b16o2bob2obo18b36o$24b2obob4o$25bobo5bo$24bo3bob3o$4b 19o2b4obo15b42o$3bo19b2o20bo42bo$25bob2obo$22bob2obob4o$25bobo5bo$22bo
bo3bob3o$25b4obo$o22b2o20bo42bo$b22o2bob2obo15b42o$24b2obob4o$25bobo5b o$24bo3bob3o$4b19o2b4obo18b36o$3bo19b2o23bo36bo$25bob2obo$22bob2obob4o
$25bobo5bo$22bobo3bob3o$25b4obo$6bo16b2o26bo30bo$7b16o2bob2obo21b30o$
24b2obob4o$25bobo5bo$24bo3bob3o$10b13o2b4obo24b24o$9bo13b2o29bo24bo$25bob2obo$22bob2obob4o$25bobo5bo$22bobo3bob3o$25b4obo$12bo10b2o32bo18b
o$13b10o2bob2obo27b18o$24b2obob4o$25bobo5bo$24bo3bob3o$16b7o2b4obo30b 12o$15bo7b2o35bo12bo$25bob3o$22bob2obo2bo$25bobobo$22bobo3bo$25b3o$18b
o4b2o38bo6bo$19b4o2bo38b6o$24b2o4$71b3o$70bo2bo$73bo$69bo3bo$69bo3bo$
73bo$70bobo!  The first one only retracts in one dimension, but the second one is clean. Maybe call the whole thing "Permian-Triassic Extinction" or "Great Dying"? 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 dvgrn Moderator Posts: 5888 Joined: May 17th, 2009, 11:00 pm Location: Madison, WI Contact: ### Re: Challenges dvgrn wrote: A for awesome wrote:So -- what about a pattern that goes the other way? This is somewhat unrelated, but I think a subpattern like one of these might have a place in that pattern... The first one only retracts in one dimension, but the second one is clean. Maybe call the whole thing "Permian-Triassic Extinction" or "Great Dying"? Huh, maybe something along those lines, yeah. I had thought of "Gnab Gib", a reference to Douglas Adams' _Restaurant at the End of the Universe_, but didn't really like the name enough. I don't remember that anyone ever published an inverted spacefiller -- a "space-emptier" -- though I suppose it probably wouldn't be too hard to come up with something less trivial than the following, by sticking two back ends of diamond-shaped greyships onto a big patch of agar. Code: Select all x = 78, y = 40, rule = B3/S23 38bo3bo3bo3bo3bo3bo3bo3bo3bo3bo$39bo3bo3bo3bo3bo3bo3bo3bo3bo3bo$40bo3b o3bo3bo3bo3bo3bo3bo3bo3bo$41bo3bo3bo3bo3bo3bo3bo3bo3bo3bo$38bo3bo3bo3b o3bo3bo3bo3bo3bo3bo$39bo3bo3bo3bo3bo3bo3bo3bo3bo3bo$40bo3bo3bo3bo3bo3b o3bo3bo3bo3bo$41bo3bo3bo3bo3bo3bo3bo3bo3bo3bo$10bobo25bo3bo3bo3bo3bo3b o3bo3bo3bo3bo$10bobo26bo3bo3bo3bo3bo3bo3bo3bo3bo3bo$8bobobobo25bo3bo3b o3bo3bo3bo3bo3bo3bo3bo$8bobobobo26bo3bo3bo3bo3bo3bo3bo3bo3bo3bo$6bobob obobobo21bo3bo3bo3bo3bo3bo3bo3bo3bo3bo$6bobobobobobo22bo3bo3bo3bo3bo3b
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3bo3bo3bo3bo3bo3bo$2bobobobobobobobobobo19bo3bo3bo3bo3bo3bo3bo3bo3bo3b o$2bobobobobobobobobobo20bo3bo3bo3bo3bo3bo3bo3bo3bo3bo$4bobobobobobobo bo19bo3bo3bo3bo3bo3bo3bo3bo3bo3bo$4bobobobobobobobo20bo3bo3bo3bo3bo3bo
3bo3bo3bo3bo$6bobobobobobo23bo3bo3bo3bo3bo3bo3bo3bo3bo3bo$6bobobobobob
o24bo3bo3bo3bo3bo3bo3bo3bo3bo3bo$8bobobobo23bo3bo3bo3bo3bo3bo3bo3bo3bo 3bo$8bobobobo24bo3bo3bo3bo3bo3bo3bo3bo3bo3bo$10bobo27bo3bo3bo3bo3bo3bo 3bo3bo3bo3bo$10bobo28bo3bo3bo3bo3bo3bo3bo3bo3bo3bo$38bo3bo3bo3bo3bo3bo 3bo3bo3bo3bo$39bo3bo3bo3bo3bo3bo3bo3bo3bo3bo$40bo3bo3bo3bo3bo3bo3bo3bo 3bo3bo$41bo3bo3bo3bo3bo3bo3bo3bo3bo3bo$38bo3bo3bo3bo3bo3bo3bo3bo3bo3bo$39bo3bo3bo3bo3bo3bo3bo3bo3bo3bo$40bo3bo3bo3bo3bo3bo3bo3bo3bo3bo$41bo
3bo3bo3bo3bo3bo3bo3bo3bo3bo!

toroidalet
Posts: 1019
Joined: August 7th, 2016, 1:48 pm
Location: my computer
Contact:

### Re: Challenges

[quote="A for awesome"]
1. Who can find the non-totalistic rule with the most speeds exhibited by spaceships with <=10 cells in any phase?/quote]
I can find 4:

Code: Select all

x = 44, y = 11, rule = B2i3-ck/S02-i3-ck
3o13bo12b3o10bo$o14bobo10b2ob2o8bobo$bo13bobo23bobo$16bo25bo2$16bo25bo
2$16bo3$29b3o!

5 cell c/4 diagonal, 8 cell 3c/14, 10 cell 6c/29, 7 cell c/6.
Challenge: find the fastest diagonal spaceship possible.
Also the fastest ship in a rule with no survival conditions or b2a
"Build a man a fire and he'll be warm for a day. Set a man on fire and he'll be warm for the rest of his life."

-Terry Pratchett

A for awesome
Posts: 1901
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1
Contact:

### Re: Challenges

toroidalet wrote:Challenge: find the fastest diagonal spaceship possible.
3c/4 diagonal spaceship here. I think this is, in fact, the fastest possible.
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

dvgrn
Moderator
Posts: 5888
Joined: May 17th, 2009, 11:00 pm
Contact:

### Re: Challenges

A glider-to-c/3-spaceship converter whose RLE fits in a forum posting and so can be run in LifeViewer.

(No fair just writing to Nathaniel and asking him to bump up the maximum number of bytes in a post by 10K.)

Posts: 1906
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

### Re: Challenges

A for awesome wrote:3c/4 diagonal spaceship here. I think this is, in fact, the fastest possible.
I think so as well, and here's why:
First, we look at rules without B0.
A fast spaceship in a rule without B1c will have its leading edge travel orthogonally, forcing a maximum diagonal speed of c/2.
B1c, however, forces lightspeed diagonal expansion in all directions, preventing the existence of spaceships, or interesting non-replicator OFF-background patterns of any kind for that matter.
Therefore, any diagonal ship faster than c/2 must have B0.
By similar reasoning to the non-B0 case, at least one of the even-step rule and the odd-step rule must have B1c but both cannot or all patterns will explode.
Therefore, the fastest possible speed is the fastest speed at which the pattern does not experience B1c in two consecutive cycles.
The leading edge must then alternate between moving orthogonally and diagonally every generation.
This gives two maximum-speed paths for the leading edge, in which the leading edge travels one cell along the path each generation:

Code: Select all

x = 25, y = 12, rule = B3/S23
o18bo$o18bo$b2o17bo$3bo16bo$3bo17bo$4b2o15bo$6bo15bo$6bo15bo$7b2o14bo$9bo13bo$9bo14bo$10b2o12bo!  As you can see, the left path corresponds to 3c/4 diagonal, and the right corresponds to (2,1)c/2 as mentioned by A for Awesome below the post he linked. Therefore, 3c/4 diagonal is the fastest possible diagonal speed, and if (2,1)c/2 is proven infeasible, the fastest possible speed in general. (EDIT 3-26) Realized that theoretically, you could have any ordering of the two travel directions, giving a speed of (2h+k,h+2k)/(2h+2k) for any integer h,k > 0. This equates to a Euclidean speed of 1 + (h^2+k^2)/(2h+2k)^2, so 3c/4 diagonal is actually the lowest-speed path out of all paths of this type and (2,1)c/2 is the highest. However, as "compound" fast paths are harder to search for and have higher period (>=6, although that may not be considered "high" anymore), I still expect 3c/4 to remain the fastest speed. LifeWiki: Like Wikipedia but with more spaceships. [citation needed] Saka Posts: 3138 Joined: June 19th, 2015, 8:50 pm Location: In the kingdom of Sultan Hamengkubuwono X ### Re: Challenges Easy challenge: Find which ones are hand-made and which ones are ctrl+5 (Hint: there are 2 of each) Code: Select all x = 72, y = 48, rule = B/S012345678 11bob2ob6o2bobo16b3ob2ob2obo4bo$14b3obob2ob2obo17bob2obobob3o2bo$2b2o 7bobo2bo2bobo2bobo16bo2b4o5b2obo$bobo10bo2bob3obo2bo16bobo4bo2b3ob2o7b
3o$o2bo7b4obobob2ob4o18b5o2b3ob2o7bo3bo$3bo7bobo2bo2bobo2bobo16bo3b2o
5bob2o6bo5bo$3bo7bob6o2bob4o19b2ob4ob2o2bo5bo5bo$3bo7b2obobobob3ob2o
18b2ob6ob3obo11bo$3bo9b2ob2o3bobob2o16bobo4bo4b3o12bo$3bo7b3ob2obo2bob
o2bo16b2o4b3o2b3obo10bo$3bo7bobo2b3o2bobob2o16b5obobo2bo3bo9bo$3bo7b2o
bo2bob3obobo19bob2obobob5o8bo$3bo7bobob2obo2bo2b2o17bo2bob5o3bobo7bo$b
5o5bobob2obobobob3o16b3o4b4o3b2o6bo$11bob4ob3ob3obo16b2ob3o3b2obo8b7o$
11bobobob3obob2obo18b2o4bobo2b3o17$12bobo3b3o4b2o16b2obobo2b4obobo$14b
2obob3o2b3o17b2o2b2o2b2obob2o$5o6bo2bo2b4obob2o20b2o2bo2bo3bo5bo5bo$5b
o6b2o2bobo3bo3bo17bob9o8bo5bo$5bo5b2o3bobo3bo2b2o16bo3b4o6bo5bo5bo$5bo
6b4o2b3obo2b2o18b2o6bo2bo6bo5bo$5bo6bo2b3o2b7o17b2o2b5ob4o5bo5bo$5o8b
2obob3ob2obo20b2ob5o2b2o5b9o$5bo6bo2bobob2ob5o17bobo3b2o2bo14bo$5bo5bo
2bobo2bob3o22b2o5b2obo12bo$5bo5bobobo2bob3obo20bo3b3obob2o12bo$5bo5bob
3ob5o2bo18bob5o2bob2obo11bo$5bo5b2o2bo5bo2bo18bo4b2ob2ob4o11bo$5o6b2ob
2o2b2o4b3o16bob2o7bob2o11bo$12bo3b2o2b7o16bo2b2ob4o3bo$18bo3bobobo17bo
4b2o2b3o2bo!

Airy Clave White It Nay

Code: Select all

x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!  (Check gen 2) _zM Posts: 172 Joined: June 26th, 2016, 3:07 pm ### Re: Challenges I guess 1 and 3. Creator of multiple rules that may or may not be what you'd expect Saka Posts: 3138 Joined: June 19th, 2015, 8:50 pm Location: In the kingdom of Sultan Hamengkubuwono X ### Re: Challenges _zM wrote:I guess 1 and 3. 50% Right! Airy Clave White It Nay Code: Select all x = 17, y = 10, rule = B3/S23 b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!

(Check gen 2)

Gamedziner
Posts: 796
Joined: May 30th, 2016, 8:47 pm
Location: Milky Way Galaxy: Planet Earth

### Re: Challenges

Saka wrote:Easy challenge: Find which ones are hand-made and which ones are ctrl+5 (Hint: there are 2 of each)

Code: Select all

x = 72, y = 48, rule = B/S012345678
11bob2ob6o2bobo16b3ob2ob2obo4bo$14b3obob2ob2obo17bob2obobob3o2bo$2b2o
7bobo2bo2bobo2bobo16bo2b4o5b2obo$bobo10bo2bob3obo2bo16bobo4bo2b3ob2o7b 3o$o2bo7b4obobob2ob4o18b5o2b3ob2o7bo3bo$3bo7bobo2bo2bobo2bobo16bo3b2o 5bob2o6bo5bo$3bo7bob6o2bob4o19b2ob4ob2o2bo5bo5bo$3bo7b2obobobob3ob2o 18b2ob6ob3obo11bo$3bo9b2ob2o3bobob2o16bobo4bo4b3o12bo$3bo7b3ob2obo2bob o2bo16b2o4b3o2b3obo10bo$3bo7bobo2b3o2bobob2o16b5obobo2bo3bo9bo$3bo7b2o bo2bob3obobo19bob2obobob5o8bo$3bo7bobob2obo2bo2b2o17bo2bob5o3bobo7bo$b 5o5bobob2obobobob3o16b3o4b4o3b2o6bo$11bob4ob3ob3obo16b2ob3o3b2obo8b7o$11bobobob3obob2obo18b2o4bobo2b3o17$12bobo3b3o4b2o16b2obobo2b4obobo$14b 2obob3o2b3o17b2o2b2o2b2obob2o$5o6bo2bo2b4obob2o20b2o2bo2bo3bo5bo5bo$5b o6b2o2bobo3bo3bo17bob9o8bo5bo$5bo5b2o3bobo3bo2b2o16bo3b4o6bo5bo5bo$5bo 6b4o2b3obo2b2o18b2o6bo2bo6bo5bo$5bo6bo2b3o2b7o17b2o2b5ob4o5bo5bo$5o8b 2obob3ob2obo20b2ob5o2b2o5b9o$5bo6bo2bobob2ob5o17bobo3b2o2bo14bo$5bo5bo 2bobo2bob3o22b2o5b2obo12bo$5bo5bobobo2bob3obo20bo3b3obob2o12bo$5bo5bob 3ob5o2bo18bob5o2bob2obo11bo$5bo5b2o2bo5bo2bo18bo4b2ob2ob4o11bo$5o6b2ob 2o2b2o4b3o16bob2o7bob2o11bo$12bo3b2o2b7o16bo2b2ob4o3bo$18bo3bobobo17bo 4b2o2b3o2bo!  I guess 1 and 2 are hand-made. 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!


Saka
Posts: 3138
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

### Re: Challenges

Gamedziner wrote:
Saka wrote:Easy challenge: Find which ones are hand-made and which ones are ctrl+5 (Hint: there are 2 of each)

Code: Select all

x = 72, y = 48, rule = B/S012345678
11bob2ob6o2bobo16b3ob2ob2obo4bo$14b3obob2ob2obo17bob2obobob3o2bo$2b2o
7bobo2bo2bobo2bobo16bo2b4o5b2obo$bobo10bo2bob3obo2bo16bobo4bo2b3ob2o7b 3o$o2bo7b4obobob2ob4o18b5o2b3ob2o7bo3bo$3bo7bobo2bo2bobo2bobo16bo3b2o 5bob2o6bo5bo$3bo7bob6o2bob4o19b2ob4ob2o2bo5bo5bo$3bo7b2obobobob3ob2o 18b2ob6ob3obo11bo$3bo9b2ob2o3bobob2o16bobo4bo4b3o12bo$3bo7b3ob2obo2bob o2bo16b2o4b3o2b3obo10bo$3bo7bobo2b3o2bobob2o16b5obobo2bo3bo9bo$3bo7b2o bo2bob3obobo19bob2obobob5o8bo$3bo7bobob2obo2bo2b2o17bo2bob5o3bobo7bo$b 5o5bobob2obobobob3o16b3o4b4o3b2o6bo$11bob4ob3ob3obo16b2ob3o3b2obo8b7o$11bobobob3obob2obo18b2o4bobo2b3o17$12bobo3b3o4b2o16b2obobo2b4obobo$14b 2obob3o2b3o17b2o2b2o2b2obob2o$5o6bo2bo2b4obob2o20b2o2bo2bo3bo5bo5bo$5b o6b2o2bobo3bo3bo17bob9o8bo5bo$5bo5b2o3bobo3bo2b2o16bo3b4o6bo5bo5bo$5bo 6b4o2b3obo2b2o18b2o6bo2bo6bo5bo$5bo6bo2b3o2b7o17b2o2b5ob4o5bo5bo$5o8b 2obob3ob2obo20b2ob5o2b2o5b9o$5bo6bo2bobob2ob5o17bobo3b2o2bo14bo$5bo5bo 2bobo2bob3o22b2o5b2obo12bo$5bo5bobobo2bob3obo20bo3b3obob2o12bo$5bo5bob 3ob5o2bo18bob5o2bob2obo11bo$5bo5b2o2bo5bo2bo18bo4b2ob2ob4o11bo$5o6b2ob 2o2b2o4b3o16bob2o7bob2o11bo$12bo3b2o2b7o16bo2b2ob4o3bo$18bo3bobobo17bo 4b2o2b3o2bo!  I guess 1 and 2 are hand-made. 50% Airy Clave White It Nay Code: Select all x = 17, y = 10, rule = B3/S23 b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!

(Check gen 2)

_zM
Posts: 172
Joined: June 26th, 2016, 3:07 pm

### Re: Challenges

1 and 4?
Creator of multiple rules that may or may not be what you'd expect

A for awesome
Posts: 1901
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1
Contact:

### Re: Challenges

_zM wrote:1 and 4?
If not, then necessarily 2 and 3.
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

drc
Posts: 1664
Joined: December 3rd, 2015, 4:11 pm
Location: creating useless things in OCA

### Re: Challenges

Obviously 1 and 3.
This post was brought to you by the letter D, for dishes that Andrew J. Wade won't do. (Also Daniel, which happens to be me.)
Current rule interest: B2ce3-ir4a5y/S2-c3-y

A for awesome
Posts: 1901
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1
Contact:

### Re: Challenges

drc wrote:Obviously 1 and 3.
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

Gamedziner
Posts: 796
Joined: May 30th, 2016, 8:47 pm
Location: Milky Way Galaxy: Planet Earth

### Re: Challenges

This somehow feels similar to Mastermind (a board game)

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!  Saka Posts: 3138 Joined: June 19th, 2015, 8:50 pm Location: In the kingdom of Sultan Hamengkubuwono X ### Re: Challenges _zM wrote:1 and 4? You won! I used 2 different methods to make them: 1. Line by line (For 1) 2. Random clicking (For 4) Airy Clave White It Nay Code: Select all x = 17, y = 10, rule = B3/S23 b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!

(Check gen 2)

muzik
Posts: 3500
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Challenges

Seems there indeed is a (2,1)c/2 (compared with c/2 orthogonal and diagonal from the same rule):

Code: Select all

x = 8, y = 25, rule = B012356/S2347
4b3o$4bo2bo$4bo2bo2$4bo2bo$4bo2bo$4b3o4$5b3o$5bobo$4obo$ob2obobo$4o3bo
4$4b3o$4bobo$7bo$b2o2bobo$bo2b2obo$b2o$3b3o!  Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace! A for awesome Posts: 1901 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 Contact: ### Re: Challenges muzik wrote:Seems there indeed is a (2,1)c/2 (compared with c/2 orthogonal and diagonal from the same rule): Code: Select all x = 8, y = 25, rule = B012356/S2347 4b3o$4bo2bo$4bo2bo2$4bo2bo$4bo2bo$4b3o4$5b3o$5bobo$4obo$ob2obobo$4o3bo 4$4b3o$4bobo$7bo$b2o2bobo$bo2b2obo$b2o$3b3o!

That's actually (2,1)c/4.
Last edited by A for awesome on November 5th, 2017, 4:04 pm, edited 1 time in total.
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

83bismuth38
Posts: 453
Joined: March 2nd, 2017, 4:23 pm
Location: Still sitting around in Sagittarius A...
Contact:

### Re: Challenges

Find a Polythlonia rule, which is a rule that allows all (or most) polythlons, one of which is the pentadecathlon.
Find a Beconia rule, same as above except with beacons. except the beacon blocks get bigger.
Find a Toadia rule, same as above but they get longer instead of just bigger in general. I have examples for this one:
x = 2, y = 3, rule = B3/S2e3
bo$2o$o!
x = 2, y = 4, rule = B3/S23
bo$2o$2o$o! And a big toad: Code: Select all x = 2, y = 5, rule = B34-air/S34-ai bo$2o$2o$2o$o! Last edited by 83bismuth38 on April 14th, 2017, 2:27 pm, edited 1 time in total. 83bismuth38 Posts: 453 Joined: March 2nd, 2017, 4:23 pm Location: Still sitting around in Sagittarius A... Contact: ### Re: Challenges Insane challenge: make a rule where a blinker and a big blinker co-exist: Code: Select all x = 1, y = 5, rule = B3-a/S1258 o$o$o$o$o!  Code: Select all x = 1, y = 3, rule = B3/S23 o$o$o!  or at least, any variation of the big blinker. (central single-celled startor, rotor on outside, period rotates 90 degrees) also, side quest thing, see if it can be formed into a Blinkeria rule. Code: Select all x = 8, y = 10, rule = B3/S23 3b2o$3b2o$2b3o$4bobo$2obobobo$3bo2bo$2bobo2bo$2bo4bo$2bo4bo$2bo!