Speed Limits

[dani]

As you know, c/2 and c/4 are the speed limits for conways game of life for orthogonal and diagonal spaceships respectively. In seeds it is c and c/2. The rules have the formula of c/2*(total cells moved) and c/(total cells moved). Knightships are covered by this formula, as a ship moving (2,1) could accomplish this in 6 and 3 steps.

It's easy to see that non-B2a rules use the CGOL formula and B2a rules use the seeds formula (B2a can be substituted with B1e or B2a), right?

In non-totalistic rules, specifically in two cases, this gets tricky.

The first is rules that have S4w (I think S2a is also required but I don't know the exact transitions to make this travel possible. There also might be a special case for other transitions like S4w) which can actually have diagonal ships between c/4 and c/3, a couple soups in B3/S234w and Movostill 3 can verify this. There was also a (2,1)c/5 knightship posted in a Move relative that I can't find.

The second case is for rules like JustFriends which, for some reason, cannot have c/2-c/3 spaceships. I know even less about this limit than the other one so I won't try and ramble on.

My question is: are there other speed limits for other rules? What is the speed limit for rules like LongLife?

[Majestas32]

Think c/3 diag exists In some b2ce3ai rules too

[HotWheels9232]

As you know, c/2 and c/4 are the speed limits for conways game of life for orthogonal and diagonal spaceships respectively. In seeds it is c and c/2. The rules have the formula of c/2*(total cells moved) and c/(total cells moved). Knightships are covered by this formula, as a ship moving (2,1) could accomplish this in 6 and 3 steps.

It's easy to see that non-B2a rules use the CGOL formula and B2a rules use the seeds formula (B2a can be substituted with B1e or B2a), right?

In non-totalistic rules, specifically in two cases, this gets tricky.

The first is rules that have S4w (I think S2a is also required but I don't know the exact transitions to make this travel possible. There also might be a special case for other transitions like S4w) which can actually have diagonal ships between c/4 and c/3, a couple soups in B3/S234w and Movostill 3 can verify this. There was also a (2,1)c/5 knightship posted in a Move relative that I can't find.

The second case is for rules like JustFriends which, for some reason, cannot have c/2-c/3 spaceships. I know even less about this limit than the other one so I won't try and ramble on.

My question is: are there other speed limits for other rules? What is the speed limit for rules like LongLife?

LongLife's speed limit is probably 0c/1

[Haycat2009]

As you know, c/2 and c/4 are the speed limits for conways game of life for orthogonal and diagonal spaceships respectively. In seeds it is c and c/2. The rules have the formula of c/2*(total cells moved) and c/(total cells moved). Knightships are covered by this formula, as a ship moving (2,1) could accomplish this in 6 and 3 steps.

It's easy to see that non-B2a rules use the CGOL formula and B2a rules use the seeds formula (B2a can be substituted with B1e or B2a), right?

In non-totalistic rules, specifically in two cases, this gets tricky.

The first is rules that have S4w (I think S2a is also required but I don't know the exact transitions to make this travel possible. There also might be a special case for other transitions like S4w) which can actually have diagonal ships between c/4 and c/3, a couple soups in B3/S234w and Movostill 3 can verify this. There was also a (2,1)c/5 knightship posted in a Move relative that I can't find.

The second case is for rules like JustFriends which, for some reason, cannot have c/2-c/3 spaceships. I know even less about this limit than the other one so I won't try and ramble on.

My question is: are there other speed limits for other rules? What is the speed limit for rules like LongLife?

LongLife's speed limit is probably 0c/1

Hard to tell, more llikely something like c/160,000,346

[May13]

...

My question is: are there other speed limits for other rules? What is the speed limit for rules like LongLife?

LongLife's speed limit is probably 0c/1

Hard to tell, more likely something like c/160,000,346

I suspect that the speed limits of LongLife are near c/9 orthogonal and c/9 diagonal. c/9 partials:

Code: Select all

x = 76, y = 18, rule = B345/S5
9bobobo3bo19bo29b2o$7bobob2o3b2o$5bobob8o18b2ob2o25b6o$4b3o2bo3b3obo$
3b4ob3o4bobo15b2o5b2o21bo2bo2bo2bo$2b4obob3o2b2o16bo9bo21b3o2b3o$3b2o
3b3ob2o17b3obobobob3o17b5ob2ob5o$b2o2bobo3b3o18bobo5bobo19bob2ob2ob2ob
o$4bobobob2obo16b2ob2o5b2ob2o15b2o2bobo2bobo2b2o$7o2b4o18bo2bo5bo2bo
18bo2bo4bo2bo$2bob3ob2ob2o47bo3b2ob2ob2o3bo$3o2bob4o20b3o2bobo2b3o20b
8o$b2o3b2ob2o50bobobo4bobobo$ob2o2b3o55bobo2bobo$2b2obo$2b4o$b2o$2ob2o
!

Edit: longer and wider c/9o partial:

Code: Select all

x = 18, y = 18, rule = B345/S5
8b2o2$6b6o2$4bo2bo2bo2bo$5b3o2b3o$2b5ob2ob5o$3bob2ob2ob2obo$b2o2bobo2b
obo2b2o$3bo2bo4bo2bo$b2o2b2ob2ob2o2b2o$5b8o$2o2bobo4bobo2b2o$2bo2bobo
2bobo2bo$2o3b8o3b2o$bo2b3o4b3o2bo$5obo4bob5o$2b2o3bo2bo3b2o!

Looped:

Code: Select all

x = 18, y = 18, rule = B345/S5
8b2o2$6b6o2$4bo2bo2bo2bo$5b3o2b3o$2b5ob2ob5o$3bob2ob2ob2obo$b2o2bobo2b
obo2b2o$3bo2bo4bo2bo$b2o2b2ob2ob2o2b2o$5b8o$2o2bobo4bobo2b2o$2bo2bobo
2bobo2bo$2o3b8o3b2o$bo2b3o4b3o2bo$5obo4bob5o$2b2o3bo2bo3b2o!
[[ THEME 0 LOOP 9 TRACK 0 -1/9 ]]