New sawtooth rule

[fluffykitty]

Here's a sawtooth rule:
Sawtooth.rule:

Code: Select all

@RULE Sawtooth
0 empty
1 puffer 1
2 puffer 2
3 debris
4 left ship
5 right ship
6 left reflector (useless)
7 right reflector
@TABLE
n_states:8
neighborhood:Moore
symmetries:none
#Ship motion
0004000004
4000000000
0000000505
5000000000
#Puffer motion
0002000001
1003000002
2003000003
#Interaction:3-4
##Gen 1
0004000304
##Gen 2+
3004000304
4000000300
##Gen x
3004000204
##Gen x1
3004000104
##Gen x2
4000000205
2004000003
##Gen x3
5000000300
#Interaction:4-6
##Gen 1
0004000064
##Gen 2
4000000060
0504000004
##Gen 3
4600000000
0064000004
0000000465
##Gen 4
5000000060
4060000000
#Interaction:5-7
##Gen 1
0070000504
##Gen 2
4070000000
@COLORS
0 0 0 0
1 255 0 0
2 255 127 0
3 127 0 255
4 255 255 0
5 0 255 255
6 0 255 0
7 255 0 255

Sawtooth.rle:

Code: Select all

x = 4, y = 2, rule = Sawtooth
3.G$BD!

[simsim314]

Hey just for fun, I made sawtooth rule with only 3 states. I think it would be challenge to make 3 states sawtooth rule with 8 symmetries (rotate+reflect). It would be even more challenging to make 2 state sawtooth rule, and 2 state rule with symmetries. I think it's fun exercise:

Code: Select all

@RULE Sawtooth3State

@TABLE
n_states:3
neighborhood:Moore
symmetries:none

#particle + reflector + stable unit
2,0,0,0,0,0,0,1,0,1
1,0,0,2,0,0,0,0,0,0
0,0,0,0,0,0,0,2,0,2
2,2,2,2,0,0,0,0,0,2
2,2,0,0,0,0,0,2,2,2
2,0,0,0,0,2,2,2,0,2
2,0,0,2,2,2,0,0,0,2
0,0,2,0,0,0,0,2,0,2
0,2,2,0,0,0,0,2,0,1
2,0,2,1,0,0,0,0,0,1
1,2,2,0,0,0,0,2,0,0
0,0,0,2,0,0,0,0,0,2
1,0,2,0,0,0,0,2,0,0
2,0,0,1,0,0,0,0,0,1
1,0,0,0,0,0,0,2,0,0

#spaceship
2,0,0,0,1,1,0,0,0,0
2,1,1,0,0,0,0,0,0,0
0,0,0,2,1,0,0,0,0,2
0,0,2,1,2,0,0,0,0,2
0,0,1,2,0,0,0,0,0,2
2,2,0,1,0,2,0,0,0,1

#delete puff
0,0,0,2,0,0,0,1,0,2
1,0,0,2,0,0,0,1,0,2
2,0,0,1,0,0,0,1,0,1

#reflect puffer
0,1,2,0,0,0,0,2,1,1
0,1,0,0,0,0,0,1,1,2
1,0,0,1,2,1,0,1,0,0
1,1,1,2,0,0,0,0,1,0
2,1,0,0,0,0,0,1,1,0
0,0,0,0,0,0,2,1,0,2

And a sawtooth itself:

Code: Select all

x = 8, y = 4, rule = Sawtooth3State
6.2B$B5.2B$2A.AB$B!

[fluffykitty]

Code: Select all

@RULE Sawtooth3State

@TABLE
n_states:8
neighborhood:Moore
symmetries:none
...

Shoudn't that be n_states:3?
By the way, very interesting.

[simsim314]

Shoudn't that be n_states:3?

Woops fixed it now.

[fluffykitty]

And anyway I don't see why you can't just add symmetry to your current rule. (And Life has sawtooths but I don't think you mean that, I think you mean a specialized rule. Am I right?)

EDIT:After thinking about it for some time, I realized that you are probably thinking of a rule using this design. Correct?

[simsim314]

why you can't just add symmetry to your current rule

Well symmetry removes degree of freedom, which requires more "tricks" embedded into the rules. The current rule will just mess up if you add rotation symmetry, and it's natural, because some special cases which were only in certain orientations in no symmetry rule, will be much more common.

And Life has sawtooths

Well obviously we need to define "limited sawtooth". Say your sawtooth starts from 3 cells, mine from 10, smallest Life sawtooth is probably few dozens cells at least. The challenge is obliviously to have a rule with small and "clean" sawtooth. This is the advantage of designed rules, one can "optimize" the rule to work nicely for certain purpose.

[fluffykitty]

This is the advantage of designed rules, one can "optimize" the rule to work nicely for certain purpose.

Okay, I get it.

why you can't just add symmetry to your current rule

Well symmetry removes degree of freedom, which requires more "tricks" embedded into the rules. The current rule will just mess up if you add rotation symmetry, and it's natural, because some special cases which were only in certain orientations in no symmetry rule, will be much more common.

Well, where does your rule get messed up? (My rule will obviously get messed up because my signals do not have tails.)

[simsim314]

Well for starters the "2" state is expandes into two directions (left and right). If you use symmetry it would expand up and down, so the growing puffer will not work.

Now I'm not saying it would be hard to solve all the issues, it's just harder.

[fluffykitty]

Well I made a 4 state rule with rotate4 symmetry based on your rule...but that doesn't count right? I think it's impossible to make a symmetric 3-state "limited sawtooth" rule or a 4-state rule with higher symmetry. Basically I changed the state of the puffer and the puffer interaction to state 3. I also had to add some cleanup rules. Anyway here's the rule:
Sawtooth4State.rule:

Code: Select all

@RULE Sawtooth4State

@TABLE
n_states:4
neighborhood:Moore
symmetries:rotate4

#particle + reflector + stable unit
2,0,0,0,0,0,0,1,0,1
1,0,0,2,0,0,0,0,0,0
0,0,0,0,0,0,0,2,0,2
2,2,2,2,0,0,0,0,0,2
2,2,0,0,0,0,0,2,2,2
2,0,0,0,0,2,2,2,0,2
2,0,0,2,2,2,0,0,0,2
0,0,2,0,0,0,0,2,0,2
0,2,2,0,0,0,0,2,0,1
2,0,2,1,0,0,0,0,0,1
1,2,2,0,0,0,0,2,0,0
0,0,0,2,0,0,0,0,0,2
1,0,2,0,0,0,0,2,0,0
2,0,0,1,0,0,0,0,0,1
1,0,0,0,0,0,0,2,0,0

#spaceship
3,0,0,0,1,1,0,0,0,0
3,1,1,0,0,0,0,0,0,0
0,0,0,3,1,0,0,0,0,3
0,0,3,1,3,0,0,0,0,3
0,0,1,3,0,0,0,0,0,3
3,3,0,1,0,3,0,0,0,1

#delete puff
0,0,0,2,0,0,0,1,0,2
1,0,0,2,0,0,0,1,0,2
2,0,0,1,0,0,0,1,0,1

#reflect puffer
0,1,2,0,0,0,0,3,1,1
0,1,0,0,0,0,0,1,1,3
1,0,0,1,3,1,0,1,0,0
1,1,1,3,0,0,0,0,1,0
3,1,0,0,0,0,0,1,1,0
0,0,0,0,0,0,3,1,0,2

#delete sparks
3,0,3,0,0,0,0,0,0,0
3,2,0,0,0,0,3,0,1,0
1,0,0,2,3,0,0,0,0,0
2,0,0,0,0,3,0,1,0,1
0,0,0,0,0,0,3,2,0,2

Sawtooth4State.rle:

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x = 14, y = 14, rule = Sawtooth4State
4.CAC$5.A2$5.A$5.B7.C$9.BA.2A$6.2B5.C$C5.2B$2A.AB$C7.B$8.A2$8.A$7.CAC
!

[fluffykitty]

Here's a 5 state rotate4reflect rule:
Sawtooth5State.rule:

Code: Select all

@RULE Sawtooth5State

@TABLE
n_states:5
neighborhood:Moore
symmetries:rotate4reflect

#particle + reflector + stable unit
2,0,0,0,0,0,0,1,0,1
1,0,0,2,0,0,0,0,0,0
0,0,0,0,0,0,0,2,0,2
2,2,2,2,0,0,0,0,0,2
2,2,0,0,0,0,0,2,2,2
2,0,0,0,0,2,2,2,0,2
2,0,0,2,2,2,0,0,0,2
0,0,2,0,0,0,0,2,0,2
0,2,2,0,0,0,0,2,0,1
2,0,2,1,0,0,0,0,0,1
1,2,2,0,0,0,0,2,0,0
0,0,0,2,0,0,0,0,0,2
1,0,2,0,0,0,0,2,0,0
2,0,0,1,0,0,0,0,0,1
1,0,0,0,0,0,0,2,0,0

#spaceship
3,0,0,0,1,1,0,0,0,0
3,1,1,0,0,0,0,0,0,0
0,0,0,3,1,0,0,0,0,3
0,0,3,1,3,0,0,0,0,3
0,0,1,3,0,0,0,0,0,3
3,3,0,1,0,3,0,0,0,1

#delete puff
0,0,0,2,0,0,0,1,0,2
1,0,0,2,0,0,0,1,0,2
2,0,0,1,0,0,0,1,0,1

#reflect puffer
0,1,2,0,0,0,0,3,1,1
0,1,0,0,0,0,0,1,1,4
1,1,4,1,4,1,0,1,0,0
1,1,1,4,0,0,0,0,1,0
4,1,0,0,0,0,0,1,1,0
0,0,0,0,0,0,4,1,4,2

Sawtooth5State.rle:

Code: Select all

x = 10, y = 10, rule = Sawtooth5State
CAC$.A2$.A$.B2$2.2B$2.2B5.C$5.BA.2A$9.C!