Skip to content
[alpha!] An advanced cellular-automaton-specification language that transpiles to Golly's.
Branch: master
Clone or download
Fetching latest commit…
Cannot retrieve the latest commit at this time.
Type Name Latest commit message Commit time
Failed to load latest commit information.

CA rules “in a nutshell”
A transpiler from a reimagined Golly ruletable language to the traditional format. See examples/ for examples, and if none of this makes any sense to you and you aren't sure how you got here, check out the layman's README.



  1. Download & install Python 3.6 or higher (support for < 3.6 hopefully coming soon)
  2. Either:
    1. Execute the terminal command pip install -U git+git:// (or whichever of the pip command's variations works for you; you may need to try python -m pip install, python3 -m pip install, on Windows py -m pip install, ...) to install via pip directly,
    2. OR git clone this project, then cd to its directory and execute pip install -U . (using the correct one of the pip install variations discussed above)
  3. Write your own "nutshell" rule file, then continue with the Usage section below.


The pip install will add a command nutshell-ca for use in terminal. If this for any reason does not work for you, you may instead either:

  1. Run python -m nutshell instead of nutshell-ca, or
  2. git clone Nutshell as in step 2.ii above, and then run from its root directory as a substitute for nutshell-ca.
$ nutshell-ca transpile [infile] [outdir] [-v | -q | -s | -c | -p | -t | -f]
(alternatively, `nutshell-ca t ...')

The output file will be written to outdir with a .rule extension and the same filename as infile.
Supported flags, though there's more info in --help (note that -v and -q can come either after or before the keyword transpile/t with no difference):

  • -v: Verbose. Can be repeated up to four times, causing more info to be displayed each time.
  • -q: Quiet. Opposite of the above, but only has one level.
  • -s: Source. Writes each Nusthell @TABLE line, as a comment, above the line(s) it compiles to in the final ruletable output. (If the compiled line is from an auxiliary-transition specifier, the specifier is printed instead along with its line number as normal.)
  • -c: Preserve comments. Causes comments in the Nutshell's @TABLE to be copied into the final output as faithfully as possible (i.e. as closely as possible to their original positions).
  • -t [HEADER]: Change the "COMPILED FROM NUTSHELL" header that is added by default to transpiled rules. (If -t is given no argument the header will be removed)
  • -f TRANSITION: Find a certain transition defined within a table section; requires, of course, that the rule have a @TABLE segment to search within. If a certain cell isn't behaving the way it's supposed to, you can -f the transition it's undergoing, and nutshell will find the offending transition for you (rather than you having to guess at what you typo'd).
    Transition should be given in the standard Golly form C,N,...,C' -- that is, state of the current center cell, then its neighborhood, and finally the state it transitions into on the next tick.
    Use * and ? as "any state" wildcards, difference being that ? will tell you what state(s) can be used in its position.
    Old example here!

Glossary of Nutshell-specific terms

  • variable: Either a literal statelist or a name referring to one.
  • expression: Anything that resolves to a statelist: statelists themselves, varnames, and/or operations.
  • statelist (or state-list, state list): An ordered sequence of cellstates or expressions, written literally. This is referred to as a "variable" in Golly, but in Nutshell it's more important to distinguish it from the prior terms.
  • directive: A declaration following the form name: value that describes something about a ruletable.
  • term: One individual element of a transition napkin.
  • napkin (or transition napkin): Refers to the cells in another cell's neighborhood including each one's state. In contrast, the term "neighborhood" refers only to the positions of these cells. (Originally coined by Conwaylife forum member 83bismuth38, with the long form "bowling napkin", to refer to a table that visualizes all possible transitions in a given neighborhood; a misconstrual of this coinage led to the term's Nutshell sense.)

What's new


First off: no directive is mandatory in Nutshell. Here is each directive's default value (i.e. the value it's initialized to before @TABLE is parsed):

  • neighborhood: Moore
  • symmetries: none
  • states: ?

Two things to note regarding the final item: first, that the n_states directive has been changed to states, and second that it accepts a value of ?, which tells Nutshell to infer the amount of cellstates in a rule by checking the maximum cellstate value referred to -- be it in a statelist, constant declaration, or a literal number in a transition napkin. This means that the writer needn't bother keeping track of how many cellstates a rule uses, and because ? is states's default value, it also means that a rule doesn't have to specify states: at all.

Additionally, all directives ignore whitespace in their values -- so one may write, say, symmetries: rotate 4 or neighborhood: von Neumann. The symmetries directive can take a Python import path for custom symmetry types, and the neighborhood directive a series of compass directions for a custom neighborhood; these will be elaborated upon later on.

# Nutshell
states: 5
symmetries: rotate4 reflect
neighborhood: von Neumann
# Golly
neighborhood: vonNeumann
n_states: 5
symmetries: rotate4reflect

Lastly, the symmetries directive can be used multiple times within a file, allowing the writer to switch symmetries partway through a rule. During transpilation, differently-symmetried transitions will be expanded into the "lowest" (least-expressive) Golly symmetry type specified overall. (There is also, unlike in Golly, no enforced ordering of the neighborhood and symmetries directives; either can come before the other.)


Semicolons are allowed alongside commas to separate different terms, and as a visual aid their use as a "final" separator (that is, separating a transition's napkin from its resultant cellstate) is strongly encouraged.

# Nutshell
neighborhood: von Neumann

0, 1, 2, 3, 4; 5
# Golly
0, 1, 2, 3, 4, 5

Individual cellstates of a transition may be prefixed with a compass direction for clarity, and a range of compass directions can be indicated using double..dots; this can displace repetition of a given cellstate.

# Nutshell
neighborhood: von Neumann

0, N 1, E..S 3, W 1; 4
# Golly
0, 1, 3, 3, 1, 4

Additionally, if all given terms of a transition have a compass-direction tag, any omitted ones will be filled in with the variable any (introduced below). Note that, to ensure intent, this is only valid if there is not a single term given without a compass direction.

# Nutshell
neighborhood: von Neumann

0, N 1, S 2; 3
# Golly
neighborhood: vonNeumann

0, 1, any.0, 2, any.1, 3

Transitions, whose terms are listed in clockwise order, by default use the Golly-canonical ordering -- usually C, N, ..., C' (center cellstate, northern cellstate, ..., new center) -- but they are allowed to start on a different compass direction if explicitly specified.

# Nutshell
neighborhood: von Neumann

0, E..S 3, W..N 1; 4
# Golly
0, 1, 3, 3, 1, 4

Under certain symmetries, however, compass directions have no meaning -- these symmetry types utilize a different, tilde-based shorthand. Nutshell's implementation of Golly's permute symmetry uses it like so:

# Nutshell
symmetries: permute

0, 1 ~ 3, 2 ~ 5; 9   # Specifying amount of each term (three 1s and five 2s)
0, any ~ 2, 2, 6; 9  # Specifying some amounts (two "any"s) and leaving the rest to be distributed evenly (three 2s, three 6s)
0, 1, 2; 9           # Specifying nothing and letting all terms be distributed evenly (four 1s, four 2s)
any, any; 0          # Ditto above (8 "any"s)
# Golly
0, 1, 1, 1, 2, 2, 2, 2, 2, 9
0, any.0, any.1, 2, 2, 2, 6, 6, 6, 9
0, 1, 1, 1, 1, 2, 2, 2, 2, 9
any.0, any.1, any.2, any.3, any.4, any.5, any.6, any.7, any.8, 0

If the "unspecified" terms cannot be distributed perfectly into the table's neighborhood, precedence will be given to those that appear earlier; 2, 1, 0 under Moore, for instance, will expand into 2,2,2,1,1,1,0,0, but 0, 1, 2 will expand into 0,0,0,1,1,1,2,2.


All variable names are unbound, always, because needing to define eight separate "any state" vars is ridiculous.

# Nutshell
variable = (1, 2, 3, 4)

0, variable, variable, 0, 1, 2, 0, 2, 0; 1
# Golly
var variable.0 = {1, 2, 3, 4}
var variable.1 = variable.0

0, variable.0, variable.1, 0, 1, 2, 0, 2, 0, 1

That's not to say, however, that there is no concept of binding variables in Nutshell! Rather, it's that the variable names themselves are not intrinsically bound by anything. Nutshell's idea of binding is explained later on.

Also allowed is the use of state-list literals directly in transitions as 'on-the-spot' variables; no need to define them prior.

# Nutshell
(0, 1, 2), 3, (4, 5), 6, 7, 8, 9, 0, 1; 10
# Golly
var _random_name_A.0 = {0, 1, 2}
var _random_name_B.0 = {4, 5}

_random_name_A.0, 3, _random_name_B.1, 6, 7, 8, 9, 0, 1, 10

The varnames "live" and "any" are predefined in Nutshell, assigned respectively to a rule's nonzero cellstates and all of its cellstates.

# Nutshell
states: 5

a = live
b = any
# Golly
var a.0 = {1, 2, 3, 4}
var b.0 = {0, 1, 2, 3, 4}

As in Golly, variables do not nest; placing a variable or state-list inside another simply unpacks it thereinto.

Variable names

Varnames are alphanumeric (and case-sensitive) with three exceptions:

  • Underscores are allowed.
  • The first character of the name must be alphabetical.
  • The name as a whole cannot match one of the eight compass directions: N, E, S, W, NE, SE, SW, NW.


Variables can contain or be represented by "operations", with the binary operators *, -, and <</>> or the unary operators - and --.

These operations also don't need to be assigned to variable names beforehand. All of the expressions below are perfectly valid if used directly in a transition, just like the "on-the-spot" state-lists mentioned above.

Note: The binary operators are left-associative. Precedence rules can be skirted by placing operations in their own single-element statelists, like (any-3)*2.

An exclamation mark followed by an expression (as a whole line) will cause the expression's result to be printed: !(1, 2, 3)-(3, 4) will print (1, 2), for instance, and !any will print the contents of variable any. This can help in debugging complex, multi-operation variable expressions if need be.

n * m ("Multiplication")

Not commutative. Has the highest precedence.

# Nutshell
a = (1, 2) * 2  # variable 'times' integer (repeats the variable m times)
b = 2 * (1, 2)  # cellstate 'times' variable (repeats the cellstate to match the variable's length)
c = 0 * 3       # cellstate 'times' integer (repeats the cellstate m times)
d = b * 3 * 2   # operations can be chained if needed
e = (2*b, 1*(1,2), 0*3)  # ...and, like all expressions, can be placed inside a literal statelist
# Golly
var a.0 = {1, 2, 1, 2}
var b.0 = {2, 2}
var c.0 = {0, 0, 0}
var d.0 = {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2}
var e.0 = {2, 2, 2, 2, 1, 1, 0, 0, 0}

n - m ("Subtraction")

Acts as a difference operation does between two sets. Has the lowest precedence.

# Nutshell
a = (1, 2, 3, 1) - 1    # variable 'minus' cellstate (removes the cellstate from the variable)
b = (1, 2, 3) - (2, 3)  # variable 'minus' variable (removes common elements from the former)
c = (3, 4, 5) - 5 - 4   # chaining again
d = (a-2, (3, 4)-3)     # again, operations can be placed inside statelists
# Golly
var a.0 = {2, 3}
var b.0 = {1}
var c.0 = {3}
var d.0 = {3, 4}

n >> m, n << m ("Rotation")

Rotates a statelist in either direction. m is modulo'd by the statelist's length.

# Nutshell
a = (1, 2, 3)
b = a << 1

0, N..W 0, NW a; [NW: a >> 1]
# Golly
var a.0 = {1, 2, 3}
var b.0 = {2, 3, 1}

0, 0, 0, 0, 0, 0, 0, 0, 1, 3
0, 0, 0, 0, 0, 0, 0, 0, 2, 1
0, 0, 0, 0, 0, 0, 0, 0, 3, 2

Be aware that ordering is unlikely to be reflected / preserved in Golly output, because variables are converted into Python set objects just before being written to the Golly rulefile; this means that it's just as likely for the above to result in var a.0 = {1, 2, 3} and var b.0 = {1, 2 3}. The Nutshell-enforced ordering can always be observed, however, in the result of an operation (like mapping) that spreads a variable out over multiple transitions.

-n, --n ("Negation")

These are shorthand for, respectively, live-n and any-n. Has higher precedence than "subtraction".

# Nutshell
states: 4

a = -2
b = --2

c = live-2
d = any-2
# Golly
var a.0 = {1, 3}
var b.0 = {0, 1, 3}

var c.0 = {1, 3}
var d.0 = {0, 1, 3}

They can be chained indefinitely as well; -----3 is a syntactically-valid expression that will be parsed as --(--(-3)), as is some_varname-------5 (subtracting --(--(--5)))). This is probably not too useful in practice, but... you never know.


Though not exactly an operation, a range of cellstates can be expressed as two numbers (lower and upper bound) separated by double..dots, optionally with a step greater than 1.

# Nutshell
a = (3..6)         # lower..upper
b = (0, 2..5, 10)  # ranges and normal states can be interspersed normally
c = (1, 2+4..10)   # step+lower..upper
# Golly
var a.0 = {3, 4, 5, 6}
var b.0 = {0, 2, 3, 4, 5, 10}
var c.0 = {1, 4, 6, 8, 10}

Ranges differ from the expressions described above in that they cannot be used "bare" -- you always have to surround them with parentheses or curly brackets as shown in a = (3..6) as they're only allowed within a statelist.


In a Golly table, variables are what we might call "name-bound": a variable name used once in a transition can refer to any of the states it comprises, but from then on that same name can only refer to the first state it matched, like how back-referring to a regex group matches the exact same text rather than applying the group's pattern anew. In other words, with var a={1,2}, the sequence a,a can match 1,1 and 2,2 but not 1,2 or 2,1, because the name a is bound to the first cellstate it matches.

This behavior is intentional, but it comes with a side-effect: if the writer should wish for the above sequence to match 1,2 or 2,1 without any of the binding, then they must define two separate variables, var a={1,2} and var b=a, writing the sequence as a,b.

This doesn't seem bad at all on a small scale. It's convenient to be able to do it both ways, after all. However, in nearly any large project, this forces each variable definition to be duplicated up to nine times (depending on the neighborhood, of course) which gets messy and tedious to keep track of, making it an easy source of headaches and bugs and often both.

Nutshell's key innovation (and the only supra-syntactical thing, in fact, that it mandates be done differently than in Golly's @TABLE) is in noting that the name of a variable doesn't need to hold any particular meaning, only its value within a given transition. Thus, rather than binding to a variable's name, we can simply use... some other way of referring to nothing except the value it holds at a given point.


This is handled in a straightforward manner by using compass directions as "indices" of a transition. To bind to a previous variable, just refer to the compass direction it appeared at by wrapping it in [brackets] (and by referring to the origin cellstate as [0] since, being at the center, it has no nameable compass direction):

# Nutshell
any, any, any, [0], [NE], 0, 1, 3, 2; [N]
any, N..E [0], SW..W any, 0; [W]
(1, 2), N..NW 0; [0]
# Golly
var _random_name.0 = {1, 2}

any.0, any.1, any.2, any.0, any.2, 0, 1, 3, 2, any.1
any.0, any.0, any.0, any.0, any.1, any.2, any.3, any.4, 0, any.4
_random_name.0, 0, 0, 0, 0, 0, 0, 0, 0, _random_name.0

Note that in symmetry types where compass directions have no meaning -- the same symmetry types mentioned in Transitions, in fact, that use ~ as a shorthand rather than specifying compass-direction ranges -- Nutshell enforces the use of numbers, not compass directions, to bind to. For instance, under permute symmetry, the Golly transition 0, some_var, 0, 0, 0, 0, 0, 0, 0, some_var is replicated as 0, some_var ~ 1, 0; [1] and not 0, some_var ~ 1, 0; [N].

Multiple successive bindings to a previous term, as long as it is an expression, can be compressed like so:

# Nutshell
neighborhood: von Neumann

0, N..W [any]; 1
# Golly
0, any.0, any.0, any.0, any.0, 1
# Nutshell
symmetries: permute
neighborhood: von Neumann

0, [(1, 2)] ~ 3, [any]; [1]
# Golly
var _random_name.0 = {1, 2}

0, _random_name.0, _random_name.0, any.0, any.0, _random_name.0

The first transition is equivalent to 0, any, E..W [N]; [N] and the other to 0, (1, 2) ~ 1, [1] ~ 2, any ~ 1, [3]; [1].


Now that we've introduced binding by compass-direction index rather than by name, we can extend the concept into a second type of reference: mapping one variable to another. For example, "mapping" the variable (0, 1, 2) to the variable (2, 3, 4) says if the former is 0 to return 2, if 1 then to return 3, and if 2 then to return 4; this single mapping can thus replace what would otherwise require a separate transition for each of 0->1, 1->2, and 3->4. The syntax is [compass direction: expression], like an extension to the binding syntax:

# Nutshell
a = (2, 3)
b = (4, 1)

0, (1, 2), E..NW 0; [N: (3, 4)]  #1
a, a, [N], [0], E..W 0, NW [0: b]; 10  #2
(1, 2, 3), N..NW 0, [0: (a, 1)]  #3
# Golly
var a.0 = {0, 1}

0, 1, 0, 0, 0, 0, 0, 0, 0, 3  #1
0, 2, 0, 0, 0, 0, 0, 0, 0, 4  #1

2, a.0, a.0, 2, 0, 0, 0, 0, 0, 4, 10  #2
3, a.0, a.0, 3, 0, 0, 0, 0, 0, 1, 10  #2

1, 0, 0, 0, 0, 0, 0, 0, 0, 2  #3
2, 0, 0, 0, 0, 0, 0, 0, 0, 3  #3
3, 0, 0, 0, 0, 0, 0, 0, 0, 1  #3

A statelist used in a mapping can end with an ellipsis, ..., which indicates that any remaining cellstates are to be mapped to the last value:

# Nutshell
(1, 2, 3, 4, 5), [0: (3, 5, ...)], NE..NW 0; 1
# Golly
var _random_name.0 = {2, 3, 4, 5}

1, 3, 0, 0, 0, 0, 0, 0, 0, 1
_random_name.0, 5, 0, 0, 0, 0, 0, 0, 0, 1

If a variable is too small to map to, an error will be raised that can be rectified by either (a) filling it out with more cellstates, or (b) using the ... as above. However, if the "map-to" is larger than its "map-from", extraneous values will simply be ignored.

References are in essence single cellstates, so they can be used anywhere a cellstate would -- not just as their own whole transition state. This means references can be used as operands of the *, -, & -- operators and as cellstates in variables (including in statelists of mappings, meaning they can be nested indefinitely).

# Nutshell
neighborhood: von Neumann
states: 6

(1, 2), --[0], (3, 4, 5)-[0: (3, 4)], ([0: (4, 3)], 5); [0: ([N], [E])]
# Golly
var _random_name_A.0 = {0, 2, 3, 4, 5}
var _random_name_B.0 = {0, 1, 3, 4, 5}
var _random_name_C.0 = {3, 5}
var _random_name_C.1 = _random_name_C.0
var _random_name_D.0 = {4, 5}
var _random_name_D.1 = _random_name_D.0

1, _random_name_A.0, _random_name_C.0, _random_name_C.1, _random_name_A.0; 0
2, _random_name_B.0, _random_name_D.0, _random_name_D.1, _random_name_D.0; 0

Auxiliary transitions

In general, the motion of a moving cell can only be described in Golly through two disconnected steps: first, a cell dies, and an independent, dead cell is born in the next tick with the other's cellstate. This, though logical in the context of a cellular automaton, is hard to describe as intuitive to the human writer; Nutshell for this reason provides a way of describing auxiliary transitions affecting other cells in the neighborhood than the central one, sharing as much of the same napkin as possible.

Auxiliaries are set off from the main transition with an arrow, and each individual auxiliary-transition specifier can take one of four forms. First, the simplest syntax compass direction:cellstate indicates that a single cell of state cellstate should be birthed in the specified direction:

# Nutshell
neighborhood: von Neumann

0, N 1, E 2, S 3, W 4; 5 -> N:3  S:2  # Birth a state-3 cell to the north and a state-2 cell to the south
# Golly
0, 1, 2, 3, 4, 5
1, any.0, any.1, 0, any.2, 3
3, 0, any.0, any.1, any.2, 2

N:3 says to birth a state-3 cell to the north; the northern cell here was originally in state 1 and the center cell in state 0. The transition implied by this auxiliary, then, is that any state-1 cell with a state-0 cell to its south should turn into state 3 come the next generation, and similarly, S:2 states that any state-3 cell to whose north is a state-0 cell should become of state 2.

More of the transition napkin is shared in fuller neighborhoods:

# Nutshell
0, 1, 2, 3, 4, 5, 6, 7, 8, 9; 10 -> N:3  NE:0
# Golly
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
1, any.0, any.1, 2, 3, 0, 7, 8, any.2, 3
2, any.0, any.1, any.2, any.3, 3, 0, 1, any.3; 0

Just to run through what's happening, let's take a graphical look at the main cell's Moore napkin:

8 1 2
7 0 3
6 5 4

And these are the Moore neighborhoods of a cell A and the cell to its north B, where @ represents a shared cell:

b b b
@ B @
@ A @
a a a

Superimposing the above napkin and replacing the @ symbols gets us:

b b b
8 B 2
7 0 3
a a a

So in the N:3 auxiliary, the cells shared between the main cell and the cell to its north in clockwise order are 2, 3, 0 (the A cell itself), 7, and 8. These values are reflected in the second Golly-output transition, and it's a similar process for the NE:0 auxiliary --

  b b b          b b b
a @ B b        a 1 B b
a A @ b        a 0 3 b
a a a          a a a  

-- where the shared cells in B's neighborhood are 3, 0 (the A cell itself), and 1, as shown in the third Golly transition above.

As a simple practical example, the transition 1, N..NW any; 0 -> NW:1 describes (under symmetries: none) a signal that travels to its northwest at all costs, or (under another set of symmetries, say symmetries: rotate4) a cell that acts as a two-dimensional spacefilling replicator.

A second type of auxiliary takes the form compass direction[compass direction] and, as the brackets suggest, is analogous to a binding. It indicates that the cellstate that appeared toward the second compass direction should be birthed toward the first:

# Nutshell

# compass directions E and S shown for clarity but, of course, not required
1, 0, 0, E (1, 2, 3), 0, S 4, 0, 0, 0; 2 -> S[E]
# Golly
var _random_name.0 = {1, 2, 3}

1, 0, 0, _random_name.0, 0, 4, 0, 0, 0, 2
4, 1, _random_name.0, 0, any.0, any.1, any.2, 0, 0, _random_name.0

The transition napkin is copied in the exact same manner as described before, but the resultant cellstate (_random_name.0) is a binding rather than a single state. An error will be raised if the cells in each compass direction specified do not share any neighbors.

An example: (1, 2, 3), N..NW any; 0 -> S[0] E[E] says that cells of state (1, 2, 3) should be sent south (the [0] in S[0] refers to the input state) and that, when this happens, the cell to their east should stay as is (for instance, to override a later transition).

The third type of auxiliary, given the relationship established above between bindings and mappings, is a natural extension of the previous binding-like form into what's essentially a mapping. It uses the syntax compass direction[compass direction: expression]:

1, 0, 0, E (1, 2, 3), 0, S 4, 0, 0, 0; 2 -> S[E: (5, 6, 7)]
var _random_name.0 = {1, 2, 3}

1, 0, 0, _random_name.0, 0, 4, 0, 0, 0, 2  # main transition
4, 1, 1, 0, any.0, any.1, any.2, 0, 0, 5   # S:5
4, 1, 2, 0, any.0, any.1, any.2, 0, 0, 6   # S:6
4, 1, 3, 0, any.0, any.1, any.2, 0, 0, 7   # S:7

Anything valid in a mapping statelist is also valid here (references too), with one addition: an underscore, _, says not to make an auxiliary transition at all for its cellstate.

# Nutshell
1, 0, 0, E (1, 2, 3), 0, S 4, 0, 0, 0; 2 -> S[E: (_, 6, 7)]

1, 0, 0, E (1, 2, 3), 0, S 4, 0, 0, 0; 2 -> S[E: (5, _, ...)]  # Underscores can be extended with the ellipsis as well
# Golly
var _random_name.0 = {1, 2, 3}

1, 0, 0, _random_name.0, 0, 4, 0, 0, 0, 2  # main transition
4, 1, 2, 0, any.0, any.1, any.2, 0, 0, 6   # S:6
4, 1, 3, 0, any.0, any.1, any.2, 0, 0, 7   # S:7

1, 0, 0, _random_name.0, 0, 4, 0, 0, 0, 2  # main transition
4, 1, 1, 0, any.0, any.1, any.2, 0, 0, 5   # S:5

Finally, as a shorthand for this last form in cases where both compass directions are the same, one can simply write compass direction[expression] -- S[(1, 2, 3)], for instance, will be understood as S[S: (1, 2, 3)].

Precedence and "hoisting"

As you may have noticed, auxiliary transitions are output in the order of their Nutshell specifiers. This plays into Golly's transition-precedence rules, where the first matching transition from the top down for a given napkin is selected, meaning that earlier transitions always override later ones -- likewise, an auxiliary will (should an appropriate situation arise) always override any that follow it.

In some cases, auxiliaries will need to override the main transition and not just each other, meaning that (unlike in the examples above) they'll have to be output before it. This can be indicated using the arrow => rather than ->, with an otherwise-thoroughly-identical syntax:

# Nutshell
0, 1, 2, 3, 4, 5, 6, 7, 8, 9 => S:1

0, (0, 1), 2, 3, 4, 5, 6, 7, 8, 9 => S:1  E[N] -> N:0  # can also be ` -> N:0 => S:2  E[N]`
# Golly
var _random_name.0 = {1, 2}

5, 0, 3, 4, any.0, any.1, any.2, any.3, 6, 7, 1  # S:1
0, 1, 2, 3, 4, 5, 6, 7, 8, 9  # main transition

5, 0, 3, 4, any.0, any.1, any.2, any.3, 6, 7, 1  # S:1
3, 2, any.0, any.1, any.2, 5, 6, 0, _random_name.0, _random_name.0  # E[N]
0, _random_name.0, 2, 3, 4, 5, 6, 7, 8, 9  # main transition
_random_name.0, any.0, any.1, 2, 3, 0, 7, 8, any.2, 0  # N:0


Auxiliaries can be assigned a different set of symmetries than their main transition:

# Nutshell
symmetries: none

0, NE 0, E..N any; 1 -> E:3  rotate4(NE[E: (1, 2, 3, 4, 5)]  N:0  NE[N])
# Golly
0, any.0, 0, any.1, any.2, any.3, any.4, any.5, any.6, 1  # main transition

any.0, 0, any.1, any.2, any.3, any.4, any.5, 0, any.6, 3  # E:3

any.0, 0, any.1, 0, any.2, any.3, any.4, any.5, any.6, 0  # N:0
any.0, any.1, any.2, any.3, any.4, 0, any.5, 0, any.6, 0  # N:0
any.0, any.1, any.2, 0, any.3, 0, any.4, any.5, any.6, 0  # N:0
any.0, 0, any.1, any.2, any.3, any.4, any.5, 0, any.6, 0  # N:0

0, any.0, 0, any.1, any.2, any.3, any.4, any.5, any.6, any.0  # NE[N]
0, any.0, any.1, any.2, 0, any.3, any.4, any.5, any.6, any.2  # NE[N]
0, any.0, any.1, any.2, any.3, any.4, 0, any.5, any.6, any.4  # NE[N]
0, any.0, any.1, any.2, any.3, any.4, any.5, any.6, 0, any.6  # NE[N]

Symmetry-specifier groups cannot be nested.

...handy as that is, though, it's still missing something. Consider the following transition:

# Nutshell
states: 5
neighborhood: von Neumann

symmetries: none  # Forcing expansion into `none` symmetry
symmetries: rotate4

0, live, 2, 3, 4; [N] -> N[N]
# Golly

# 0, live, 2, 3, 4; [N]
0, 2, 3, 4, live.0, live.0
0, 3, 4, live.0, 2, live.0
0, 4, live.0, 2, 3, live.0
0, live.0, 2, 3, 4, live.0
# N[N]
live.0, 0, any.0, any.1, any.2, live.0
live.0, any.0, any.1, 0, any.2, live.0
live.0, any.0, 0, any.1, any.2, live.0
live.0, any.0, any.1, any.2, 0, live.0

Though the N[N] auxiliary appears to be saying "keep to the north whatever's there", what it actually says is "keep the live cell where it is, even though it won't always be to the north thanks to rotate4". This may seem to be rectifiable by placing the N[N] under none symmetry, like so:

# Nutshell
states: 5
neighborhood: von Neumann

symmetries: none
symmetries: rotate4

0, live, 2, 3, 4; [N] -> none(N[N])
# Golly

# 0, live, 2, 3, 4; [N]
0, 2, 3, 4, live.0, live.0
0, 3, 4, live.0, 2, live.0
0, 4, live.0, 2, 3, live.0
0, live.0, 2, 3, 4, live.0
# N[N]
live.0, any.0, any.1, 0, any.2, live.0

...but what that actually results in, as shown in the second codeblock, is the auxiliary's being applied in the exact same fashion, just only to the north. To actually change this behavior, include an exclamation mark after the symmetry type's name:

# Nutshell
states: 5
neighborhood: von Neumann

symmetries: none
symmetries: rotate4

0, live, 2, 3, 4; [N] -> none!(N[N])
# Golly

# 0, live, 2, 3, 4; [N]
0, 2, 3, 4, live.0, live.0
0, 3, 4, live.0, 2, live.0
0, 4, live.0, 2, 3, live.0
0, live.0, 2, 3, 4, live.0
# N[N]
live.0, any.0, any.1, 0, any.2, live.0
2, any.0, any.1, 0, any.2, 2
3, any.0, any.1, 0, any.2, 3
4, any.0, any.1, 0, any.2, 4

This indicates to Nutshell that the auxiliary should remain "stationary" while the main transition's symmetries are applied. If it were written here as rotate4!(N[N]) instead of none!(N[N]), the Golly output would contain a rotate4 expansion of each of the final four lines.

Inline-rulestring transitions

In addition to those normal Golly-style transitions, Nutshell allows the use of rulestring segments (either Hensel-style or totalistic) to specify a transition napkin.

These transitions' syntax is initial, <rulestring / foreground state(s) / background states>; resultant. Consider the isotropic non-totalistic rule tlife:

# Nutshell
0, <3 / 1 / 0>; 1
1, <2-i34q / 1 / 0>; 1

symmetries: permute
any, any; 0

Its output file is a touch too big to paste, but it:

  1. Interprets 0, <3 / 1 / 0>; 1 as "a state-0 cell surrounded by 3 state-1 cells (and otherwise state-0 cells) will turn into state 1," then expands this into the permute-symmetry transition 0, 1, 1, 1, 0, 0, 0, 0, 0, 1.
  2. Interprets 1, <2-i34q / 1 / 0>; 1 as "a state-1 cell surrounded by a configuration matching 2-i, 3, or 4q of state-1 cells (and state-0 cells otherwise) will remain state 1," then expands this into the appropriate rotate4reflect-symmetry transitions.
  3. Proceeds as though the user had typed these expanded transitions out themself.

Each of the inline-rulestring lines comes with an implicit "transition-local" switch to rotate4reflect symmetry (if using a Hensel-exclusive rulestring with letters and whatnot) or to permute symmetry (if using a totalistic rulestring), but other transitions are not affected! This means that, in the Life table, the transition any, N..NW any; 0 is actually still under symmetries: none and will thus cause the whole table to be normalized into the same; the tlife table has symmetries: permute to prevent this. In general, an inline-rulestring transition can be read as being preceded by a switch to either symmetries: rotate4reflect or symmetries: permute (whichever is appropriate) and being followed by a switch back to the previous symmetries.

For another example, WireWorld could be expressed as follows:

# Nutshell
@NUTSHELL WireworldTest
: {Head} Electron head
: {Tail} Electron tail
: {Wire} Conductor/wire

0080FF: Head
FFF: Tail
FF8000: Wire

symmetries: permute
(Head, Tail), any; [0: (Tail, Wire)]
Wire, <12 / Head / (0, Tail, Wire)>; Head

...which takes advantage of some things described below, viz. the @NUTSHELL & @COLORS segments.

References can be used here as well, but they look a little bit different: rather than referring to a compass direction, they must refer to either 0 , BG, or FG -- respectively, the input, background, or foreground state(s).
For instance, the resultant state of 0, <23 / (0, 1) / (1, 2, 3)>; [FG: (3, 2, 1)] is a mapping from the variable (1, 2, 3); if it were instead [BG], then it would be a binding to the variable (0, 1). (References are valid within the <> section as well, as is the "inline binding" syntax.)
Lastly, the same inline-binding syntax that allows [expression] ~ 5 or N..NW [expression] to be shorthand for, respectively, expression, [1] ~ 4 and N [expression], NE..NW [N] is usable here:

# Nutshell
0, <2 / (1, 2) / 0>; 3
0, <2 / [(1, 2)] / 0>; 3
# Golly
var _a0.0 = {1, 2}

0, _a0.0, _a0.1, 0, 0, 0, 0, 0, 0, 3
0, _a0.0, _a0.0, 0, 0, 0, 0, 0, 0, 3

Note that binding to a Hensel-notation napkin is tricky business, because unlike in a permute-symmetry napkin, positions do matter -- in these cases FG and BG will give you the first available cell from the northmost one, which may not be a fine-enough level of control. In such cases it's probably best not to bind at all to the foreground/background states, but if one must, then compass directions can be used to refer to the cell at that position in a neighborhood's canonical orientation.
Note, this is only an issue with a rotate4reflect-requiring Hensel-notation rulestring, as in 0, <2-i34q / (1, 2) / 0>; [FG]. It is not an issue with a permute-symmetry rulestring as in 0, <23 / (1, 2) / 0>; [FG], and it even is a non-issue with Hensel rulestrings if the bound-to term is guaranteed to be the same cellstate everywhere: <0, 2-i34q / [(1, 2)] / 0>; [FG].


The rulestrings do not strictly have to be Hensel rulestrings -- that is just the default. Placing a modifier after the rulestring will cause it to be interpreted differently. Currently-available modifiers:

  • hensel, which is an alias for the default behavior.
  • !hensel, which turns the rulestring into its complement. <012345-i6 !hensel / 1 / 0> is <5i78 / 1 / 0>
  • force-r4r, which makes <3 force-r4r / 1 / 0> expand into a series of B3 rotate4reflect transitions rather than a single B3 permute transition as with <3 / 1 / 0>. Needed for Brew.ruel, and likely in a lot of cases where a macro needs to apply to some inline-rulestring transitions.
  • b0-odd, which applies Golly's odd-generation B0-rule transformation to the given rulestring. See examples/BeeZero for usage.

These are user-creatable in the exact same manner as symmetries, although the API for this has not yet been made user-friendly.

Custom neighborhoods

The neighborhood directive can be given a comma-delimited list of compass directions rather than a name, which makes the CA use those compass directions (in the listed order) as its neighborhood. Nutshell will then expand all transitions into the smallest encompassing Golly neighborhood.

# Nutshell
neighborhood: N, SE, SW
0, 1, 2, 3; 4
2, N 4, SE 2, SW any; 1
# Golly
neighborhood: Moore

0, 1, any.0, any.1, 2, any.2, 3, any.3, any.4, 4
2, 4, any.0, any.1, 2, any.3, any.4, any.5, any.6, 1

Custom symmetry types

The implementation of the above-mentioned symmetry-switching also allows, conveniently, for nonstandard symmetries to be defined and then simply expanded by Nutshell into one of Golly's symmetry types. Provided by Nutshell is a small "standard library" of sorts that comes with the following:

  • symmetries: nutshell.ExplicitPermute: Permute symmetry, but differs in that it does not attempt to infer the desired amounts of its given terms: if a term is given with no tilde, it is treated as ~ 1 rather than being spread out across the transition like symmetries: permute would do.
  • symmetries: nutshell.AlternatingPermute: Permutational symmetry, like symmetries: permute, but only between every second cell in a napkin. Under the Moore neighborhood, this means that cellstates are permuted between orthogonal neighbors and, separately, between diagonal neighbors; under vonNeumann, that cellstates are permuted between opposing pairs of neighbors; and, under hexagonal, between [N, SE, W] and [E, S, NW].
    This symmetry type supports the tilde-based shorthand in the same manner as symmetries: nutshell.ExplicitPermute, but it only spreads terms out within their permute space (as in, 0, 1, 2; 0 results in the Moore transition 0, 1, 2, 1, 2, 1, 2, 1, 2; 0 because the 1 and 2 are distributed into alternating slots).
  • symmetries: nutshell.Rotate2: Identical to Golly's hexagonal rotate2, but allows Moore and vonNeumann as well.
  • symmetries: nutshell.ReflectVertical: Vertical reflection.
  • symmetries: nutshell.\ReflectDiagonal: Reflection about the NW-SE diagonal axis.
  • symmetries: nutshell./ReflectDiagonal: Reflection about the SE-NW diagonal axis.
  • symmetries: nutshell.XReflectDiagonal: Reflection about both diagonal axes.
  • symmetries: nutshell.ExplicitPermute: Permute symmetries, but there is no automatic expansion of tilde-omitted terms; omission of a tilde here is equivalent to ~ 1. An error will be raised if an incorrect amount of terms results.

In addition, although the API for it is somewhat clunky at present, you as the user are allowed to define your own custom symmetries via Python classes. See documents/ for more detail.


Nutshell's occasional concision, usually by compression of many similar Golly transitions into just a few, can also mean that the user does not get as fine-grained a level of control over those transitions' ordering. Consider, for example, Brew: it and its higher-statecount variants ostensibly have a three-line Nutshell representation, but this representation actually produces the following...

any.0, 1, 1, 1, _a0.0, _a0.1, _a0.2, _a0.3, _a0.4, 1
any.0, 2, 2, 2, _b0.0, _b0.1, _b0.2, _b0.3, _b0.4, 2
any.0, 3, 3, 3, _c0.0, _c0.1, _c0.2, _c0.3, _c0.4, 3

1, 1, 1, _a0.0, _a0.1, _a0.2, _a0.3, _a0.4, _a0.5, 1
2, 2, 2, _b0.0, _b0.1, _b0.2, _b0.3, _b0.4, _b0.5, 2
3, 3, 3, _c0.0, _c0.1, _c0.2, _c0.3, _c0.4, _c0.5, 3

...whereas the real Brew matches the following.

any.0, 1, 1, 1, _a0.0, _a0.1, _a0.2, _a0.3, _a0.4, 1
1, 1, 1, _a0.0, _a0.1, _a0.2, _a0.3, _a0.4, _a0.5, 1

any.0, 2, 2, 2, _b0.0, _b0.1, _b0.2, _b0.3, _b0.4, 2
2, 2, 2, _b0.0, _b0.1, _b0.2, _b0.3, _b0.4, _b0.5, 2

any.0, 3, 3, 3, _c0.0, _c0.1, _c0.2, _c0.3, _c0.4, 3
3, 3, 3, _c0.0, _c0.1, _c0.2, _c0.3, _c0.4, _c0.5, 3

Notice: these are the exact same transitions, only intertwined, and this crucial difference prevents the Nutshell version from behaving as it should.

Nutshell 0.4.0 introduced macros, Python functions invoked from Nutshell that can modify spans of resultant transitions. The weave macro that comes with Nutshell, for example, can be used in Brew.ruel as follows:

From 83bismuth38.

symmetries: permute
states: 4

weave: 1
any, [live] ~ 3, --[1]; [1]
live, [0] ~ 2, --[0]; [0]
weave: \

live, any; [0: (any-1) << 1]

000: 0
F00: 1
0F0: 2
00F: 3

It will operate here on the two lines flanked by weave: directives, ending when the macro is invoked with a backslash (as if that is the end of a block; imagine curly braces from weave: 1 { to weave: \ }). Macros can also be passed additional arguments: here, weave: 1 passes the value 1 to the function behind the macro. (Multiple arguments, if necessary, are separated by whitespace.)

At transpile-time, the weave macro is passed (a) a list of transitions that corresponds to the first codeblock above (having out-of-order transitions), and (b) the value 1 from the weave: 1 invocation. It then returns a new list corresponding to the second codeblock above (with correctly-ordered transitions), and this is what is written to the final output file.

Nested macros are applied innermost first, and all macros must have a macro_name: \ end line or else they will not be run. weave doesn't show it, but macros of course aren't limited to just reordering transitions -- they can also add or remove them as needed.

The current "standard library" of macros currently consists of two:

  • weave: With chunk_size = 1:
    Given a group of Nutshell transitions [a, b, c] producing the Golly transitions [a0, a1, a2, ..., b0, b1, b2, ..., c0, c1, c2, ...], reorder the Golly transitions as [a0,b0,c0, a1,b1,c1, a2,b2,c2, ...] -- in other words, "weaving" groups of transitions together.
    With chunk_size = 2, produces
    [a0,a1,b0,b1,c0,c1, a2,a3,b2,b3,c2,c3, ...]
    And so on for higher chunk_size values. Extraneous transitions (ones that don't divide evenly into chunk_size) are left at the end rather than discarded.
    Note that weave will appropriately order transitions resulting from inline rulestrings, despite their being from the same line.

  • reorder: For when really fine control is necessary. Takes a series of numbers corresponding to the Nutshell transitions covered by this macro, where 1 is the first transition and 2 the second and so on, and reorders the resultant Golly transitions according to their ordering.

    For instance, given a series of numbers 1 1 2 3 1 4 2 and operating over the sequence of Nutshell transitions
    [a, b, c, d, e]
    corresponding to the following set of Golly transitions
    [a0, a1, a2, a3, b0, b1, c0, c1, d0, d1, e0]
    The macro will return:
    [a0, a1, b0, c0, a2, d0, b1, a3, c1, d1, e0]

    Notice how, after the last specified transition (b1), extras are tacked on to the end- in as close to their original order as possible.

    If an input ends with a bracketed sequence of numbers, that sequence is repeated ad infinitum. That is to say that 1 [2 3 4] is interpreted as 1 2 3 4 2 3 4....

See documents/ for details regarding implementation of custom macros.

Non-table-related changes

  • The preferred file extension is .ruel, both a holdover from when this project was named rueltabel and a simple-but-recognizable variant of "rule" to distinguish nutshell files from standard .rule files. This obviously isn't enforced anywhere, however, and may also be subject to change.
  • Comments in every segment (barring @NUTSHELL, where everything after the first word is a comment) start with # and stretch to the end of a line.
  • All segments are optional. Nutshell will in addition transcribe "non-special" segments as is, meaning that a file can have a @RULE segment rather than @NUTSHELL and it will be transcribed into the output file untouched.
  • The other "special" nutshell segments like @TABLE and @ICONS and @COLORS, none of whose names differ from their Golly-format counterparts, will still be ignored if their header is immediately followed by the comment # golly -- either on the same line (after whitespace) or on the very next.

The @NUTSHELL segment

This segment replaces Golly's @RULE. It allows constants, which carry over to and are usable in the @TABLE, @COLORS, and @ICONS segments, to be defined alongside a description of each state. Take the following example:

1: Data
2: Signal over empty space {SIGNAL}
: {DATA_SIGNAL} Signal moving through data
3: {GUN} Gun, releases one signal every other tick
: {GUN_2} "Dormant" gun in between signals


Note the following few things:

  • There is no curly-bracketed {NAME} on the first line, but it does have a number + colon at the start.
  • The second and fourth lines have both a number + colon at the start and a curly-bracketed {NAME}.
  • The third and fifth lines have an initial colon and a bracketed {NAME}, but no number before the colon.

What they mean:

  • There will be no named constant aliased to the cellstate "1", but that state will be 'reserved'. (Stay tuned for this term's definition.)
  • The names SIGNAL and GUN will be usable in later segments as aliases for, respectively, cellstates 2 and 3. The literal numbers 2 and 3 can also be used, and they'll refer to the same cellstates; they are also 'reserved'.
  • The names DATA_SIGNAL and GUN_2 will be usable in later segments, but we don't intend to use their numerical cellstate values at all.
    During transpilation, these names will be given cellstates in sequential order, starting from 1 and skipping any previously-'reserved' cellstates.

The above will transpile to this, also stripping the {NAME}s:

@RULE foo
1: Data
2: Signal over empty space
4: Signal moving through data
3: Gun, releases one signal every other tick
5: "Dormant" gun in between signals

...and all references to constants will be replaced with their appropriate cellstate value. Note that Nutshell does not stop you from using the cellstate of an "auto-numbered" constant, so if you accidentally or purposely refer to 4 and 5 in your @TABLE or elsewhere there won't be an error thrown -- make sure you can keep track of your constants!

Also: it is strongly recommended that constant names start with an uppercase letter and variable names with a lowercase one. The initial capital helps visually distinguish the former from the latter.

The @COLORS segment

This segment allows multiple states with the same color to be defined on the same line as each other, and for a color to be written either as a triplet of base-10 R G B values, like in Golly, or as a hexadecimal color code. As a result of its allowing multiple colors, the "key/value" order, if you will, has been switched: the color now goes first on a line, followed by all the states it's assigned to. A range sans parentheses/curly brackets can be used here as well.

For instance: FFF: 2 4 6 8 10 says to assign the color #FFFFFF to states 2, 4, 6, 8, and 10, and can also be written as FFF: 2+2..10 or FFFFFF: 2+2..10 or 255 255 255: 2+2..10.

The state listing can also contain @NUTSHELL-defined constant names -- which substitute for one cellstate each -- or @TABLE-defined variable names, which cause the color to be applied to every state within the variable.

The color can additionally be expressed as a gradient rather than a single color. If this is done, the gradient will distribute itself across all given cellstates rather than applying a single color to each. See the following example:

# Nutshell
FF0..00FFF0: 3, 4, 6
# Golly
3 255 255 0
4 170 255 80
5 85 255 160

The @ICONS segment

This segment is based around Golly's RLE format instead of XPM data; the idea is that you're likely going to be in Golly anyway when you're fiddling with a rule, so it'll be easier to quickly copy/paste an RLE in and out of a blank Golly tab than it'd be to edit XPM images in your text editor. Non-normalized icons are automatically centered & uniformly resized to the nearest Golly icon dimensions (7x7/15x15/31x31).

Each individual XRLE pattern listed represents one icon, and to assign this icon to some cellstate, include the state or its @NUTSHELL-defined constant in a comment immediately above the icon's RLE pattern. @ICONS can additionally take here a varname defined in @TABLE, in which case it will apply the icon to every cellstate within that variable. Multiple cellstates can be assigned to by listing them individually (as long as each cellstate appears either with whitespace on both sides or with whitespace before and a comma after) or by describing them with a range literal sans parentheses/curly brackets.

Before further explanation, here's a simple example:


FFF: 3

@ICONS       # Alternatively:
0: 303030    # .  303030
1: D0D0D0    # A  D0D0D0
2: 9CF       # B  9CF

#C Up arrow 1 2
x = 10, y = 9, rule = //10

#C Down arrow: 4, 5
x = 10, y = 9, rule = //10

Pixel colors in an icon are determined by those directive-like lines before the XRLEs. 0: 303030, for instance, says that state 0 (symbol .) in an icon should represent the hex color #303030 (Golly's default background color), 1: D0D0D0 says that state 1 (the symbol A) represents the hex color #D0D0D0, and so on. The cellstate's symbol also can be written instead of its number, as in . 303030 / A D0D0D0 / B 9CF (notice, no colon) if it's easier to read.
Nutshell comes with a utility to aid in creating these icons (accessible as nutshell-ca icon genrule <nutshell file> <outdir>) that generates a B/S012345678 ruletable whose @COLORS segment mirrors the colors in the nutshell file's @ICONS.

The rule of each RLE is ignored; just choose one with enough cellstates for its pattern to be pastable into Golly. Note that the icons don't have to be in sequence or even present (the pre-icon comments determine ordering); if a certain state's icon is omitted, like state 3's above, and it doesn't come after the highest-numbered state with an icon (in which case it can & will be safely ignored), it will be made as a solid square colored according to what's assigned to that state in @COLORS.

If a missing cellstate is not addressed in @COLORS or if there is no @COLORS to use, an error will be raised -- but to mitigate this, you can define a gradient with which to fill missing states. The syntax for this is ? <hex color> <optional separator, ignored> <hex color> (spaces required), where the first hex color is the gradient's start and the second its end; this goes with the other color definitions before the RLEs.
The gradient relies on the states: or n_states: directive in @TABLE to compute its medial colors, but if there is no @TABLE or if it's written as @TABLE #golly (i.e. marked as "don't touch, Nutshell") then the n_states won't be available. In this case you may append to the gradient line a bracketed number indicating the rule's "n_states" value, as in ? <hex color> <optional separator> <hex color> [<n_states>].

@COLORS colors will always take precedence over the gradient, except when the cellstate in @COLORS has an *asterisk before it.

Additionally: If you have a Golly ruletable with its own @ICONS and do not wish to convert it to the Nutshell format manually, there is a tool nutshell-ca icon convert <rulefile> <outdir> that can do it for you.

Multiple icon sizes can be indicated by repeating the @ICONS segment -- if you wish to do this, place your differently-sized icons under @ICONS:7, @ICONS:15, and @ICONS:31 respectively. Note that the numbers are not checked, so one could totally place 15x15 icons under @ICONS:7 -- they're just there to distinguish the multiple segments before coalescing them into a single @ICONS in the Golly table.

You can’t perform that action at this time.