ACML - Automates Cellulaires en caML
ACML is a cellular automata simulator that focuses on easy definition
and exploration of arbitrary rules and initial configurations.
In a few words
- any rule in dimension 1 or 2 with large neighbourhood and large number of states
- rules and configurations can be defined through arbitrary OCaml functions
- deterministic or stochastic cellular automata
- parametrized families of rules possibly with random generation
within the family
- large built-in collection of predefined rules
- programmable, scriptable, extensible via plugins
- not slow, e.g. on my laptop:
- can run and display at 60fps a 2D CA of radius 5 (Bosco) on a
200x200 torus, and Game of life at 160fps
- can run (without display) at 6500 steps/second an elementary
CA on a torus of size 10000
- compatible with several formats: table, RLE, PNG, JPEG, SVG, LaTeX/Tikz
- GTK interface or command-line
Typical target usage: mine!
- You're attending a conference on cellular automata, the speaker
presents an interesting example and you want to play with it immediately without interrupting him/her nor stealing his/her
computer. Then you start to think of a possible variant of the example, then another one, and you quickly come to a whole family of
rules that you want to explore quickly by adjusting some
- Later, you start more serious investigations and want to test
some conjecture on a large family of small examples. The test
involves creating particular initial configurations and running the
examples until some event occur. In addition you want to save the
configuration reached in each case, and of course you want to let the
whole test run autonomously during the night.
- Finally, you're in the process of writing a scientific paper/talk
and need to illustrate it your with various figures. Some are simple
screenshots, others are full Tikz code to produce a space-time
diagram where some states are given a name typeseted in
LaTeX. Moreover, the cellular automaton you want to define is big and
very structured, so the best way to describe its transition
rule is by using a high-level programming language.
Basic usage: launch and watch
Launching ACML without any command-line option gives you an interface
with two windows: a control window
with many buttons, and a view
where the simulation is displayed. Using the control window should be more or
less intuitive. You can also interact with ACML through the view
window (click Help button to know how).
Inside ACML, there's a lot of predefined cellular automata and
families. Click "Open.." to get the list. You can also directly enter
names in the main input text box at the top of the control
window. From the command line, you get these lists in this way:
To have an idea of what ACML can do, you can also try these command
lines (try one line at once, control window desactivated, just watch):
acml --nogtk --run life
acml --nogtk --run bosco
acml --nogtk --run 54
acml --nogtk --run sandpile
acml -vx 200 -vy 500 -x 100 -y 250 --nogtk --run fire
acml --nogtk --run B3678/S34678
acml --nogtk --run --refresh_rate 100 langton
acml --nogtk --run majority --- neighborhood Moore states 5 radius 4
If you like animated GIFs, try this long line (needs ImageMagick's
echo "Wait..." && acml --quiet --batch random_cyclic --stop 200 --shooting --shootfile tmp_ihopethisisafreshname.png && convert -delay 10 -loop 0 tmp_ihopethisisafreshname*.png surprise.gif && rm tmp_ihopethisisafreshname*.png && echo "Now open surprise.gif"
More about the command line:
acml "brian's brain" --quiet --identify
The core concept: transformations instead of objects
The core concept of ACML is to manipulate transformations or
procedures that produce cellular automata, rather than manipulating
cellular automata directly. A procedure can (potentially) produce a
whole set of different cellular automata depending on the context
In ACML, the result of such a procedure is called an object
procedure itself is called a family
. We can therefore schematize the situation as follows:
- object= cellular automaton + initial configuration +
- context= values of parameters (user interface or command line)
+ random number generator state + ...
- family : context → object
Moreover, in ACML, a family
is always given by its source
code. Therefore, ACML is capable of saving the current object
as a new
source code which is essentially the pair: family + context prior to
- parameters: exploring large families of cellular automata
by quickly adjusting parameters instead of painfully openning them
one by one. Parameters can be anything, you are free to introduce
them in your source code.
- compacity: for large structured rules, for highly symetric rules,
for huge randomly generated rules, 'source code + parameters +
random seed' is vastly better than any table-based format
- readability/reusability: for instance, you can write the
code to define a family as "an additive cellular automata updates
each cell to the sum of its neighbors modulo the number of
states". It's clear, indepependant of the dimension, the number
of states or the neighborhood (which are just parameters). Later
you can copy/paste this code and easily add a parameter called
"alpha" to define another family as "an affine cellular automata updates
each cell to alpha plus the sum of its neighbors modulo the number of
states". Code is often reusable.
On the contrary "111→1, 110→0, 101→0, 100→1,
011→0, 010→1, 001→1, 000→0 " is both
uncomprehensible and not reusable.
- shortcuts and naming conventions: you want "life", "bosco",
"Brian's brain"? Easy: an object can be referenced as a pair (family
+ parameters). Therefore, you can implement any naming convention you
want as a function "string → family + parameters". ACML already understands
things like "110", "B2/S345", etc. To know the exact list:
ACML can work on the current object like any other simulator
(start/stop simulation, screenshot, etc). But it also has a current
family which allows you to change the current object.
- Make All: apply the family transformation and gives
you the result as a new object
- Make Conf: apply the family transformation and gives
you the result, but keeping the old cellular automaton
- Make Other: apply the family transformation and gives
you the result, but keeping both the old cellular automaton and the
In this example, you can explore the family of classical cyclic cellular
automata (you can get detailed information on the current
family/object by clicking the info icon at the top-right corner of
the control window).
- To start/stop the simulation, click on the Simulation button (upper toolbar).
- To generate a new CA from the family and a new configuration,
adjust parameters as you want and then click on Make All (upper toolbar).
- To generate only a new initial configuration and keep the same
automaton, click on Make Conf (upper toolbar). You
can also change the configuration type (bottom right).
- When you obtain an interesting rule, click on Save (right toolbar) to save it (automaton with current parameters) as an ACML source file.
- When you see some nice configuration, click on Snap (left toolbar) to save it as an image file.
A small program's worth a thousand clicks
The primary goal of ACML is to allow quick writing and testing of new automata rules. To achieve this the key features are:
- rules as programs: to define a transition rule you have the full expressive power of a high-level programming language (OCaml). For instance, the transition rule of Brian's Brain cellular automaton can be written like this:
let transition_rule me howmany = match me with
| Excited → Refractory
| Quiescent when howmany Excited = 2 → Excited
| _ → Quiescent
- automtic compilation/dynlink process: you write the source
in OCaml, click Open... (right toolbar) in the user
interface, select your file and ACML do the rest. For the
impatient, you can also enter code directly from the command line:
acml "fun me howmany -> if (howmany 1 = 3 && me = 0) or (me = 1 && howmany 1 <= 4 && howmany 1 >= 3) then 1 else 0"
But there is a shorter way to obtain the same as above :)
- parameters: instead of a single rule, your source code can
describe a whole family of rules depending on some parameters. Then,
without changing the source code, you can adjust the parameters from
the user interface (or command line) and easily test all the rules in the family. From
the programmer's point of view, adding a parameter is as simple as
inserting in the code a line of the form:
let x = bool_param a "left/right symmetric" false in
- everything is programmable: you are not only free to write
new automata rules, but also new initial configurations, new ways to
display the universe, new ways to measure quantities along time, new
ways to interact with the mouse, etc. Moreover, all this comes with
a simple plugin system which allows to factorize code. For instance,
a line of code of the form:
add_modif a ~key:"b" "Turn to 0/1" (Map (function 0 -> 0 | _ -> 1));
gives you a new mouse action which turns all non-zero states into 1s
inside the selected zone. It is selectable from the control window,
or directly by holding key "b" while selecting a zone with the mouse
in the view window.
- reproducibility: ACML can manage random seeds for you. If
you use pseudo-randomness apropriately in your source files, you can
generate and simulates as many rules on as many configurations as
you want and just click Save when you're happy: a new
source file is saved and opening it will reproduce exactly your last
- the code is visible: first, ACML is open source. Second,
the code of each rule, family of rules, plugin, etc is accessible
from within the interface in flew clicks. We think that, frequently,
exposing the code (or portion of code) is the best way to explain
what exactly does some function.
So let's write programs for ACML!
WANRING! OcamlSDL version 0.9.0 (and maybe also some earlier versions) contains a bug in mouse click detection.
OcamlSDL version 0.9.1 works.
ACML should compile on any plateform where you can install these prerequisite (tested on Ubuntu Linux and Mac OSX).
Debian-based linux distributions
On Debian-based linux distributions
(tested with several Ubuntu distributions), you should get all you need with this single command-line:
sudo apt-get install ocaml ocaml-findlib libsdl-ocaml-dev liblablgtk2-ocaml-dev libcairo-ocaml-dev libzip-ocaml-dev libnum-ocaml-dev
If your OS has some kind of packaging system, you may find corresponding package names starting from the list above.
Alternatively, you can use GODI
(source code OCaml distribution). The following list of GODI packages should be sufficient:
godi-ocaml-all godi-findlib godi-lablgtk2 godi-ocamlsdl godi-cairo godi-zip
To install these packages, external libraries (e.g. SDL, GTK+2 and CAIRO) must be installed on your system (they are not provided by GODI).
This installation method works on MacOS (tested on 10.6 and 10.4, using fink
for external libraries).
In the src/
directory of the decompressed archive, type:
sudo make install
In case of a compilation failure, it might be necessary to do run make clean
before another make
In the directory src/builtin
, you can add or remove as much ACML source files as you want. Each file can contain a family of cellular automata or a plugin. During the compilation, all these families or plugins are embedded in the binary.
- Is there a FAQ in preparation? Yes, just ask me frequent questions.