Cellex is a cellular automaton exploration tool. It works with monodimensional automaton only and allows automaton using up to six states, each represented by a color, with a neighborhood size of up to 11 cells, though the engine can work with up to sixteen states, or with a neighborhood of size 11.
The application includes the following parts:
- The view, or display -- this is where the cellular automaton is displayed
- The top toolbar, which provides some controls for the view.
- The automaton editor
The view canvas supports click and drag, allowing panning using the mouse.
Please note that:
- when the zoomed simulation is of the same width or of smaller width than the canvas, the view of the simulation is locked in the center of the canvas and the horizontal canvas moves are not possible
- when the cellular automaton is being played, the vertical component of the mouse panning is disabled, i.e. only the horizontal component is considered.
The following shortcuts are available:
- Arrows to pan the camera by small steps
- Page up/down and home/end to pan the camera by large steps
-and+to decrease and increase the zoom level (_and=work too)[and]to half and double the play speed{,|and}to move the camera to the left end, the center or the right end of the simulation0to reset the simulation to the beginning- The directional arrows move the camera in the given direction by a twelfth of the width or of the height of the view
- The Home / End / PageUp / PageDown keys move the camera by the full width or height of the view
When the view is selected, it also supports the following keyboard actions:
- Space does play/pause
- Enter plays a single step of cellular automaton
The top toolbar is composed of a play/pause button, a full screen button, a button to open the automata gallery, an automaton randomization button, an automaton input widget, a genesis selector, a differential mode selector, and finally, a settings button.
The automaton input widget allows to input an automaton descriptor. For automata with more than two colors, the number of colors must be specified in the descriptor, e.g. "3 colors". For automata whose neighborhood is larger than 3 cells, the neighborhood size must be specified, e.g. "neighborhood size 5". Finally, the rule number or code number of the automaton must always be specified, e.g. "rule 901" or "code 376".
Example: neighborhood size 5, 3 colors, code 86_429
The genesis selector allows to choose how the starting state of the automaton should be generated. The genesis selector offers a preset of options:
-
Impulse 1, Impulse 3, Impulse 5 and Impulse 7 are deterministic. They all correspond to a starting position where all but one or two cells are dead. Their names are chosen because of the binary notation of each number: 3 is written
0b11and 5 is written0b101. -
Random 10%, Random 50% and Random 90% are genesis states randomly generated states. The percentage is the likelihood to be alive, for each cell.
Please note that the random used in the simulator is generated with a seed. This allows the random of the application to be deterministic. It makes the initial state of the application reproducible, given the seed. The seed parameter can be found in the Topology section of the settings panel.
Note that next to the seed input field is a dice button. This dice allows to randomly generate a new seed, to obtain a new initial state.
The automaton editor shows the resulting cell of for each of all the possible combinations of states. Clicking on a result cell allows to change the automaton.
This selector has two possible values: "loop" and "border". It controls the behavior of the border of the simulation.
In the setting "loop" the borders behave as if the cell just out of the simulation, was the value of the other border, effectively making the space of the simulation a closed ribbon. In this setting, the "Border Left" and "Border Right" fields are disabled.
In the setting "border" the borders ignore the values present at the other border of the simulation. Instead, their values are dictated by the "Border Left" and "Border Right" fields. These two fields are documented in their own section, below.
The width sets the length of the ribbon i.e. the size of the space the in which the simulation runs.
The seed is the value used to generate any random value if the generation of top border and side borders. The seed can be retrieved and set from the seed field.
Pressing the "Random seed" button will generate a random seed from a non-deterministic source of random (the browser's Math.random function). To be specific, the random seed button uses the following:
Math.random().toString(36).slice(2).toUpperCase()Constraints: None. The seed can be any string, though the seed text field always
replaces the empty seed by the single underscore (_).
The border top, border left and border right fields have a simple syntax inspired from regexes (a programming text parsing tool). This syntax uses the following grouping ideas:
()the pair of outermost parenthesis denotes cycling of the pattern inside it. The top border must contain exactly two of these outermost pairs. The side borders must contain exactly one.()with the exception of the outermost pair, parenthesis represent grouping. This allows to repeat a specific pattern a certain number of time. e.g. is a shortcut for the following pattern[]square brackets denote randomness, though they can be deterministic if used with a single value{}curly braces denote repetition
Example:
1((01){9}[01]{2})is equivalent to1(010101010101010101[01][01])
Here are commented examples of valid top borders:
(0)represents a deterministic initialization to a dead state, this is usually an uninteresting genesis.(1)represents a deterministic initialization to a live state, this is usually an uninteresting genesis.(0)1(0)represents the genesis ofImpulse 1: A single one, and infinite zeros one each side(0)11(0)represents the genesis ofImpulse 3.(0)101(0)represents the genesis ofImpulse 5.([01])represents the genesis ofRandom 50%.([00000000001])represents the genesis ofRandom 10%.([01111111111])represents the genesis ofRandom 90%.
Here are commented examples of valid side borders:
(0)is the always-dead border.(1)is the always-living border.([01])is the border whose liveliness is random, with a probability of 50% for each cell. Note that the random values depend on the random seed, just like for the top border.111(0)is the border that is alive for the first three generations, then dead forever.(01)is the border that alternates between death and live at each generation.(0001)is the border that is alive only every four generations(000[01])is the border that has a 50% chance of being alive every 4 generations.
The zoom field controls how big cells are in the zoomed up view. The size of a single square cell will be S x S S is the zoom value.
Note the x2 and /2 buttons will refuse to go past 0.25 or past 64.
The width and the height field allow reading and setting the size the canvas, in pixel.
In the context of 1d cellular automaton, the generation is the equivalent to the temporal position.
The temporal axis corresponds to the Y axis, the vertical axis.
The spatial axis corresponds to the X axis, the horizontal axis.
The generation field shows what the exact value of the current generation at the top of the view is. The spatial position is the x coordinate of the cell at the center of the view. Note that the origin of the spatial axis is the center of the automaton, so this coordinate can be negative.
This fields are redundant with the panning feature of the view, but it allows precise reading and setting of the spatial position and the generation.
Constraints:
- The generation must be a positive number
- The spatial position must belong to a range that is dynamically computed, depending on the simulation width and the canvas width. That range is centered on 0 and the size of the range is the difference between the simulation width and the canvas width, taking zoom into account. If that difference turns out to be negative, then the size of the range is 0.