The application includes the following parts:
- The view, or display -- this is where the cellular automaton is displayed.
- The view header and the view footer provide some controls for the view.
Please note the theme of the application as well as that of the view can be changed via a dropdown selector at the bottom of the Controls section, in the Theme subsection. This feature is documented in this page.
The view displays the current cellular automaton.
The view supports click and drag, allowing panning using the mouse. Note that when the cellular automaton is being played, the vertical component of the mouse panning is disabled, i.e. only the vertical component is considered.
The view, when selected, also supports the following keyboard actions:
- Space does play/pause
- Enter does a single step
-and+do zoom decrease and increase (_and=work too)[and]do halving and doubling the speed{,|and}do go to the left end, the right end or the center- The directional arrows move the camera in the given direction by a twelfth of the width or the height of the view
- The Home / End / PageUp / PageDown keys move the camera by the full width or height of the view
The view header has three parts:
- the rule input
- the genesis selector
- the autosizing buttons
The rule input allows to choose an elementary rule between 0 and 255, to be displayed.
The genesis selector allows to choose what the how the starting state of the automaton should be generated. The genesis selector offers a preset of options:
-
Impulse 1, Impulse 3 and Impulse 5 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 by the simulator is obtained from a seed. This allows the application's random to be deterministic. It makes the initial state of the application reproducible, given the seed. The seed parameter can be found in the advanced interface, in the simulation controller panel.
Next to the genesis selector is a dice button. This dice allows to randomly generate a new seed, to obtain a new initial state.
The autosizing part has two buttons:
- Autosize or "Fit view to window"
- Crop Simulation or "Fit simulation to view"
The autosize button shrinks or expand the view, to match the space available in the window.
The crop simulation button reduces or increases the length of the simulation space to match the size of the view, ensuring the full width of the simulation fits in the view, at the current zoom level.
The view footer has two parts:
- the navigation block
- the play block
The navigation block allows zooming in and out, and panning using arrows.
The play block allows starting and pausing the vertical autoscroll of the automaton, changing the play speed, and showing a single new generation.
The application has two panes allowing the user to select rules, and helping them find interesting ones. These are:
- The Rule Table
- The Old Rule Selection
The rule table is a spatial representation of all 255 available rules. It allows choosing one rule to be displayed in the view. It has a criterion selector to the right which allows highlighting rules matching a given criterion.
The old rule selection section lists a number of interesting rules, grouped by the criterion which makes them interesting.
The rule criteria are for the most part the result of the author's own exploration of the 256 rules. They are not the result of published researches, with one exception: the rule classes.
The rule class 1 to 4 are that of Stephen Wolfram, see Wikipedia.
All text fields require pressing Enter to validate the input.
The border text fields are multiline, and thus require pressing shift+Enter.
The rule editor shows the current rule written in base 10, base 2, base 4 and base 16. It allows editing it in any of these bases.
This pane lists automata obtainable by transformation over the current rule. If a transformation yields the same automata, it is listed as a property of the rule.
These properties are:
- Left-right symmetry -- the automata obtained by flipping the left and the right in the input of the local transition function.
- Color symmetry -- the automata obtained by flipping the colors both in the input and in the output of the local transition function.
- Both symmetries -- self descriptive: the two above symmetries.
Furthermore, the symmetries are also applied to the "output complement" of the rule. The "output complement" is the rule obtained by flipping the color of the output of the rule, but not that of the input. Interestingly, the algebraic operation corresponding to a color output complement of an elementary rule is x => 255 - x, making it very easy to compute.
All the controls in this pane influence the values used for the computation of the simulation.
The simulation controller has seven inputs. These are:
- The simulation topology selector (loop / border)
- The field controlling the generation of the genesis (or top border)
- The two fields controlling the generation of the left and right borders, when relevant
- The width of the simulation
- The seed for generating any random values used in the simulation
- A button to generate a new seed
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.
The border fields are documented 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, in version 0.1.5 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 border fields are multiline, and thus require pressing Shift+Enter to be validated. Pressing enter adds a new line.
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:
()parenthesis denote repetition of the pattern inside (and it's called a cycle)[]square brackets denote randomness, though they can be deterministic if used with a single value
Note that currently, the syntax does not support nesting groups of any kind. Top border should contain one or two groups. The side borders (left and right) should contain exactly one group.
Here are commented examples of valid top borders:
(0)This represents a deterministic initialization to a dead state, this is usually an uninteresting genesis.(1)This represents a deterministic initialization to a live state, this is usually an uninteresting genesis.(0)1(0)This represents the genesis ofImpulse 1: A single one, and infinite zeros one each side(0)11(0)This represents the genesis ofImpulse 3.(0)101(0)This represents the genesis ofImpulse 5.([01])This represents the genesis ofRandom 50%.([00000000001])This represents the genesis ofRandom 10%.([01111111111])This represents the genesis ofRandom 90%.
Here are commented examples of valid side borders:
(0)This is the always-dead border.(1)This is the always-living border.([01])This 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)This is the border that is alive for the first three generations, then dead forever.(01)This is the border that alternates between death and live at each generation.(0001)This is the border that is alive only every four generations(000[01])This is the border that has a 50% chance of being alive every 4 generations.
All the controls in this pane influence the values used for displaying the computation, but none influence the way it is computed.
The display controller has 7 number inputs and a few more buttons. These are:
- Zoom
- Width, Height
- Generation, Spatial Position
- Speed
- Precise generation value
- "Show all panning buttons" checkbox
The zoom field controls how big cells are. For the time being, it needs to be a multiple of 6. The size of a single square cell will be S x S where S is a sixth of the zoom value. Please note that the zoom value displayed in the view footer is S, it is the value of zoom divided by 6.
This field is redundant with the zoom controls at of the display footer, but it provides a much finer control. In most web browsers, the zoom field allows scrolling on it to change the value.
Constraints:
Zoom must be a value between 1 x 6 (6) and 64 x 6 (384).
The width and the height field allow reading and setting the size of the canvas, in pixel. Note that width and height can also be automatically adjusted to the window using the autoresize "Fit view to window" button of the header of the view.
Constraints: These numbers must be positive.
In the context of 1d cellular automaton, the generation is the equivalent to the temporal position.
The temporal position corresponds to the Y axis, the vertical axis.
The spatial position 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 allows to show and set the position of the leftmost visible cell on the automaton's ribbon. Note that the origin of the spatial axis is the center of the automaton, so this coordinate is negative most of the time.
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 position must belong to a range that is dynamically computed, depending on the simulation width and the canvas width.
This field sets the speed at which the view is scrolled down.
The speed field is redundant with that of the footer of the view, but it allows setting it with a lot more precision.
Constraints: The speed must be an integer between 1 and 256, included.
The application allows to choose between different color themes. There are light theme and dark themes. The default theme for the application is a dark theme.
There are two theme fields:
- App Theme -- the application theme
- Display Theme -- the display theme
The application theme is used for the titles, texts and buttons. The display theme is the theme used for the view: for coloring the living cells.
By default, the display theme is set to copy the value of the application theme.
If the display theme is a dark theme, the dead cell will be black, colored #000. Conversely, for a light theme, they will be white #FFF. The color for living cells is the color given in the name. Note that the living cell color can never be #FFF nor #000. This guarantees the ability to tell which is which.
The application has an info section, at the bottom. This section:
- lists existing alternative web-based elementary Cellular Automaton simulators
- provides the application Changelog
Note: the link to the Github page is at the top right of the application.