The applet: instructions

There are lots of applets on the web which simulate Langton's ant on the square grid, usually allowing the user to change the states in a few cells before letting the ant run. Our applet does a lot more than this: you can switch between the different grids (including general graphs, which you are allowed to edit), you can run the ant forward and backward, you can highlight its trace, mark certain cells, and load some interesting initial configurations. File I/O is not included in this version, due to the security restrictions imposed to applets.

Contents:

: Go to the applet (link and warnings)
: How to use it
: What's available in the initial configurations
: Download Java classes and source

The way to the applet

Click here to open the applet. This will cause a new window to pop up, and will try to create it with the maximum size available on your screen. If you don't want this to happen (it may be annoying), then you can click here to open it in the present window, with the present size... But remember that in Netscape applets are not resized when you resize the window that contains it.

Warning for Linux users: We have seen the applet hanging up in Linux... And not only did Netscape hang up, but the whole terminal session. Any help from Linux-experienced Java programmers is welcome (for the source code, see below).

Instructions

As you will see, there is a control panel with buttons and boxes on the left, and a simulation panel on the right. We will describe first the elements on the left, starting with the top one. Then we will explain how to edit the configurations on the right.

Please take note that there are many elements in the control panel; a low-resolution screen configuration, or a web browser with too many toolbars, may hide some buttons from view. This is why we recommend opening the applet in a maximized window.

The Control Panel

Steps label: The number of steps the ant has walked. The number will decrease (even to negative values) if the ant walks in reverse mode.
Reset button: Sets the states of all nodes/cells to white (left state). If a regular grid is selected, the size is updated, using the size boxes.
Grid selection: Here you can choose to work on the hexagonal, triangular or square grids, or on general graphs. When you change from one grid type to another, the default configuration is loaded, which is an empty configuration of the size described in the size boxes, for the regular grids, or a default graph, in the other case.
Show Grid checkbox: Checking this will show the graph that underlies the regular grids, thus helping you to see why we call the triangular grid "triangular", etc. It has no effect if "General" is selected.
Thorus checkbox: If this is checked, the regular grids have the periodic boundary condition: the leftmost cells are considered neighbors of the rightmost ones, ant the top cells are neighbors of the ones at the bottom. If you uncheck it, the ant will freeze when it comes to a border. It is automatically checked/unchecked (and disabled) by the special constructions of the logical devices, which are not supposed to be used twice, anyway.
Random fill button and box: The box is expected to contain a number d between 0 and 100. When the button is pressed, each node/cell is set to black or to white by flipping a coin, with probabilities d/100 and 1-d/100, respectively.
Iterate button and box: The box is expected to contain a non-negative integer; when the button is pressed, the system will be iterated that number of time steps, forwards or backwards in time, depending on the state of the Reverse checkbox.
Auto checkbox: Toggle automatic iteration of the system on and off.
Reverse checkbox: Reverses "the arrow of Time".
Load choicebox: Allows selection between several starting configurations. See below for more information on its content.
H and V size boxes: Use these boxes to set the horizontal and vertical dimensions of the grid. When the Reset button is pressed, they will be use for resizing.
Trace checkbox and Reset trace button: When the checkbox is activated, the border of the cells/nodes visited by the ant are painted black. Use the button to reset these marks.

Editing the Simulation Panel

Grids:

Left-clicking on a cell will toggle its state from white to black and vice versa.
Right-clicking on the cell where the ant (or rather, its abdomen) is placed, will change its direction clockwise.
You can move the ant by dragging it (i.e.: move the mouse with the left button pressed).
Right-clicking on any other cell will toggle a mark around on or off. The mark is a yellow line around the cell, used to highlight particular spots.

Graphs:

Right-clicking on a node where the ant is not placed, will place it there.
Right-clicking on the node where the ant is placed, will change its direction clockwise.
Left-clicking on a node will toggle its state from white to black and vice versa.
You can move a node by dragging it.
You can create/delete an edge by dragging the mouse from one node to the other, while pressing the right button (or while holding the Control Key down).
You can create a node by clicking in any empty place.
You can delete a node by moving it outside of the simulation panel.

The available configurations

For the hexagonal grid:

Duplicate: The device to perform the duplication of a boolean variable. The highlighted cells at the top are the input, and must be set to black, to represent a value of true. If they are white, they represent false. The answer is written in the highlighted cells of the bottom. See the page about our results.
Period 92: A configuration for which the ant's trajectory is bounded, with period 92. Remember that such configurations do not exist for the square and the triangular grids.

For the square grid:

And, Not, Copy, Duplicate and Cross: The devices to perform the Boolean operations AND and NOT, to copy a value, to copy it with duplication, and to cross two values while copying them. The highlighted cells at the top are the inputs: they must be set to black, to represent a value of true. If they are white, they represent false. The answer is written in the highlighted cells of the bottom. The highlighted cells inside the configurations are showing where the special crossing and joining configurations are placed. See the page about our results.
Highway: The start of the ant's highway. Once the ant enters the quadrant enclosed by the highlighted cells, it will never leave it, and after a while it starts building the highway.
Iterate 200K! : A little surprise, after enough iteration. Notice that the ant can be used as a simple criptographic system.

For the triangular grid: nothing. For general graphs:

A graph : A small default graph.
A tree : A graph without cycles.
No strings : A graph without strings in its cycles; for this kind of graphs, if they are planar and planarly represented, the period of the ant's system is linearly bounded in the number of nodes.
Expon. 1 : Some graphs of a family where the periods of the ant's system grow exponentially as the number of nodes increases.
Expon. 2 : A member of a family of graphs without strings in their cycles, but where the periods do also grow exponentially (the trick: they are drawn in a non-planar way).
G(4,5) : A fragment of the infinite hyperbolic bi-regular graph Gamma(4,5): the degree of the graph is 5, and the degree of the dual graph is 4. Alas, it's too small to notice the behavior we've described in the publications. See the page about our results.

Download classes and source

By clicking here you can download a zipped file which contains the source code of the applet, the compiled classes, this html file and the html where the applet is opened; thus you can unzip it to a directory, and run the whole thing offline. This is also a chance for Linux users that have trouble with the browser: try to run it with the Appletviewer.

The code is not copyrighted; anyway, I think it would be fair at least to mention the name of the programmer (Andrés Moreira) if you use the applet somewhere.

If you want to modify it, I apologize in advance for the absence of comments, the bad Java style, and the spanglish in the names of variable and methods. If you do any valuable extension to the program, please let me know ( mailto:anmoreir@dim.uchile.cl), and check the copyright information.

Last updated: 03-31-2002.
Contact: agajardo@dim.uchile.cl