XAutomaLab by Michael Creutz Physics Department Brookhaven National Laboratory Upton, NY 11973 creutz@bnl.gov Play God over your own universe. With AutomaLab you control the microphysics of a discrete world of cellular automata. This two-dimensional land is an array of cells (initially 198 by 198) displayed as pixels on an X-window screen. Each cell can be alive or empty, with evolution occurring in discrete time steps. Empty cells are grey, newborn ones are red, older living ones are blue, and cells that have just died are green. When the tracer is turned on, old life leaves a legacy by shading the background color. In one time step, the fate of each cell depends on the number of its living neighbors. Using Boolean gadgets, you control when a new live cell will be born on an empty site and when a living one will survive. Another gadget lets you pick which neighbors, up to the eight nearest neighbors, are counted. To be more precise, if a particular birth gadget is set and if that number of selected neighbors to a dead cell are alive, then that cell will become alive on the next time step. If a survivor gadget is set, then a living cell with that number of live neighbors will survive the updating. With mouse selections you determine whether the boundary of your universe is dead, alive, or periodic. A final boundary choice, called "flow," is alive on the top and dead on the sides and bottom. The quit, pause and clear gadgets should be self explanatory. When the system is paused, a click outside the playfield or any specific gadget will update the system a single step. Finally, you can toggle individual cells on and off by pressing a mouse button and sketching over your world. The save button saves the current configuration as "xautomalab.gif," a standard gif file that you can print or manipulate with any graphics program that likes gif files. The restore gadget will reload a previously stored configuration. The rule used to create a stored configuration is not itself stored or restored. Note that for the save feature to work you need write permission on the directory from which you are running. Since sketching when the cells are small is rather imprecise, the save/restore buttons can be useful for creating special initial configurations. Using the big block size, sketch your desired configuration while the system is paused. Save it, and then switch to a smaller block size. Finally reload the picture at this new resolution. When your fancy spaceship works, be sure to save a copy of the image. The restore function will take any valid gif picture. Try copying some unrelated picture to xautomalab.gif and then hit the restore button. You can then watch your favorite rule dissolve the picture. The cell size buttons determine how many screen pixels are used per cell. This defaults to one. The window can also be resized to give different lattice sizes. With the eight neighborhood there are 18 birth/survivor buttons. This means there are 2^18=262,144 possible rules in this case. Other neighborhoods give many more, all selectable with the mouse. Indeed, it is unlikely that you will be able to try them all. In addition, the number of possible universes is further doubled using the "xor past" gadget, which probably needs some explanation. When this is activated, the new state is finally XOR'ed with the history one time step back. Thus if a cell was alive in the past, the new state is the opposite of what the birth and survivor gadgets want. The reason for doing this is to produce reversible rules. If the history and current states are interchanged, the system will go backwards through the sequence of configurations from which it came. An analogy is reversing all the momenta of a bunch of atoms. This interchange is accomplished by the "reverse" gadget, which interchanges young and moribund cells. Without the Xpast gadget set, the reverse gadget does not appear. If this seems confusing, try this: With the Xpast gadget set, clear the screen, draw some small picture, select a random rule from the birth and survivor gadgets, and let the system evolve until the screen becomes a mess. Then hit the reverse button and watch the initial picture reappear. Try repeating this experiment, but alter a single pixel with the mouse at the time of the reversal. The starting rule is one I particularly liked at the time I last updated the program. It may change with further updates. Watch it for a while and then try other things. A particularly well known rule is Conway's classic cellular automaton model "life." This uses the eight cell neighborhood and a new cell is born for exactly three live neighbors, while a living cell dies with less than 2 (lonely) or more than 4 (overcrowding) neighbors. Another well-known rule is Fredkin's modulo two model which uses the 4 cell neighborhood. Here a state flips if it has an odd number of active neighbors and is unchanged otherwise. Start with some small picture and observe how the initial state is replicated. If you want to try a rule running from a random start, run for a while with some chaotic rule (i.e. most rules with births on one neighbor) and then switch to your rule of choice. Xautomalab is based on my earlier Amiga program Automalab, which appeared on the May 1991 issue of Jumpdisk. That version used direct access the Amiga graphics chips for speed. Comparing this X version to the previous illustrates the awesome power of the Amiga Blitter. If you have an Amiga and want a copy of Automalab, check in the www site mentioned below. The program is written in C and should compile on anything supporting xwindows. It is best on a color display. With monochrome, only the living cells show. To compile "cc -O -o xautomalab xautomalab.c -lX11" should do it, unless your X11 libraries are in a peculiar place. This program and some related things are available via "http://thy.phy.bnl.gov/www/xtoys.html" on the World Wide Web. It is still evolving, and the latest version can be found there. The colors are defined in the subroutine openwindow. An easy way to change them is to use the chart of X11 color names, which should be in any Xwindow programming guide. This program with source is freely distributable.