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Xlife(6) Games Manual Xlife(6) NAME Xlife - Conway's Game of Life and other cellular automata, for X SYNTAX xlife [-display disp] [-geometry string] [-l pattern-lib] [patternfile] lifeconv -ACDIMPRSpv? [-l pattern-lib] [-g n] file DESCRIPTION brings up a single window in which the user may experiment interactively with cellular automata. In its default mode, the program helps the user play with John Horton Conway's `Life' game. By default Xlife will run in a window taking up 4/5ths of your screen; you can use your window manager's Zoom or Resize feature to make it fill the whole screen. This window is a viewport on a universe which is effectively unbounded (4.2 billion on a side). Exactly the universe is a big torus. If an initial pattern is specified, it will be loaded on startup, before Xlife accepts commands. The -geometry option sets the Xlife window size and position as per usual for X applications. The -display option sets the display to use; overrides the DISPLAY environment variable. The -l option allows you to specify a pattern list library-file for name matching (default is `named-patterns'). lifeconv is a format-conversion utility that translates between several different file formats for saving patterns. It takes a pattern file argu- ment and writes the conversion to standard output. Conversion options are described in the LOAD FILE FORMAT section below. The -g option permits you to evolve a loaded pattern for a given number of generations before saving. The -l option is the same as above. The -? option shows the usage summary. The -v option outputs version information and exits. A utility table2r may convert table-format file with rules to r-format. This utility is written in awk. COMMANDS Tab Change state 1 cells of tentative pattern to active state. It is useful for the creation of multirules pattern. ! Place random cells on the area of the universe on the screen. # Change tentative-display mode. By default the tentative-pattern cells are displayed in normal state colors but with a bounding box. In the alternate (`wireframe') mode, tentative-pattern cells are displayed as open rectangles in the load-box color, but with no bounding box. Wireframe mode is useful when you are try- ing to match a loadscript to a template active pattern. It is also useful to compare two patterns. $ Toggle running display of changed-cell count in per-generation status line. This count makes evolution slightly slower. % Set a percentage density for a randomly filled area. Default is 90%. ( [ { Set a marker at current mouse position. There are three markers, one for each of these characters. ) ] } Go to a marker (make it the current mouse position). The marker jumped to by each closing bracket is that set by the correspond- ing open-bracket command. *,= Toggle showing of speed in the number of generations per second. +,= Zoom the view in, magnifying the area around the mouse cursor. At zoom scale N, cells are two to the power N pixels wide; the default cell size is scale 4, 16 pixels on a side. Scale range is -10 to 6; at scales -1, -2 and -3 a single pixel represents the logical or of a square sample of 4, 16, and 64 pixels respec- tively. The same effect has the movement of mouse wheel up. < Slow down evolution; increase delay by 10 msec. > Speed up evolution; decrease delay by 10 msec. - Zoom the view out. The same effect has the movement of mouse wheel down. . Center the universe view on the cursor (also Button 3 in normal mode). / Show quantity of cells of different kinds (colors). 0 Center the median position of the live boxes. 1,End Move your view of the universe diagonally down and left. 2,Down Move your view of the universe down. 3,PageDownMove your view of the universe diagonally down and right. 4,Left Move your view of the universe left. 5 Center the universe on the screen (based on average position of the cells). 6,Right Move your view of the universe right. 7,Home Move your view of the universe diagonally up and left. 8,Up Move your view of the universe up. 9,PageUp Move your view of the universe diagonally up and right. ? Help for xlife. This help may be used as a menu. @ Toggle 2-state automata history. The history provided by addi- tion of 5 new states: the new cell state 2 means that this cell is dead but was alive earlier, the new states 3 and 4 mean marked ON and OFF respectively (they may be changed to each other so they will always remain marked), the new state 5 means `start ON' (becomes normal marked OFF cell, the state 3, when it dies), the new state 6 means `boundary OFF' (can never turn ON). The his- tory may be also activated by addition of `+' suffix to the string determinating rules. A Add comments. B Benchmark. Enter number of generations and get time. This is also the fastest mode of the evolution. C Clear the universe and discard current load script. If there is a boxed pattern, clear that instead. D Discard current load script, including any tentative pattern, but leave cell population intact. (Helpful for using an old pattern as a template to construct a load script). E Rotate pseudocolor display modes for 2-state automaton. In dis- play mode 0 (the default) all live cells are displayed normally. In display mode 1, new cells are shown in state 2 color. In dis- play mode 2, new cells are shown in state 2 color and dying ones in state 3 color. In display mode 3, dying cells are shown in state 3 color. In display mode 3, only cells changed from the previous generation are shown (whether alive or dead). Has no effect on N-state automata or a tentative pattern. It has also no effect when scale is below 8:1. F Load n-state rules from a given file (see the N-STATE SUPPORT section below). The file with rules may be given by absolute path or just by name of the rules. In the latter case all subdi- rectories of the default directories will be searched. G Generate tentative loaded or active pattern for one or more steps. H Toggle history record mode. It is fast mode for any type of au- tomaton. Use `h', These colors maybe changed by `X' command. I Force tentative pattern to be incorporated into main pattern (au- tomatic with g, h, o, l, and W commands). J Jump to (x,y) location - make it the current mouse position. K Discard comments associates with current pattern. It also clears #K line. L Immediately reload, at the cursor, a copy of the last pattern loaded. M Toggle display of a grid mesh overlaying the board. N Change the file's internal name. O Set current mouse position to be the origin of displayed coordi- nates. P Toggle the oscillation check mode. The `g' command evolution stops whenever it detects an oscilator in this mode. This com- mand compares the starting pattern with the next patterns. So it just checks whether a given pattern is an oscillator. Q Quit R Change the (2-state) rules in "stays alive on"/"born on" or B0..8/S0..8 format. The standard rules are 23/3 (alive on two or three neighbors, birth on three neighbors for an empty cell) or B3/S23 or S23/B3. Its possible to use third component which must be number between 3 and 256. This number sets age limit for the cells. So /2/3 establishes Brian's Brain rules and 345/2/4 - Star Wars'. Alternatively, enable a payoff matrix with the syn- tax <float>$<float> as described in the PRISONER'S DILEMMA sec- tion. It is possible to use named rules. The words "life", "seeds", "wireworld", "lifehistory", "life+", and "brian" (for "brian's brain") are recognized. S Save the universe to a file adding extension `.l', along with any comments created via `A'. If there is currently a boxed pattern, only the boxed pattern is saved. It is possible to select a for- mat for the saved pattern. See section MAIN LOAD FILE FORMAT for the details. T Set up the topology. It is possible to select the rectangular area with connected edges (anchor ring, tore) or the rectangular plain. The letter `Q' (quasiplain) means very big torus - this is the default mode. The letter `T' means limited torus and the letter `P' means limited plain. You should enter rectangle's width and height in the latter cases. The sizes of the rectangle will be rounded up to the multiples of 8. The size 0 means pseudoinfinity. The bounded area center is the initial origin of coordinates. For example, `T16,0', `T8x8', `P0,64', `T4096,4096', `T8X512', `P400*400', `Q' may be used to set up the topology. It is possible to use previous setup. If `T512,512' topology is used then the set `64x' will set `T64*512'. You may set bordered plain with any form for the 2-state automata in the history mode - you should draw borders with 6th color. U Undo load of tentative pattern. V View comments. W Write (and flush from memory) script of loaded patterns into a file with `.l' extension. When loaded, this script corresponds the earliest ancestor of current pattern that can be recon- structed from loaded patterns (it does not include changes made with mouse: flips, rotates, and moves). X Load palette from a file with extension .colors (default). This file consists of lines of text. Any blank lines or lines start- ing with `#' are ignored. The specification of the RGB colors for one or more states should use the lines like these: color=1 0 0 255 #0000ff color=2 255 0 0 color=4 255 255 0 cyan color=5 255 0 255 Y Yank out active pattern. If tentative one exists then move ten- tative pattern to the universe. Z Restore default palette. ^ Set seed for random number generator. a Add n-state transition - 6 digits (one old state, one for each orthogonal neighborhood cell, and one new state) or filled S(N*C)R form. The new rule will be logged to the file new.tran- sitions (this requires write permission for the directory with last loaded pattern). b Display the xmin/xmax and ymin/ymax values of the live cells. c Toggle showing of cell count. Active cell count makes evolution a bit slower. d Duplicate tentative pattern. Allows to create multiple copies of the same object interactively. Just press `d' and then mouse button 1. f Set evolution speed for `g' to high (no delay between evolu- tions), the default. g Toggle running the game. Evolve/Stop. Incorporate any tentative pattern. Then step through generations until something excep- tional happens, like still life or stability or a key pressed or possible oscillation detection (the last only if a `P' period check is set) or like an `i' timer running out. h (Hide) stop displaying after each generation, does not iconify. This mode maybe up to several times faster than established by g- command. However j-command with proper step gives faster speed and more comfortable output. i Set up timer. Set the maximum number of generations to perform for following `g' or other evolution commands. A zero value (the default) is interpreted as "never stop". This command is very similar to 'G'. j Set jump length (step) for the command `g'. The value 0 or 1 means no jump. The greater value means faster speed. k Pick up color from the pattern's cell. l Load (actually add) pattern to the universe from a file with ex- tension `.l' (default), `.life', `.rle', `.mcl', `.lif', or `.cells'. This lets you overlay multiple saved states to make for some interesting effects. Loaded pattern is (default) ini- tially considered tentative, and may be manipulated in various ways before incorporating it into main pattern. (To indicate this, it's surrounded by a bounding box.) Clear the universe if you want to start from scratch. It is possible either to select pattern at the widget list directly or to enter pattern name - this will start the search for the requested pattern at current and library directories. There are two modes to load patterns. The first mode is direct. It directly place pattern to the ac- tive pattern space. Directly loaded pattern isn't added to the save script. The second mode is tentative. It allows pattern manipulations before its addition to the pattern space. m Set evolution speed for `g' to medium (250 msec delay). n Goto next object. This command allows to find far ships, etc. o Incorporate any tentative pattern, then forward one generation. p Toggle running display of mouse position. Position is only for reference during a session, and does not effect coordinates of saved points. r Redraw the screen. s Set evolution speed for `g' to slow speed (500 msec delay). t Test n-state transition. Enter 5 digits (start state and 4 neighbors states), get result state. u Undo manipulations of the tentative pattern, but not the load (tentative pattern is restored to the original position and in- dentation). v View internal variable values and other information. x Change pivot position of the tentative points to the current po- sition of the mouse. COMMANDS IN SHIFT MODE PageUp, PageDown, Home, End, 1, 2, 3, 4, 6, 7, 8, 9 and cursor keys move the universe faster. COMMANDS FOR WIDGET PageUp, PageDown, Home, and End keys scroll the list. Esc key makes exit from the widget. Shift-PageUp key sets upper directory. Left and Right cursor keys or Tab move the active position to the previous/next widget item. Up and Down cursor keys move the active position within the list. Printable symbols maybe used to type filename. Return key is used to acti- vate the widget item. Backspace and Delete keys remove last inputted char- acter. MOUSE WHEEL controls vertical scrolling of the universel. It also scrolls the list with the widget. BUTTON BINDINGS IN NORMAL MODE 1 Activate a cell at the cursor, giving it the currently selected state. In a 2-state automaton cells are always activated with state 1. In an N-state automaton, you pick your current color as described in N-STATE SUPPORT below. 2 Delete a cell at the cursor (force it to state 0). To clear a region select it by mouse and press C. 3 Erase any previous selection box. If you drag the cursor with button 3 held down, then release it, the rectangle between the press and release points is boxed and made tentative (as though it had just been loaded and not yet incorporated). The tentative pattern can then be moved, flipped, and rotated before re-incor- porating it. If you've just clicked at a tile then this tile be- comes the center of the screen. BUTTON BINDINGS WITH TENTATIVE PATTERN LOADED 1 Move pattern to current position. 2 Flip pattern about its x-axis. 3 Rotate pattern clockwise about its origin. BUTTON BINDINGS WITH STATE WINDOW 1 Select state. 2 Set color for the state. WIDGET OPTIONS Load pattern and Load pattern part modes The radio buttons choose direct or tentative mode. The direct mode sets to load pattern directly into the active space. This removes previous pat- tern. The tentative mode (default) sets to load pattern into tentative space. This allows to tranform a pattern before the addition to the active pattern. Save pattern mode The radio buttons allow to specify one of A D I M P R S. For details on the A D I M P R formats, see the LOAD FILE FORMAT section below; `S' format is a sequence of P blocks, one for each blob in the picture, with appropri- ate offsets for each. Save script mode Two radio buttons are for collected or plain format. The plain format is just a list of inclusions. The collected one resolves all inclusions in the saved file. See the PATTERN INCLUSION section below for more details. MAIN LOAD FILE FORMAT A .l image file is an ordinary text file consisting of lines terminated by the newline character. It is interpreted as one or more image sections separated by section lines beginning with `#'. Lines led by `##' are con- sidered as hidden comments and ignored. Some format directives may use the offsets which are useful with direct load mode and with I-format. These offsets are ignored in the tentative load mode. Each image section is interpreted according to the format letter following its section line #. The format letters are: A - Absolute Each following line is interpreted as an absolute (x,y) coordinate pair for a cell to be put in state 1 (default). This format is deprecated and should not be used for new patterns. However it is default - it is used in absence of any format directive. The -A option of lifeconv emits it. B name and E - Pattern blocks Patterns enclosed by #B <name> and #E lines are skipped when loading a whole file, but may be accessed by adding :<name> to the file name. They are useful for bundling related patterns into the same file. Access is by sequentially skipping lines not in the block, so excessive numbers of blocks in the same file may slow down the loading process. Pattern blocks may not be nested. Relative image sections (D, I, M, P, ...) are normally drawn with 0,0 at the center of the universe. This may be changed by including a pair of whitespace-separated integers after the format character. If this is done, these will be interpreted as a pair of x and y offsets, and the image sec- tion will be drawn with its upper left corner displaced by those offsets. A leading image section with no header line is treated as though it had a `#A' header. Thus, version 1.00 image files will load properly. C - Comment Lines beginning with "C" are comments that the user may have automatically written to the save file, and which may be viewed from within Xlife. D [xoff [yoff]] - Relative to the previous coordinate pair Each following line is interpreted as a (x,y) coordinate pair relative to the previous one, for a non-empty cell. The first is relative to the de- fault (0,0) or if they are given to (xoff, yoff). The -D option of life- conv emits it. I [xoff [yoff [rotate [flip [delay]]]]] - include A #I line should have whitespace-separated fields after the #I consisting of a pattern name and five optional integer parameters (x, y offsets, rota- tion, flip, and delay as defined in section on inclusion, below). The named pattern is loaded as if it had been included in the image at this point with the given transformation applied. The offsets, if present, dis- place the load point of the pattern relative to the center of the pattern space. The include facility is useful for assembling `sampler' collections of interesting patterns, as well as maintaining structured representations of complex patterns. See also PATTERN INCLUSION and STRUCTURED PATTERN EDITING sections. K outcome string - special comment This string should define the results of the evolution of the pattern. M [xsize, ysize] [xoff [yoff]] - run-length encoding with optional sizes and offsets. The sizes are ignored by the current version of xlife. Only the characters b, $, !, the letters from A to X and from o to y, and the digits 0 until 9 should appear except whitechars which are ignored. The data is ordered a row at a time from top to bottom, and each row is ordered left to right. A $ represents the end of each row and an optional ! represents the end of the pattern. For two-state rules, a b represents an off cell, and an o represents an on cell. For rules with more than two states, a . represents a zero state; states 1..24 are repre- sented by A..X; states 25..48 by pA..pX; states 49..72 by qA..qX; 241..255 by yA..yO. The pattern reader is flexible and will permit b and . inter- changeably and o and A interchangeably. Any of state character can be led ahead by a positive integer, which then is interpretated as the repettion of that character. Any illegal character will be interpretated as whitechar and ignored. The -M option of lifeconv emits this format. N - Name This line contains the internal name of the pattern (which may differ from the the name of the file. O - Owner This line contains information on the person who wrote the file, it is written in the form: id "name"@machine date, for example. #0 jb7m "Jon C. R. Bennett"@sushi.andrew.cmu.edu Fri Jan 12 18:25:54 1990 A 0 (zero) may be used instead of O (xlife generates it during S command execution). Note: This timestamp line has changed format at least three times since Xlife 1.0. It is probably not wise to try and parse these unless you see known format version ID (on the first line of the file). P [xoff [yoff]] - Picture with optional offset coordinate pair. Each line in the section is interpreted as a scan line of a relative image. Each * character turns the corresponding cell on. All other characters leave the corresponding cell off. For multi-state automata, characters may be letters, @, ~, and digits, with '*' corresponding to 1. The -P option of lifeconv emits this format. R [xoff [yoff]] - Relative with optional offsets Each following line is interpreted as a (x,y) coordinate pair relative to the center of the pattern space. These relative image sections are nor- mally drawn with 0,0 on the center of the pattern space. This may be changed by including a pair of whitespace-separated integers after the for- mat character. If this is done, these will be interpreted as a pair of x and y offsets, and the image section will be drawn with its upper left cor- ner displaced from the cursor position by those offsets. The -R option of lifeconv emits this format. T survivedigits/borndigits - Set new transition rules This line defines a new set of 2-state rules. survivedigits and borndigits are each a sublist of digits out of the range 0 up to 8, counting the num- ber of neighbours when the central cell in the neighbourhood survives/is born to state ON. For example the default and classical rules for Conway's Game of Life are: #T 23/3. You may use also named rules like with `R' com- mand: `wireworld', `seeds', `life', `lifehistory' or `life+', `brian'. It is possible to add topology after `:'. For example, `life+:T200,200' means Life with History rules at the torus grid. You may also use rules defini- tion in `B0...8/S0...8' notation, where the digits after B specify the counts of live neighbors necessary for a cell to be born in the next gener- ation, and the digits after S specify the counts of live neighbors neces- sary for a cell to survive to the next generation. U filename - Use Format is #U followed by a filename. It loads a rule-set file just as if the user had typed in the name. If the named file is already loaded, it will not be reloaded. It is possible to add topology after `:' like with `#T' directive. X filename - palette for the piXels It loads a palette-set file with given name. More section formats may be added in the future. PATTERN INCLUSION The #I command, as described above, has the following format: #I <pattern> <x> <y> <rotate> <flip> <delay> Any prefix of fields that includes a pattern name is acceptable, with the natural defaults (no delay, no flip, no rotate, no y or x offset). In the above <pattern> is a pattern name (described below); <x>,<y> are integers representing horizontal and vertical off- sets; and <rotate> is an integer that specifies the number of times the pattern is rotated 90 degrees clockwise around the ori- gin. Any rotation value (positive or negative) is ac- ceptable, as all are taken mod 4 (true mod, not "%"). <flip> is a multiplier (1 or -1) for the y coordinate that specifies a flip about the x-axis. Other integers are accepted and silently mapped to 1. <delay> is an integer specifying the number of generations to perform before loading the pattern (negative values have same effect as 0). Note that all of the transformations applied to an in- cluded pattern are taken relative to the pattern that includes it. Thus, loading an assemblage of included patterns works as one would expect. A pattern name takes one of the following three forms: <file> include whole file <file> (like old format) <file>:<name> include pattern block <name> in <file> :<name> include pattern block <name> in current file (Note that <file>: is not allowed.) A file may also include literal or pattern blocks. A pattern block is a pattern given in any acceptable format between a line containing "#B <name>" and another line containing "#E". Pattern blocks are skipped when including a whole file. (Note that pattern blocks cannot be nested.) The -I and -C options of lifeconv may be useful for collecting inclusions from multiple files into a single self-contained file. When you save a pattern in `I' mode, the program automatically does a pat- tern analysis to detect `blobs' (completely connected regions of live cells). Repeated blobs are recognized, even if they are rotated or re- flected. If there is only one blob, the save output is identical to #P format. Otherwise the output is a list of blobs followed by #I lines that will recreate the saved pattern. This has two advantages: duplicate blobs are only written once, and common pattern elements are recognized and named (so the save file is also a census). The elements container for this recognition is the file "named-patterns" (or file selected by -l option at startup). It specifies the name of a file containing the names of patterns to be recognized and named when doing I-format (structured) saves. A leading slash distinguishes an absolute pathname; otherwise the relative name is searched for beneath the LIFEPATH or default directories (as for a pattern file). Each line of this file contains up to three fields; a pattern name, a pattern file or file:block reference (as for the `l' command) and a cycle length. When the cycle length is 0, only one recognition template is generated from each entry; when it is nonzero, one is generated for each step in the cycle (with steps after 0 distinguished by a number suffix on the name). Thus, for example, an entry that reads glider ss:glider 2 Will generate two recognition templates, one named `glider' and another named `glider2'. The cycle length is optional and defaults to 0; the sec- ond field is optional and defaults to the value of the first. Comments (led by #) and blank lines are ignored. This name container is only acti- vated for the life rules. The file "named-patterns" default content referes to the file "match.l" which contains named patterns list in the #B/#E-format. N-STATE SUPPORT Xlife includes support for automata with up to 64 states using the (von- Neumann-style) 4-cell rotationally symmetric neighborhood (rotate4, de- fault), rotate4reflect or absence of symmetry; to invoke it, load a rule- set file using the `F' command. It is also possible to use the (Moore- style) 8-cell rotationally symmetric neighborhood for the special cases: WireWorld and 3-components (generations) rules with up to 256 states. The Moore style maybe also used in the general case but only up to 11 states. These two cases are established by `#T' form in a pattern file or by direct manual input after the `R' command (use recognized words or a form like 345/2/4). Many interesting automata including the Wireworld-4 construct and the UCC described in E. F. Codd's 1968 ACM monograph can be implemented by specifying appropriate transition functions. Don't rotate or flip pattern with non-symmetrical rules! When Xlife is used in this mode, the program uses color to indicate states. Pattern picture files may contain digits to specify the states of picture cells; `*' is interpreted as 1. Color-picker radio buttons are set up at the right-hand side of the input window; by clicking your cursor on a but- ton, you set button 1 to paint with that color. You can return to 2-state mode with the `R' command. Refer to the rule-set file `codd.r' for an example of transition definition syntax. Each line contains either a directive or 6 digits or letters arranged as <old-state><neighbor><neighbor><neighbor><neighbor><new-state> For <old-state> or <neighbor> you may also specify a state set; digits or letters enclosed in square brackets. This wild-cards the transition in the obvious way. You should use letters instead numbers for states above 9, so use A instead 10, B instead 11, and so on. The letter `a' means 36, `b' - 37, etc. The sign `@' means 62, `~' - 63. Comments (begun with `#') are permitted in the file. You can arrange for rulesets to be loaded automatically by putting a `#U' directive in a pattern file. When you save a pattern, a #U is automati- cally generated into the save file giving the name of the current ruleset. The directive states <maxstates> tells the code what the automaton's count of cell states is. Rule tables usually don't specify every possible set of inputs. For those not listed, the central cell remains unchanged if `passive' declaration is not used. The presence of `passive' declaration will require manual input of missed transition. So if, while evolving a pattern, the code finds a cell and neighborhood in a state for which no transition has been specified, the program queries the user for a new state, and the tuple implied is added to the database. A line of the form passive <maxstate> instructs the code that all combinations of cell and neighbor states up to and including <maxstate> for which there is no explicit rule leave the cell status unchanged. A `passive' declaration in a rules file can be partially overridden by later, explicit transition rules. The form `passive 0' is a way to say to use manual input for every missed transition. The directive nosymmetries sets absence of symmetry in rules. It may be used with Langton Ants, Per- rier loops, etc. The directive rotate4reflect sets this type of symmetry. It may be used with Bank I, II, III, IV, etc. The directive Moore sets this neighborhood. It may be used with Bank III, etc. The default symmetry is `rotate8'. This directive should precede state or symmetry de- claration. You can also specify rules depending on a neighbor count. A rule line of the form S(N*C)R with S, N, C, and R being digits, is interpreted to mean that if a cell has state S and exactly C neighbors of state N, the result state is R. For an example of usage, see the Wireworld-4 rules file. This doesn't works with `nosymmetries' or with `Moore'. Rules are checked in the order given in the file - the first rule that matches is applied. If you want (`passive' should be set in this case), you can write rules in the form of general cases and exceptions, as long as the exceptions appear first in the file. When the evolution function encounters a neighborhood for which there is no defined transition, it stops and boxes that neighborhood. You are prompted for a result state. Once you've entered it, the evolution function contin- ues and the new transition rule is appended to a new-transitions file in the current directory. This feature can't be activated because all transi- tions are defined. PRISONER'S DILEMMA MODELS In the June 1995 Scientific American, the article "The Arithmetic of Mu- tual" Help" (by Martin A. Nowak, Robert M. May and Karl Sigmund) describes an interesting class of cellular automata that model iterated Prisoner's Dilemma situations. These games can illustrate stable and winning cooper- ate/defect strategies for situations in which each agent repeatedly inter- acts with near neighbors. In the same issue, Alun L. Lloyd's "Mathematical Games" column goes into more detail about these simulations. These are two-state automata. In Alun's implementation one state always cooperates, one always defects (higher states could model Tit-for-Tat, Gen- erous Tit-for-Tat, or Pavlov). There is a payoff matrix of the following form: +-----------+--------------------+ | Payoff | Cooperate Defect | +-----------+--------------------+ | Cooperate | 1 a | | Defect | b 0 | +-----------+--------------------+ To make the game interesting, b must be greater than 1. (Lloyd's simula- tion only considers the case a = 0.) On each round, each cell first plays the game with each of its neighbors in turn. Then, each cell looks at the payoffs of its neighbors (and its own payoff) and switches to the strategy with the highest payoff). To set up such a game, use the `R' command in the following form: R<b>$<a> You may also use #T form in the pattern file. For example, to set up Lloyd's simulation, do `R1.85$0'. In these simula- tions, use the following mapping between states and strategies: 0 Quiescent. 1 Live, always cooperates. 2 Live, always defects. 3 A transition, from cooperator to defector. It behaves like defector. 4 A transition, from defector to cooperator. It behaves like cooperator. Interesting b values are in the range (1, 2]; Lloyd likes 1.85. Different values produce wide ranges of different behaviors, including stable end states, statistical equilibria and cycles with large swings. Initial clus- tering of cooperators is also important; a single cooperator will always be snuffed by surrounding defectors, but a block of 4 or more may be able to defend themselves and earn a high enough relative payoff to convert neigh- bors. Lloyd included illustrations of a 1.85 game starting with one defector in a sea of cooperators. The resulting patterns look like Persian carpets or Koch snowflake curves. OTHER FEATURES OF RULE FILES AND EDITING The directive debug NUMBER is ignored. Transition rules entered interactively are appended (commented with user ID and timestamp) to the file new.transitions in the current directory. This file can later be selectively merged with your original ruleset using a text editor. STRUCTURED PATTERN EDITING Almost all large Life patterns that exhibit well-defined behavior (such as the breeder) are in fact composed of smaller patterns that combine in a predictable way. Storing such patterns as assemblies of subpatterns can greatly aid future experimentation as well as synthesis of still more com- plex patterns. Here we'll explain the structured-editing features, and give several examples of their use. Overview of structured editing Structured editing should cut down on the number of Life patterns stored as atomic images (i.e. raw bitmaps or point sets). Once a glider gun, for ex- ample, has been defined, there should be no need to duplicate the pattern. It should instead be possible to refer to it by name, as a known mechanism with well-established properties. In fact, the glider gun itself exhibits some structure, as it is composed of two period 30 shuttles that interact to produce gliders. Ultimately, the "interesting" part of the period 30 shuttle does not seem to have any structure, and hence must be represented a picture, such as the following: ..*... .*.*.. *...** *...** *...** .*.*.. ..*... Unfortunately, it is not enough to merely place such a pattern at the cor- rect coordinates. For example, we can rotate this pattern by multiples of 90 degrees without essentially changing its behavior. While this particu- lar pattern has mirror symmetry about its horizontal dividing line, other patterns may not, so we may additionally wish to take the mirror image of a pattern. It would be undesirable to maintain eight separate bitmaps for what is really the same pattern, so we would like a facility to perform ba- sic geometric transformations on patterns to be included in more complex ones. A more subtle issue is that of timing. When placed between appropriate stabilizing objects (such as eaters or blocks) the above pattern will os- cillate with a period of 30. Hence, when defining a complex pattern, we may need to insist (in addition to any geometric transformations) that it be placed within the larger pattern at a particular phase in its cycle. By controlling position, rotation, flip, and phase shift, we may combine patterns in any desired manner. The #I extensions to Xlife makes this pos- sible, and the structured editing features make it (relatively) convenient. Ideally, the new editing features will make it possible to use the #I for- mat without ever looking at the description file. The advanced Life exper- imenter may, however, wish to modify #I lines with a text editor in order to achieve very specific effects (still more advanced CAD tools would elim- inate this need). To attempt the following examples, you should be running Xlife. You must have a copy of the file "ex.l", supplied with the release, in either the directory in which you start up Xlife, or in the pattern directory. Before trying any of the examples, type `C' to clear the workspace, if it is not already clear. Experimenting with gun collisions. Type `l' to load in a pattern. Backspace over the default directory, if there is one (probably the pattern library) and type "ex:gun". This will load the pattern "gun" from the file "ex.l" in either the pattern library or current directory. The pattern consists of a glider gun before it has produced any gliders. Get a feel for the movement, flip, and rotation operations performed with the mouse buttons. All operations are performed with respect to the origin of the pattern, which is indicated by a single dot at the smallest scales and becomes an X shape at the larger scales (zoom in on it to see this). In order to place patterns such as glider guns, it is especially important to know the direction of the outgoing glider stream. You may preview this by generating the loaded pattern with the `G' command (*not* the `g' com- mand). Initially, you will want to generate enough steps to see the stream, so type 100 when prompted for the number of steps. It is better to use `I' command before `G' with first pattern. The negative phase shifts otherwise may be produced by `W' command. The negative shifts should be edited manually. Note that the mouse buttons continue to perform transformations on the gen- erated pattern. Place the pattern as desired. It will be incorporated into the main universe when any of the commands g, h, o, l, or W are typed. To incorporate it without doing anything else, use `I'. Now, load another glider gun in the same manner. Place the two guns in such a way that their outgoing gliders collide. Not all collisions are well behaved, and you may wish to produce a specific collision, such as a clean annihilation of gliders. The references mentioned at the top, and some of the patterns supplied with Xlife, are a good source of interesting collisions. Use `G' on the second glider gun to control the phase differ- ence between the colliding gliders. Type `g' to let the pattern go and see what happens. If the collision was chosen randomly, there is a good chance that it will merely break down into chaos. Some collisions, however, produce interesting effects. Save your gun collision into a file using the `W' command. Now type `C' and use `l' to load it back in. Note that the result is not what you would expect from saving the current pattern. That is, even if the pattern did break down into chaos, the pattern written by `W' corresponds to the colli- sion as you set it up. If you type `g' then you should witness the same sequence of events as before. The file written by `W' is not a raw pattern image, but rather a "load script." That is, it gives Xlife enough information to reconstruct your placement of loaded patterns. It does not contain any changes made by drawing or erasing cells with the mouse, but such changes deviate from the philosophy of pattern structuring and should be avoided except when drawing atomic patterns. (In any case, the `S' command is provided for saving the whole image in an unstructured way.) Setting up a glider mirror. It is possible to reflect a stream of gliders as if by a mirror, using a period 30 shuttle with eaters at the ends. The mirror will not work unless the stream (from a period 30 gun) and the mirror are perfectly positioned and in phase. In general, this may involve some simple yet tedious calcu- lation or else a still more tedious process of trial and error. In the following, however, we will see how to use the editing features to produce the desired effect reasonably simply. Load in ex:gun, as before, and let it generate (with `G') until the outgo- ing stream contains 20 or so gliders. This is the stream we will be re- flecting. Now load in ex:mircollision. This pattern consists of a glider poised to be reflected from a mirror. Use rotates, flips, and `G' (one step at a time) until the the mirror glider is an exact copy of the glider furthest from the gun. Use the mouse to move the loaded pattern so that these two gliders occupy exactly the same five cells. It may help to zoom in on the pattern. Now, simply type `g' and let the pattern go. It you performed the above steps correctly, you should see a stream of gliders bouncing off the mir- ror. Add more mirrors, if desired, and save the result into a file using `W' Details of the structured save format Skip the following if you are not interested in familiarizing yourself with the details of the #I format. Take a look at the file generated by `W' in the above. It consists of a sequence of #I lines, the first containing ex:gun, and the others contain- ing ex:mircollision. The latter lines each have a delay value as their fi- nal parameter, and these parameters will most likely be in the hundreds, as this is the number of steps it takes to make the stream of gliders used as a reference. Note that the mirror is a period 30 oscillator, so we may replace all of these numbers by their values mod 30 without affecting the crucial phase difference between the mirror(s) and the gun. Do this, and look at the pattern in Xlife. Note that it takes less time to load, and that the loaded pattern does not contain a long stream of gliders. Type `g' to ver- ify that the mirrors still work (if not, make sure you computed mod cor- rectly). The resulting pattern will contain spurious gliders. These are the gliders that came with the pattern ex:mircollision. Fortunately, ex:mircollision contains ex:mirror with no moves, flips,or rotations applied. Hence, by replacing all instances of ex:mircollision by ex:mirror in your file, you will obtain the same pattern as before, but without the spurious gliders. This illustrates the notion of including extra parts in a pattern for ref- erence and eliminating them in the final edit. Use of this technique can substantially reduce the need for explicit calculation when constructing complex patterns. Constructing a Structured Pattern from a Template. Having familiarized yourself with the use of load scripts, you may wish to construct structured versions of old patterns you made in the previous ver- sion of Xlife. This can be done in a bottom-up fashion by loading in the raw image and building up subpatterns using the initial image as a refer- ence. You first need to identify the the atomic subpatterns in the old pattern. For example, in the mirror of the previous example, the atomic patterns are two eaters and the period 30 oscillator (shown earlier in this document). The template pattern should not be written into the load script, and this may be prevented by using the `D' command after this pattern has been in- corporated into the universe. The effects of having the template written to the load script are non-fatal, and may be corrected with a text editor. However, it is best to get in the habit of typing `I' (include pattern), The mirror in "ex.l" is already given in a structured way, but it will suf- fice to illustrate the technique. To place the template, load ex:mirror, and type and the oscillator (ex:oscil) and place each pattern over the cor- responding part of the old image. Use `W' to write the load script. If the original mirror had been stored as a bitmap then you would have transformed a seemingly arbitrary set of points into a structured pattern. Patterns defined in this way can later be combined into more complex pat- terns, and at any level, the pattern can be seen to be a logical combina- tion of well-understood components rather than an amorphous conglomeration of Life cells. Using the `lifeconv' utility. One seeming disadvantage of structuring patterns with the `W' command is that a pattern that used to reside in a single file may now be spread over several files. There may be too many to easily keep track of them. For the user who wishes only to use #I as a means of collecting a structured pattern into a single file, however, the -I and -C options of `lifeconv' utility are provided. The lifeconv utility takes a pattern name as an argument (with the same de- fault directories as in the `l' command). It writes a file to standard output that contains an equivalent version of the pattern in a different format. Usage is: lifeconv pattern [-ACDIMPRSp] >destination where destination is any valid file name (a .l extension is recommended). The option controls the format in which the destination file is written. These formats are identical to those described under the `S' (save) com- mand, except for C. Either -C or -I will suffice to convert a pattern with inclusions into a single-file pattern with all the inclusions resolved. The difference be- tween them is that -I does an automatic scene analysis of the file after merging all inclusions into one big picture, while -C just resolves the in- clusions textually. The one advantage of the latter method is that it pre- serves any pattern name and structure information present in the input file: -I renames all the pattern fragments. Try these options on any of the files written by `W' in examples 1, 2, and 3. Old files in #P format may not have same y coordinate when read by the new release. For best results, use "lifeconv -p name ..." on old files. This utility may also be used for conversion from other formats (MCL, LIF, ...) to native XLife format. ENVIRONMENT The program has a compiled-in default for its global pattern directory, LIFEDIR (normally /usr/share/xlife). If the the variable LIFEPATH is set to a colon-separated list of directo- ries, these directories (and their first-level subdirectories) will be searched for pattern-file names and rulesets. The default list includes "." and LIFEDIR; that is, pattern files are searched for, by default, below the current directory and below the global pattern directory. The recommended way to organize your pattern directories is to have one subdirectory per automaton. The distribution provides the following: life contains an extensive library of interesting Life patterns. life-like contains a library of interesting similar to Life patterns (seeds, life without death, highlife replicator, brian's brain, starwars, ...). codd contains transition rules and several demos. devore variation of the Codd self-replicating computer. HPP is the earliest lattice gas model. perrier this loop is a self-reproducing calculator. wireworld contains transition rules and a test pattern for the Wireworld automaton as described in the January 1990 issue of Scientific American (Computer Recre- ations, p. 146). wireworld-4 contains transition rules and test patterns for the Wireworld-4 automata. Wireworld-4 is a variant of classical Wireworld at the von-Neumann-style rotationally symmetric neighborhood. byl, chou-reggia contain small n-state replicators. langton contains famous loop and ant(s). evoloop, sexyloop, SDSR contain evolutionary replicators. pd contains patterns for Lloyd's variant of Prisoner's Dilemma games. These will be copied under LIFEDIR by a normal installation. The distribu- tion may contain additional directories with more patterns. EXPLORATION Here are some 2-state rules to experiment with: 23/3 the default, of course; Conway's "Life" rules. 1234/3 patterns "crystallize" 12345/45 patterns become contained 12345/4 same as above, but settles VERY quickly 5/12 floor tile patterns... Variations of this tend to be interesting as well. 1357/1357 replicators world... /2 seeds - most patterns expand indefinitely, some inter- esting ones. Fast gliders. 012345678/3 life without death. Ladders. AUTHORS Algorithm, implementation and file format enhancements: Jon Bennett Original X code: Chuck Silvers Enhancements to #I format and user interface: Paul Callahan Auto-sizing, load format enhancements, 8-state support, all of the non-Life automata, still-life detection, boxing: Eric S. Raymond Many new commands, subpixel resolution, M format: Achim Flammenkamp A lot of fixes, improvements, and a save/load widget: Vladimir Lidovski SEE ALSO lifeconv(6), xlife(6). Xlife(6)
NAME | SYNTAX | DESCRIPTION | COMMANDS | COMMANDS IN SHIFT MODE | COMMANDS FOR WIDGET | MOUSE WHEEL | BUTTON BINDINGS IN NORMAL MODE | BUTTON BINDINGS WITH TENTATIVE PATTERN LOADED | BUTTON BINDINGS WITH STATE WINDOW | WIDGET OPTIONS | MAIN LOAD FILE FORMAT | PATTERN INCLUSION | N-STATE SUPPORT | PRISONER'S DILEMMA MODELS | OTHER FEATURES OF RULE FILES AND EDITING | STRUCTURED PATTERN EDITING | ENVIRONMENT | EXPLORATION | AUTHORS | SEE ALSO
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