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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<html>
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<head>
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<meta name="GENERATOR" content="mkd2html 2.1.3 DL=DISCOUNT">
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<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=utf-8">
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<link rel="stylesheet"
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type="text/css"
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href="../hint.css">
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<title>Most devolving</title>
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</head>
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<body>
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<h1>Most devolving</h1>
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<p>Philip Blakely<br>
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Cambridge, UK<br>
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<a href="mailto:pmblakely@gmail.com">pmblakely@gmail.com</a></p>
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<h2>Judges' comments:</h2>
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<h3>To build:</h3>
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<pre><code>make blakely
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</code></pre>
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<h3>To run:</h3>
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<pre><code># Zoom out and make your terminal window 53 or more lines deep
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./blakely < blakely.c | head -300
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</code></pre>
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<h3>Try:</h3>
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<pre><code>./blakely < 3.dat | head -100
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./blakely - < 3.dat | head -40
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./blakely < evolve_to_3.dat | head -55
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./blakely < t0_3.dat
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</code></pre>
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<h3>Selected Judges Remarks:</h3>
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<p>This program plays Life, computes Pi to 16 digits
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if given its own source as input, and allows to check if your garden
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is a <a href="http://en.wikipedia.org/wiki/Garden_of_Eden_%28cellular_automaton%29">Garden of Eden</a>, all in one source.</p>
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<p>If you have enough time to spare, put the plan of your garden in a text file,
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and run:</p>
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<pre><code>./blakely - < garden.txt
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</code></pre>
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<h2>Author’s comments:</h2>
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<h2>Remarks</h2>
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<p>This program uses a well-known algorithm in order to display pi to
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fifteen decimal places. The source-layout itself demonstrates the importance of
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using the correct amount of whitespace in code and the clear superiority of spaces over tabs.</p>
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<p>In order to see the main feature of the code, type:</p>
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<pre><code>./blakely < blakely.c
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</code></pre>
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<p>and wait for about four seconds before using Ctrl-C (or whatever) to end the program. The
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results are best viewed in a terminal window at least 60 characters
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high and wide. Alternatively, redirect the output to a separate file
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(killing when necessary).</p>
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<h2>Overview</h2>
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<p>The program emulates John Conway’s ceullular automaton known as “The
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Game of Life”, using standard input as a starting grid. The layout of
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the source-code is such that it evolves to a digital representation of
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the first 15 decimal places of pi after 4 time steps. This was setup
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using the other feature of the program which can be demonstrated as follows:</p>
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<pre><code>./blakely - < 3.dat
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</code></pre>
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<p>The program will first display the grid given in 3.dat, and then three
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more grids (taking a few minutes to display the last). Waiting for any more grids will
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take a substantial amount of time. The final grid has been put into
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evolve_to_3.dat, and if you type</p>
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<pre><code>./blakely < evolve_to_3.dat
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</code></pre>
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<p>then the 3 will reappear after three time steps.</p>
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<p>As should now be clear, this use of program will attempt to evolve a given setup backwards in
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time according to the Life rules. The resulting grid is clearly not
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necessarily unique. The program will evolve backwards given <em>any</em> single
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command line option.</p>
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<p>When evolving forwards, the code can only be stopped by killing the
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program. In the reverse direction, the code can either be killed, or
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will stop if it is unable to find a grid that will evolve to the
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current layout correctly. This can be seen with the sample grid
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t0_3.dat, which evolves backwards by only two time-steps.</p>
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<h2>Input file format</h2>
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<p>The input files must encode a square grid, where a space is a dead
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cell, and any other character (except a newline) is a living cell. Each line must be the same
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length, and end with a single newline character \n (ASCII 10), including the last line. When
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designing grids, it may help to type full-stops in place of spaces,
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and do a global replace afterwards. Any deviation from this format will
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cause errors in the output.</p>
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<h2>Limitations</h2>
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<p>This is only an approximation to the original Life, as it takes place
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on a finite grid, with borders that are automatically killed off
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before each time step. However, when evolving backwards, the resulting
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grids will not cause any cells on the boundaries to come alive.
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As the display is performed before killing off the borders, some
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boundary cells may sometimes appear to be alive, but not be treated as
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such for the following time-step, although any living cells on the
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right border will never be displayed.</p>
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<p>The maximum grid size is currently 99 by 99 (exceeding this will cause a
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seg-fault), but changing the two 9802s to MAX_SIZE*MAX_SIZE+1 will
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solve this, although some reformatting of the
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code may have to be done to allow larger numbers.</p>
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<h2>Compiler warnings/assumptions</h2>
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<p>When compiled with the -Wall -pedantic -ansi options of gcc, some
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warnings suggesting extra parentheses occur (not necessary for anyone
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fully conversant with operator precedence). There is one unused
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variable, v, but unnamed function parameters are not permitted in ANSI
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C, so naming it is necessary, and gcc no longer warns about its
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existence, although earlier versions did.</p>
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<p>Since the program calculates ASCII character values for display, an
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ASCII based system is required to run it. Also, as mentioned above,
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any system that uses anything other than a plain ‘\n’ to end a line will cause
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problems when reading in files.</p>
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<h2>Obfuscations</h2>
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<p>Given the finely-tuned layout required to evolve into pi, this is one of the
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main obfuscations used in the code. However, running the code through the
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preprocessor, expanding the defines, and applying GNU’s indent, although
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making the location of functions and statements clear, by no means makes the
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code entirely clear. Note that expanding out the #defines does not take the
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program over the character limit. The main reason for these is to do with the
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layout, since there are few places that keywords or tokens of over 2
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characters can be fitted, and requiring the first few lines to be #includes
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would cause similar problems.</p>
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<p>Other obfuscations used are:</p>
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<ul>
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<li>Use of the classic 2[a] syntax to access the third element of the
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array a</li>
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<li>Nested ternary operators, combined with shortcut evaluation being
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required for correct operation</li>
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<li>Use of the comma operator to embed operations inside one another</li>
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<li>Calculation of ASCII codes</li>
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<li>Needlessly recursive functions</li>
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<li>Use of bitwise-operations.</li>
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<li>Storing a variable whose value could easily be found from another</li>
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<li>Use of gotos to emulate a for loop</li>
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</ul>
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<h2>Algorithm</h2>
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<p>The forwards evolution of the grid is straightforward.</p>
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<p>The reverse evolution is done using a brute-force method. As far as I
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know, a brute-force method is the only viable automatic approach for
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general grids, although more intelligent algorithms would be possible
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given more space.</p>
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<p>The program starts with an empty “trial” grid and, starting from the
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top-left, tries all possibilities for the neighbours of the current
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cell that will cause the cell to evolve to the required state. It then
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proceeds to the right and down. Thus, it only ever needs to look at
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the cells below and to the right when testing. However, the already
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defined cells above and/or to the left of the cell may mean that there
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are no possibilities that will give the correct state, in which case
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the code backtracks and tries other possibilities on previous
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cells. The program knows it has a valid grid if it gets to the last
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cell. If it cannot find a valid grid, the program exits.</p>
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<p>Since this uses brute-force, it can be very slow. (In fact, the
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various obfuscations have, at least for the gcc compiler,
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caused a substantial slowdown.)</p>
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<h2>Program layout</h2>
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<p>The “calculation” of pi was chosen purely because algorithms to find
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pi are numerous, but the Game of Life is rarely (if ever?) used for
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this purpose. Also, separate digits made determining the layout somewhat easier.</p>
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<p>Deriving the layout was the most complicated part of the program. As is clear from
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the final layout featuring pi, the grid was divided into sixteen squares,
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and layouts that would evolve to each of the nine digits required were
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found. (This used the three-by-five digit-layout embedded in, at first, a
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nine-by-nine grid, then in larger grids, until fifteen-by-fifteen was
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reached.) The fifteen-by-fifteen grids give enough blank cells around
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them that the digits will not collide when evolving.</p>
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<p>However, this did not allow for sufficient characters to fit the code
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into. Therefore it was necessary to add some regions that would quickly die off
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without expanding to collide with the digits' evolution.
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Groups of cells such as singletons, pairs, and larger groups like</p>
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<pre><code>* * * * * * * * * *
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*****************
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* * * * * * * * * *
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</code></pre>
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<p>were useful in this regard.</p>
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<p>Other problems were given by keywords which need to be all in one
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string, keywords requiring space after them, and
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multi-character tokens. Some of these problems were dealt with by
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using the #defines and #includes given in the build-script, as there
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was no way to have sufficient separate lines in the code to do this
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without causing many difficulties. Some rejigging of the grid’s layout
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as the code was fitted into its format was also done, resorting to
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trial-and-improvement in some cases. Occasional use of constructs such
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as f -= -3 was made as f += 3 could not be fitted into the required format.
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The fact that the borders would be killed off immediately was also helpful.</p>
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<p>It should be noted that evolving a full 60-by-60 grid backwards using
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this code would probably take us at least up to the heat-death of the
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universe.</p>
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<p>The command ./blakely - < blakely.c is therefore <em>not</em> recommended.</p>
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<hr />
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<TABLE><TR>
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<TD><a rel="license" href="http://creativecommons.org/licenses/by-sa/3.0/"><img alt="Creative Commons License" style="border-width:0" src="http://i.creativecommons.org/l/by-sa/3.0/88x31.png" /></a></TD>
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<TD><P>© Copyright 1984-2012,
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<A HREF="/judges.html">Leo Broukhis, Simon Cooper, Landon Curt Noll</A>
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- All rights reserved<BR>
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This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/3.0/">Creative Commons Attribution-ShareAlike 3.0 Unported License</a>.</P></TD>
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</TR></TABLE>
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