NetNews Usenet Archive 1992 #19

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Newsgroups: comp.theory.cell-automata Path: sparky!uunet!munnari.oz.au!manuel!sserve!pdact!dbell From: dbell@pdact.pd.necisa.oz.au (David I. Bell) Subject: Spaceships in Comway's Life (Part 2b) Organization: NEC Information Systems Australia, Canberra Date: Fri, 28 Aug 1992 01:39:00 GMT Message-ID: <1992Aug28.013900.27102@pdact.pd.necisa.oz.au> Keywords: life Sender: news@pdact.pd.necisa.oz.au (News Holder) Lines: 778 ----------------- [Continued from previous mail article] -------------------- Using his modified version of my program, Hartmut Holzwart recently did a search for large long period 2 spaceships. He found several dozen such ships with many possible variations. In this article I will give only a representative sample of these spaceships. Following are three variations on relatively small period 2 ships. These are related to the first long spaceship found by Dean Hickerson. [Several similar small period 2 spaceships (speed c/2)] ............ ............. ............O ............ ............. .........OOOO .........O.O .........O.O. .........OO.. ........O..O ........O..O. .......O...OO .......OO... .......OO.... .......OOOO.O ......O..... ......O...... ......O...... .....OOOOOO. .....OOOOOO.O .....OOOOOO.O ..OO.......O ..OO.......OO ..OO.......OO .O...OOO.O.. .O...OOO.OO.. .O...OOO.OO.. O...O....O.. O...O....OO.. O...O....OO.. O.....O....O O.....O...OO. O.....O...OO. OOO...OOOOO. OOO...OOOO.O. OOO...OOOO.O. ............ ............. ............. OOO...OOOOO. OOO...OOOO.O. OOO...OOOO.O. O.....O....O O.....O...OO. O.....O...OO. O...O....O.. O...O....OO.. O...O....OO.. .O...OOO.O.. .O...OOO.OO.. .O...OOO.OO.. ..OO.......O ..OO.......OO ..OO.......OO .....OOOOOO. .....OOOOOO.O .....OOOOOO.O ......O..... ......O...... ......O...... .......OO... .......OO.... .......OOOO.O ........O..O ........O..O. .......O...OO .........O.O .........O.O. .........OO.. ............ ............. .........OOOO ............ ............. ............O A section of the wicktrailer can be attached to the two center feet of the middle ship above, creating feet which are separated by a one cell gap. Hartmut found that a repeatable tagalong can be attached to that pair of feet. This tagalong is unusual in that unlike most other tagalongs which work by having cells turned on by the base ship, this tagalong works by having some cells turned off by the base ship. The following shows the base ship, the wicktrailer, and two copies of the repeatable tagalong. [Period 2 spaceship with repeatable tagalong (speed c/2)] ............................O.........O .........O.O..............OOO.......OOO ........O..O.............OO........OO.. .......OO................O.........O... ......O........O.......O.O.......O.O... .....OOOOOO.OOOO.....OOO.......OOO..... ..OO.......OO.O.....OO.O......OO.O..... .O...OOO.OO...O.....O.O.OO....O.O.OO... O...O....OO...OO....OO..OO....OO..OO... O.....O...OO...OOO..O.....OO..O.....OO. OOO...OOOO.O.....O..OO..OO.O..OO..OO.O. ....................OO.O......OO.O..... OOO...OOOO.O.....O..OO..OO.O..OO..OO.O. O.....O...OO...OOO..O.....OO..O.....OO. O...O....OO...OO....OO..OO....OO..OO... .O...OOO.OO...O.....O.O.OO....O.O.OO... ..OO.......OO.O.....OO.O......OO.O..... .....OOOOOO.OOOO.....OOO.......OOO..... ......O........O.......O.O.......O.O... .......OO................O.........O... ........O..O.............OO........OO.. .........O.O..............OOO.......OOO ............................O.........O By using two feet at the ends of two separate spaceships, this tagalong can be used to connect the two ships into one larger ship. Since the tagalong has feet of its own, two copies of it can be used to attach another copy of the tagalong to them too. The following spaceships are related, and are both extensible. Here extensible means that they contain recognizable components which can be repeated to make the ships wider. (This will be explained in more detail a little later.) The first spaceship here is important because it demonstrates a new end component for grammar-based ships. [Two similar extensible period 2 spaceships (speed c/2)] ............O.O ............O.O.. ...........O..O ...........O..O.. ..........OO... ..........OO..... .........O....O .........O....... ........OOOOO.O ........OOOOOO... .....OO........ .....OO.......O.. ....O...OOO.... ....O...OOO.O.... ...O...O....... ...O...O....O.... ...O.....O..... ...O.....O....O.. ...OOO...O..... ...OOO...OOOOO... .........OO.O.. ................. ...OOO......O.. ...OOO.....OOOOO. ..O............ ..O........O....O .O...O......... .O...O.....O..O.. O..O........... O..O........O...O O....O......... O....O.......O... OOOOO.......... OOOOO.........OOO ............... ................. OOOOO.......... OOOOO.........OOO O....O......... O....O.......O... O..O........... O..O........O...O .O...O......... .O...O.....O..O.. ..O............ ..O........O....O ...OOO......O.. ...OOO.....OOOOO. .........OO.O.. ................. ...OOO...O..... ...OOO...OOOOO... ...O.....O..... ...O.....O....O.. ...O...O....... ...O...O....O.... ....O...OOO.... ....O...OOO.O.... .....OO........ .....OO.......O.. ........OOOOO.O ........OOOOOO... .........O....O .........O....... ..........OO... ..........OO..... ...........O..O ...........O..O.. ............O.O ............O.O.. The following shows a tagalong for a slightly modified base ship. Here the tagalong works in the normal manner, by having new cells created by the base ship. This tagalong is not repeatable, however. [Period 2 spaceship with tagalong (speed c/2)] ............O.............. .........O.O.O............. ........O..O............... .......OO.....O...........O ......O.......OOO.......OOO .....OOOOOO....OOO.....OO.. ..OO.......O....O......O... .O...OOO.O.......OOO.O.O... O...O....O.......O..OO..... O.....O....O......OO...O... OOO...OOOOO........OOOO.... ........................... OOO...OOOOO........OOOO.... O.....O....O......OO...O... O...O....O.......O..OO..... .O...OOO.O.......OOO.O.O... ..OO.......O....O......O... .....OOOOOO....OOO.....OO.. ......O.......OOO.......OOO .......OO.....O...........O ........O..O............... .........O.O.O............. ............O.............. The following spaceship is one of the more complicated ships found by Hartmut Holzwart. It has a curious pattern of several long rows of ON cells within it. Possibly this hints at a pattern that could reappear at a larger scale in even larger ships. This spaceship is also extensible. [One of the more complicated period 2 spaceships (c/2)] ..............O.O......... ...........O.O..O......... ..........O..O...........O .........OO....O...O.O.OO. ........O....O...OOO.O.O.O .......OOOOO.O...O..O..... ....OO...........OOO.OO... ...O...OOOOOOOO...O....O.. ..O...O............OOO.... ..O.....OOOOOOOOO..O...O.. ..OOO...O............OOO.. ..........OOO.O.O....OOOO. ..OOO.....O..OO.O.......O. .O.....O...OO............. O...OO.O....OOOOO......... O...O..................... O...OO.O....OOOOO......... .O.....O...OO............. ..OOO.....O..OO.O.......O. ..........OOO.O.O....OOOO. ..OOO...O............OOO.. ..O.....OOOOOOOOO..O...O.. ..O...O............OOO.... ...O...OOOOOOOO...O....O.. ....OO...........OOO.OO... .......OOOOO.O...O..O..... ........O....O...OOO.O.O.O .........OO....O...O.O.OO. ..........O..O...........O ...........O.O..O......... ..............O.O......... Not all of the spaceships that Hartmut found are extensible. (I have mostly selected those that were.) The following is one of those which is not known to be extensible. [Another complicated period 2 (non-extensible) spaceship (speed c/2)] ...........O.O...........O.O ..........O..O.........OOOOO .........OO...........O...O. ........O...O........OO...O. .......OOO.O........O...O... ....OO.............OOOO...O. ...O...OOOOO......O....OOO.. ..O...O...........OOO....... ..O.....OOOO...O.O.....OOO.. ..OOO...O.....OOOOOOOOO...O. ..........O..OO........OO... ..OOO.....OO.OO...OO.O..O.O. .O.....O...OO......O..OO.O.. O...OO.O...O........OO.O.O.. O...O.....O..O.............. O...OO.O...O........OO.O.O.. .O.....O...OO......O..OO.O.. ..OOO.....OO.OO...OO.O..O.O. ..........O..OO........OO... ..OOO...O.....OOOOOOOOO...O. ..O.....OOOO...O.O.....OOO.. ..O...O...........OOO....... ...O...OOOOO......O....OOO.. ....OO.............OOOO...O. .......OOO.O........O...O... ........O...O........OO...O. .........OO...........O...O. ..........O..O.........OOOOO ...........O.O...........O.O I will now explain how many of the above ships are extensible. This could be done by extending Dean's grammar to include all the new components and how they attach to each other. But since the attachments of these new components are so obvious, an example seems easiest. The following spaceship demonstrates the new components and how they may be connected. All the components are separated from each other by a gap of one cell. You should recognize several of these from the collection of spaceships above. [Example components to make Hartmut's ships extensible (speed c/2)] .......O...... ....OOOO...... ....OO........ ..O........... ..OOOO........ .O............ OOO..O........ .OOO.......... ..O........... ...OOO.O...... ...O..OO...... ....OOO....... ......O....... ....O......... ....O.O....... ...O.......... ....O.O....... ....O......... ......O....... ....OOO....... ...O..OO...... ...OOO.O...... ..O........... .OOO.......... OOO..O........ .O............ ..OOOO........ ..O........... ....OO........ ....OOOO.O.... .......O.O.... .........OO... ........OO.... .......O..O... ......O....... ......O....... ......OOO..... .............. ......OOO..... .....O........ ....O...O..... ...O..O....... ...O....O..... ..O.OOOO...... .OOO.......... ..O.OOOO...... ...O....O..... ...O..O....... ....O...O..... .....O........ ......OOO..... .............. ......OOO..... .....O........ ....O...O..... ...O..O....... ...O....O..... ...OOOOO...... .............. ...OOOOO...... ...O....O..... ...O..O....... ....O...O..... .....O........ ......OOO..... .............. ......OOO..... .....O........ ....O...O..... ...O..O....... ...O....O..... ...OOOOO...... .............. .....OOOOO.... .....O....O... .....O..O..... ......O...O... .......O...... ........OOO... .............. ........OOO... .......O.....O ......O...OO.O ......O...O... ......O...OO.O .......O.....O ........OOO... .............. ........OOO... ........O..... ........O..... .........O..O. ..........OO.. ...........OO. .........O.O.. ......OOOO.O.. ......OO...... ....O......... ....OOOO...... ...O.......... ..OOO..O...... ...OOO........ ....O......... .....OOO.O.... .....O..OO.... ......OOO..... ........O..... ......O....... ......O.O..... .....O........ ......O.O..... ......O....... ........O..... ......OOO..... .....O..OO.... .....OOO.O.... ....O......... ...OOO........ ..OOO..O...... ...O.......... ....OOOO...... ....O......... ......OO...... ......OOOO.... .........O.... Below the standard base period 2 spaceship, there is a small component that I found which attaches to the foot of a ship, and provides a bridge to the new components. Below that is a symmetrical component with a leading "plus sign" of five cells. This component featured in many of Hartmut's first period 2 ships. But it turns out that the plus sign is optional and can be removed, splitting the large component into two smaller components. This is shown next. Following that are the same smaller components shifted with respect to each other by two cells. Finally, there is a "jellyfish" component, then the bridge and another base ship. To summerize, all the components with three cells in a row along the edge can join together, and the components with five cells in a row along the edge can join up together, possibly shifted. As an example of extending one of Hartmut's spaceships, we can take the complicated spaceship above with the several rows of ON cells. By adding more of the same kind of components already present in the ship, we can create the following new spaceship. [Example of extending a period 2 spaceship (speed c/2)] ..............O.O......... ...........O.O..O......... ..........O..O...........O .........OO....O...O.O.OO. ........O....O...OOO.O.O.O .......OOOOO.O...O..O..... ....OO...........OOO.OO... ...O...OOOOOOOO...O....O.. ..O...O............OOO.... ..O.....OOOOOOOOO..O...O.. ..OOO...O............OOO.. ..........OOO.O.O....OOOO. ..OOO.....O..OO.O.......O. .O.....O...OO............. O...OO.O....OOOOO......... O...O..................... O...OO.O....OOOOO......... .O.....O...OO............. ..OOO.......OO..O......... .............OO........... ..OOO.........OO.O........ .O.....O.......OO......... O...OO.O.................. O...O..........OO......... O...OO.O......OO.O........ .O.....O.....OO........... ..OOO.......OO..O......... ...........OO............. ..OOO.......OOOOO......... .O.....O.................. O...OO.O....OOOOO......... O...O......OO............. O...OO.O....OO..O......... .O.....O.....OO........... ..OOO.........OO.O........ ...............OO......... ..OOO..................... .O.....O.......OO......... O...OO.O......OO.O........ O...O........OO........... O...OO.O....OO..O......... .O.....O...OO............. ..OOO.......OOOOO......... .......................... ..OOO.......OOOOO......... .O.....O...OO............. O...OO.O....OO..O......... O...O........OO........... O...OO.O......OO.O........ .O.....O.......OO......... ..OOO..................... ...............OO......... ..OOO.........OO.O........ .O.....O.....OO........... O...OO.O....OO..O......... O...O......OO............. O...OO.O....OOOOO......... .O.....O.................. ..OOO.......OOOOO......... ...........OO............. ..OOO.......OO..O......... .O.....O.....OO........... O...OO.O......OO.O........ O...O..........OO......... O...OO.O.................. .O.....O.......OO......... ..OOO.........OO.O........ .............OO........... ..OOO.......OO..O......... .O.....O...OO............. O...OO.O....OOOOO......... O...O..................... O...OO.O....OOOOO......... .O.....O...OO............. ..OOO.....O..OO.O.......O. ..........OOO.O.O....OOOO. ..OOO...O............OOO.. ..O.....OOOOOOOOO..O...O.. ..O...O............OOO.... ...O...OOOOOOOO...O....O.. ....OO...........OOO.OO... .......OOOOO.O...O..O..... ........O....O...OOO.O.O.O .........OO....O...O.O.OO. ..........O..O...........O ...........O.O..O......... ..............O.O......... These new components can be combined with the branching ship components to form "loopy" structures. So we can construct spaceships with arbitrarily large holes inside them. The following is a simple example of such a spaceship. [Period 2 spaceship with hole (speed c/2)] ..........................O.............. .......................OOOO.............. .....................OOO.O............... ....................OO...O............... ....................O....OO.............. ..................O.O.....OOO.O.......... ................OOO.........O.O.......... ...............OO..O..........OO......... ..............O..O...........OO.......... ..............O..O..........O..O......... ..............O............O............. ...............O..O........O..O.......... ................OO.........O..O.......... .................OO.........OO..O........ ...............O.O...........OOO......... .............OOO.O.............O.O....... ............OO...................O....... ............O....................OO...... ..........O.O.....................OOO.O.. ........OOO.........................O.O.. .......OO..O..........................OO. ......O..O...........................OO.. ......O..O..........................O..O. ......O............................O..... .......O..O........................O..... ........OO.........................OOO... .........OO.............................. .......O.O.........................OOO... ....OOOO.O........................O.....O ....OO...........................O...OO.O ..O..............................O...O... ..OOOO...........................O...OO.O .O................................O.....O OOO..O.............................OOO... .OOO..................................... ..O................................OOO... ...OOO.O..........................O.....O ...O..OO.........................O...OO.O ....OOO..........................O...O... ......O..........................O...OO.O ....O.............................O.....O ....O.O............................OOO... ...O..................................... ....O.O............................OOO... ....O.............................O.....O ......O..........................O...OO.O ....OOO..........................O...O... ...O..OO.........................O...OO.O ...OOO.O..........................O.....O ..O................................OOO... .OOO..................................... OOO..O.............................OOO... .O................................O.....O ..OOOO...........................O...OO.O ..O..............................O...O... ....OO...........................O...OO.O ....OOOO.O........................O.....O .......O.O.........................OOO... .........OO.............................. ........OO.........................OOO... .......O..O........................O..... ......O............................O..... ......O..O..........................O..O. ......O..O...........................OO.. .......OO..O..........................OO. ........OOO.........................O.O.. ..........O.O.....................OOO.O.. ............O....................OO...... ............OO...................O....... .............OOO.O.............O.O....... ...............O.O...........OOO......... .................OO.........OO..O........ ................OO.........O..O.......... ...............O..O........O..O.......... ..............O............O............. ..............O..O..........O..O......... ..............O..O...........OO.......... ...............OO..O..........OO......... ................OOO.........O.O.......... ..................O.O.....OOO.O.......... ....................O....OO.............. ....................OO...O............... .....................OOO.O............... .......................OOOO.............. ..........................O.............. Recently I found that the "barber pole" diagonal tagalong can be used as a bridge between two spaceships. This is shown below. [Barber pole component connecting two period 2 spaceships (speed c/2)] .......O................. ....OOOO................. ....OO................... ..O...................... ..OOOO................... .O....................... OOO..O................... .OOO..................... ..O...................... ...OOO.O................. ...O..OO................. ....OOO.................. ......O.................. ....O.................... ....O.O.................. ...O..................... ....O.O.................. ....O.................... ......O.................. ....OOO.................. ...O..OO................. ...OOO.O................. ..O...................... .OOO..................... OOO..O................... .O....................... ..OOOO................... ..O...................... ....OO................... ....OOOO.O............... .......O.O............... .........OO.............. ........OO............... .......O..O.............. ......O.................. ......O....O............. ......OO.OOO............. .........OO.............. ..........O.O............ ..........OO.O........... ..........O.............. ..............O.......... ...........OO.O.......... ............OO........... .............O.O......... .............OO.O........ .............O........... .................O....... ..............OO.O....... ...............OO........ ................O.O...... ................OO.O..... ................O........ ....................O.... .................OO.O.... ..................OO..... ...................O.O... ...................OO.O.. ...................O..... .......................O. ....................OO.O. ....................O.... .....................O.O. .....................O... ......................OOO ......................... ....................O.OOO ...................OO..OO ...................O.O... ...................OO.... ...................O..... ..................OOO.... ..................O...... ..................O...... ...................O..O.. ....................OO... .....................OO.. ...................O.O... ................OOOO.O... ................OO....... ..............O.......... ..............OOOO....... .............O........... ............OOO..O....... .............OOO......... ..............O.......... ...............OOO.O..... ...............O..OO..... ................OOO...... ..................O...... ................O........ ................O.O...... ...............O......... ................O.O...... ................O........ ..................O...... ................OOO...... ...............O..OO..... ...............OOO.O..... ..............O.......... .............OOO......... ............OOO..O....... .............O........... ..............OOOO....... ..............O.......... ................OO....... ................OOOO..... ...................O..... Finally, I have discovered two different repeatable tagalongs for period 2 spaceships, and a small tagalong for them which makes the ship a period 6 spaceship. This is the only method known for making a period 6 spaceship. [Period 2 spaceship with repeatable tagalongs and period 6 tagalong (speed c/2)] .....O.O....................................................... ....O..O....................................................... ...OO.......................................................... ..O............................................................ .OOOO.......................................................... O....O......................................................... O..O........................................................... O..O........................................................... .O............................................................. ..OOOO.O....................................................... ...O...O....................................................... ....O.......................................................... ....O.O........................................................ ............................................................... ...OOO......................................................... ...OO.......................................................... ...OOO......................................................... ............................................................... ....O.O........................................................ ....O.......................................................... ...O...O....................................................... ..OOOO.O....................................................... .O............................................................. O..O........................................................... O..O........................................................... O....O......................................................... .OOOO.......................................................... ..O............................................................ ...OO.......................................................... ....O..O.O....O.O....O.O....O.O.....O....O.O.....O....O.O...... .....O.O..O..O..O.OO.O..O..O..O.OO.O.O..O..O.OO.O.O..O..O.OO.O. ........O...OO........O...OO.......O...OO.......O...OO.......OO .........O......O......O......O.....OOO....O.....OOO....O...... ..........OOOOO.O.......OOOOO.O.......OOOO.O.......OOOO.O....OO ..................OO............OO...........OO...........OO.O. ..........OOOOO.O.......OOOOO.O.......OOOO.O.......OOOO.O...... .........O......O......O......O.....OOO....O.....OOO....O...... ........O...OO........O...OO.......O...OO.......O...OO......... .....O.O..O..O..O.OO.O..O..O..O.OO.O.O..O..O.OO.O.O..O..O.OO... ....O..O.O....O.O....O.O....O.O.....O....O.O.....O....O.O...... ...OO.......................................................... ..O............................................................ .OOOO.......................................................... O....O......................................................... O..O........................................................... O..O........................................................... .O............................................................. ..OOOO.O....................................................... ...O...O....................................................... ....O.......................................................... ....O.O........................................................ ............................................................... ...OOO......................................................... ...OO.......................................................... ...OOO......................................................... ............................................................... ....O.O........................................................ ....O.......................................................... ...O...O....................................................... ..OOOO.O....................................................... .O............................................................. O..O........................................................... O..O........................................................... O....O......................................................... .OOOO.......................................................... ..O............................................................ ...OO.......................................................... ....O..O....................................................... .....O.O....................................................... In the above, the two types of period 2 tagalongs are repeated twice. The two pre-blocks at the right form the period 6 tagalong. The pre-blocks can be removed to make a normal period 2 spaceship. The final three sets of two-bit sparks can also be removed and the ship will still work. There are a few more known period 2 components that I have not mentioned in this article. The number of possible components is probably infinite. As we search larger and larger areas, we find more and more components, so that cataloging them becomes impossible. Instead of trying to catalog everything, we can search directly for objects which meet certain conditions, such as spaceships which have sparks of a desired kind. An example of this is given by the first "barber pole" spaceship in this article. The component at the front which connects the diagonal component to the rest of the ship is larger than the others, and is messy. It was searched for explicitly in order to connect the diagonal component to a known spaceship. Considering the long time interval of 20 years between the classic spaceships and these new classes, you might be surprised at the number of new spaceships that have been found in the last few years. But I am not done yet! The next article in this series will survey the period 3 c/3 spaceships. These were the first spaceships found which travel at a "non-standard" speed. That next article should appear in about two weeks.