Introduction | P2 oscillators | P2 pseudo-oscillators | P3 oscillators | P3 pseudo-oscillators | P4 oscillators | P4 pseudo-oscillators | P5 oscillators | P6 oscillator | P6 pseudo-oscillators | spaceships

The extremely rare and artificial Garden of Eden patterns can be proved to
have no predecessors, so of course they cannot be synthesized. Other than these,
however, all patterns have predecessors, so it may be theoretically possible to
synthesize them. When we say "this pattern has no synthesis", except for Garden
of Eden patterns, it is really just an informal shorthand for "this pattern
has no known synthesis *yet*", as a synthesis may be discovered or
developed later.

Most small objects can be synthesized from gliders. Buckingham completed the monumental task of synthesizing all objects up to 14 bits in the 1980s, as well as a fair number of larger objects.

Syntheses have been found for most objects on the following lists:

- Still-lifes up to 14 bits are complete, about half of the 15-bit ones are complete, and all up to 18 bits are proven to have syntheses.
- Pseudo-still-lifes up to 16 bits are complete, and all up to 19 bits are proven to have syntheses.
- Period 2 oscillators up to 17 bits are complete, and about half of the 18-bit ones are complete.
- Period 2 pseudo-oscillators up to 17 bits are complete, and all up to 18 bits are proven to have syntheses. Also, all up to 21 have syntheses except two, plus several trivial ones involving 4-6-bit objects on as-yet-unsynthesized period-2 oscillators.
- Period 3 and higher oscillators and pseudo-oscillators up to 21 bits are complete (except for 21-bit period 3, all but two of which have syntheses).
- Period 15 oscillators up to 24 bits are complete.
- Other period 8 and higher oscillators up to 25 bits are complete.
- Spaceships up to 25 bits are complete.

In addition, even though no systematic syntheses for them have been attempted, several of the larger lists have been counted and analyzed to determine which of their items can be synthesized using known methods:

- Still-lifes up to 18 bits.
- Pseudo-still-lifes up to 19 bits.
- Period 2 pseudo-oscillators up to 21 bits.
- Period 5 and higher pseudo-oscillators up to 25 bits.

The basic spaceships and pseudo-spaceships as well as most 2- and 3-spaceship flotillae of these can all also be synthesized.

The few remaining objects in the above groups with no known syntheses are shown here. Omitted are categories where all syntheses are know. Also omitted are the larger-population categories where syntheses have only been attempted for a small number of objects. (NOTE: As technology improves, objects and even entire categories may be removed from these lists.)

Several of these objects (whose costs are indicated as [x+*n*] can be
trivially synthesized from smaller objects in the same lists with costs of [x],
and only await syntheses for those smaller objects.

(Two of the categories include large numbers of oscillators using a single mechanism attached to various different still-life. These are the period 4 molds and Silver's P5s. While most in both categories can be synthesized, there are several for which syntheses are currently unknown, based on the underlying still-life. Since syntheses have not yet been attempted for all of these, the number of objects of these kinds without syntheses is not yet known. As a result, they are currently omitted from the lists below until their status can be accurately determined.)

At present, the technology for synthesis of oscillators containing large number of disconnected bits is sorely lacking.

All period 2 pseudo-oscillators up to 17 bits have been synthesized. All period 2 pseudo-oscillators up to 21 bits can be synthesized using the same techniques used for smaller pseudo-oscillators and pseudo-still-lifes, except one non-trivial one, and many trivial ones.

There are many trivial pseudo-objects, consisting of a small objects added to a large object that, itself, has eluded synthesis. These include:

- 4 19-bit pseudo-objects (shown) from a block on one of the three unbuildable 15-bit period 2 oscillators.
- 25 20-bit pseudo-objects (not shown), 8 from a boat on one of the three unbuildable 15-bit period 2 oscillators, and 17 from a block on one of ten unbuildable 16-bit period 2 oscillators.
- 169 21-bit pseudo-objects (not shown), 52 from a beacon or six-bit still-life on one of the three unbuildable 15-bit period 2 oscillators, 33 from a boat on one of ten unbuildable 16-bit period 2 oscillators, and 84 from a block on one of 21 unbuildable 17-bit period 2 oscillators.

The 4 trivial 19-bit ones, and the 1 non-trivial 21-bit ones shown here. (The 25 trivial 20-bit ones and 169 trivial 21-bit ones above are not shown.)

Block on 15-bit P2 #1 [x+2] | Block on blinkers bit pole [x+2] | Block on 15-bit P2 #5 [x+2] | Block below 15-bit P2 #5 [x+3] | Up snake on up beacon above long hook w/ tail [x] |

Unfortunately, due to time limitations, these cannot yet be shown. Most consist of a small still-life on as as-yet-unsynthesized period-3 oscillator. There are also a few consisting of two oscillators (caterer and/or jam) with adjacent rotors.

There are 2 22-bit ones:

- 2 Trans skewed poles on block.

There are 8 23-bit ones:

- 4 Trans skewed poles on boat.
- 4 Fire spitting or bowed caterer on block.

There are 45 24-bit ones:

- 18 Trans skewed poles on beehive, ship, snake or carrier.
- 8 Fire spitting or bowed caterer on boat.
- 16 Block on 20-bit P3 oscillator.
- 3 Caterer on caterer (there are four; one can be synthesized).

There are 103 25-bit ones:

- 28 Trans skewed poles on long boat, loaf, python or eater.
- 35 Fire spitting or bowed caterer on beehive, ship, snake or carrier.
- 32 Boat on 20-bit P3 oscillator.
- 6 Block on 21-bit P3 oscillator.
- 2 Jam on caterer.

(NOTE: this excludes many mold-based oscillators from 24-25 bits that are based on still-lifes from 19-20 bits that do not yet have syntheses.)

These are both easy to synthesize, but are based on one predecessor that does not yet have a synthesis.

Block on 21-bit P4 #1 [x+2] | Block below 21-bit P4 #1 [x+3] |

Elkies's P5 w/ claw and pre-block [x] | Silver's P5 before cis shil- lelagh w/ tub [x] |

These are all derived from one base 23-bit oscillator.

These are all easy to synthesize, but are based on three predecessors that do not yet have syntheses.

Crab; Quarter [x] |
25-bit c/3 orthogonal spaceship #1 [x] |
25-bit c/3 orthogonal spaceship #2 [x] |

**Other costs:**
2 gliders,
3 gliders,
4 gliders,
5 gliders,
6 gliders,
1 glider/bit,
>1 glider/bit,
unknown.

**See also:** Life objects sorted by:
counts,
frequency of occurrence,
cost in gliders,
name,
size in bits,
or type.

Copyright © 1997, 1998, 1999, 2013, 2014 by Mark. D. Niemiec.
All rights reserved.

This page was last updated on
*2015-02-19*.