Life Objects Without Known Syntheses

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:

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:

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.)



The 48 period 2 oscillators up to 17 bits without any known syntheses

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

unknown period 2 oscillators


The 199 Period-2 pseudo-oscillators up to 21 bits without any known syntheses

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:

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.)

unknown pseudo-P2

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]


The 12 period 3 oscillators up to 21 bits without any known syntheses

unknown period 3 oscillators

Up weird thing below hook w/ tail [x] Down weird thing below hook w/ tail [x] Caterer w/ skewed pole [x] Up weird thing below down boat w/ tail [x] Dual caterer [x] Candel- frobra and caterer w/ tail [x] Down weird thing below down boat w/ tail [x]
Trans skewed poles [x] Bowed caterer [x] Fire spitting [x] Fire spitting w/ head [x+3] Caterer w/ table on pre-block [x]  


The 158 period 3 pseudo-oscillators up to 25 bits without any known syntheses

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:

There are 8 23-bit ones:

There are 45 24-bit ones:

There are 103 25-bit ones:


10 period 4 oscillators up to 25 bits without any known syntheses

(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.)

unknown P4 oscillators

21-bit P4 oscillator #1 [x] 24-bit P4 oscillator #1 [x] 24-bit P4 oscillator #2 [x] 24-bit P4 oscillator #3 [x] Cis molds sharing sparks [x]
22-bit P4 oscillator #4 [x] 22-bit P4 oscillator #5 [x] 25-bit P4 oscillator #2 [x] 25-bit P4 oscillator #1 [x] Eater and block eating integral w/loaf and cis hook [x]


The 2 period 4 pseudo-oscillators up to 25 bits without any known syntheses

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

unknown P4 pseudo-oscllators

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


The 2 period 5 oscillators up to 22 bits without any known syntheses

unknown P5 oscillators

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


The 9 period 6 oscillators up to 25 bits without any known syntheses

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

unknown period-6 oscillators

P6 w/ block and head [x] P6 w/ boat and head [x+6] P6 w/ block and tub [x+5] P6 w/ table and head [x+6] P6 w/ ship and head [x+6] P6 w/ block and boat [x+7] P6 w/ carrier and head [x+12] P6 w/ boat and tub [x+11] P6 w/ beacon and head [x+7]


The 12 period 6 pseudo-oscillators up to 25 bits without any known syntheses

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

unknown P6 pseudo-oscillators

Up beacon on down skewed poles [x+6] Up beacon below down skewed poles [x+7] Down beacon on down skewed poles [x+6] Down beacon below down skewed poles [x+6] Up beacon on bowed caterer [x+6] Up beacon on fire spitting [x+6]
Down beacon on bowed caterer [x+6] Up beacon below bowed caterer [x+12] Up beacon below fire spitting [x+7] Down beacon on fire spitting [x+6] Down beacon below bowed caterer [x+8] Down beacon below fire spitting [x+6]


The 3 spaceships up to 25 bits without any known syntheses

unknown spaceships

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.

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