Life Naturally-occurring Objects

Introduction
Type: Objects | Still-lifes | Oscillators
Period: 2 | 3 | 4 | 5 | 6 | 8 | 14 | 15 | 30
Cost in gliders: 2 | 3 | 4 | 5 | 6 | >6 | >1 glider/bit



Introduction

Achim Flammenkamp conducted random seed experiments, where he ran 1,829,196 different random patterns on 2048x2048 tori, with an initial density of 0.375. Once the patterns stabilized, the resulting ash was analyzed and separated into objects, of which 50,158,095,316 were found. These were then sorted into 3798 distinct objects, of which 95 were not still-lifes. He then published lists of the 100 most common objects, and the 60 most common oscillators. These results are called "Most seen natural occurring ash objects in Game of Life" and "Natural oscillators in Game of Life" and are summarized here.

(NOTE: His methods did not find spaceships, since those can never escape a torus, but will eventually either smash into something else, or (rarely) cycle all the way around the torus to form high-period oscillators that could be weeded out by hand. They also didn't consider pseudo-objects or constellations; those were broken apart into their object components and counted with them. He did run a separate experiment, "Natural Spaceships in Game of Life" specifically to find natural spaceships. This found the four basic spaceships, plus the two basic switch-engine puffers, but no others.)

Each object has a frequency of occurrence that is defined by the number of times the object occurs divided by the total number of objects seen. One can define the rarity of an object as the inverse of its frequency of occurrence. In the sections below, each object's rarity is displayed after the number of gliders needed to synthesize it. (This is shown, rather than frequency of occurrence, because this number is small for common objects.)

Note that the frequency and rarity values (and thus the lists of objects themselves) are not absolute measures of object frequency of occurrence. Rather, they represent observed statistical results from one particular random experiment. Other similar experiments will likely produce similar but slightly different results. In fact, Flammenkamp conducted a different experiment, "Natural grown Oscillators out of Random Soup", whose statistical distributions are slightly different.

It is not surprising that objects that occur frequently in nature should also be fairly easy to synthesize. From the lists below, this usually appears to be the case, although there are a few exceptions, most notably a few period 2 oscillators.



The top 100 naturally-occurring objects

naturally-occurring objects


The top 92 naturally-occurring still-lifes

naturally-occurring still-lifes


The top 60 naturally-occurring oscillators

natural oscillators

Blinker [2] (3.038) Toad [3] (373.6) Beacon [3] (1221) Pulsar [3] (19584) Penta- decath- lon [3] (1631317) Clock [4] (1.7e6) Bipole [5] (7.6e6) Quad- pole [6] (8.2e6)
Great on-off [5] (1.2e7) Figure-8; Big beacon [4] (3.3e7) Spark coil [4] (3.6e7) Mold [5] (4.6e7) Quad- pole tie ship [7] (1.1e8) Tripole [7] (2.1e8) Mazing [5] (2.2e8) Blocker [6] (3.7e8) Jam [7] (4.0e8)
Queen bee between trans blocks [6] (5.7e8) Queen bee between cis blocks [6] (5.7e8) Up beacon on dock; Cis- beacon and dock [7] (7.0e8) Up beacon on table; Cis- beacon and table [6] (9.0e8) Down beacon on table; Trans- beacon and table [6] (9.3e8) Clover- leaf [7] (1.0e9) Up beacon on up anvil; Cis- beacon and anvil [7] (1.1e9)
Test tube baby [6] (1.3e9) Octagon II [6] (1.7e9) Unix [6] (1.7e9) Tumbler [6] (2.3e9) Test tube baby w/ two tubs; Tub test tube baby [8] (2.4e9) Down beacon on dock; Trans- beacon and dock [7] (2.5e9) Up beacon on up long bookend; Cis- beacon up and long hook [6] (3.0e9) Up beacon on cap; Cis- beacon and cap [6] (3.3e9) 1beacon [10] (3.3e9)
Up beacon on down dock w/ down mango [6] (3.6e9) Up beacon on down long bookend Cis- beacon down and long hook [6] (3.9e9) Block on griddle; Griddle and block [12]; Singular flip- flop (7.2e9) Spark coil tie boat; Boat on spark coil [5] (7.2e9) Pre- block on very long table w/ tail [11] (8.4e9) Fore and back; Complem- entary blinker [20] (8.4e9) Down beacon on up long bookend; Trans- beacon down and long hook [6] (1.0e10) Block on up candel- frobra; Trans- block and long hook eating tub [9] (1.7e10) Caterer [11] (1.3e10)
Beehive on griddle; Griddle and beehive [10] (1.3e10) Bipole tie ship; bipole on ship [8] (1.7e10) Quad- pole tie boat; Quad- pole on boat [7] (1.7e10) Block on down candel- frobra; Cis- block and long hook eating tub [12] (1.0e10) Down beacon on up bookend siamese table [10] (1.7e10) Coe's P8; Tim Coe's P8 [8] (1.7e10) Pre- block on very long table w/ tail and curl [10] (1.7e10) Down beacon on cap [8]; Trans- beacon and cap (2.5e10) Down beacon on down long bookend; Trans- beacon up and long hook [6] (2.5e10)
Beacon w/ cover [9] (2.5e10) Cavity; Eater plug [8] (2.5e10) Up boat on down candel- frobra; Cis- boat and long hook eating tub [13] (2.5e10) Beehive on down candel- frobra; Beehive and long hook eating tub [12] (2.5e10) Test tube baby w/ tub; Odd test tube baby [9] (2.5e10) Boat on griddle; Griddle and boat [13] (2.5e10) Pre- block on very long table w/ tail siamese tail [29] (2.5e10) Pre- block on very long table w/ tail and head [14] (2.5e10) Pre- block on very long table w/ feather and curl [9] (2.5e10)



The top 41 naturally-occurring period 2 oscillators

natural period 2 oscillators

Blinker [2] (3.038) Toad [3] (373.6) Beacon [3] (1221) Clock [4] (1.7e6) Bipole [5] (7.5e6) Quad- pole [6] (8.2e6) Great on-off [5] (1.2e7) Spark coil [4] (3.6e7) Quadpole tie ship [7] (1.1e8)
Tripole [7] (2.1e8) Up beacon on dock; Cis- beacon and dock [7] (7.0e8) Up beacon on table; Cis- beacon and table [6] (9.0e8) Down beacon on table; Trans- beacon and table [6] (9.3e8) Up beacon on up anvil; Cis- beacon and anvil [7] (1.1e9) Test tube baby [6] (1.3e9) Test tube baby w/ two tubs; Tub test tube baby [8] (2.4e9) Down beacon on dock; Trans- beacon and dock [7] (2.5e9) Up beacon on up long bookend; Cis- beacon up and long hook [6] (3.0e9)
Up beacon on cap; Cis- beacon and cap [6] (3.3e9) 1beacon [10] (3.3e9) Up beacon on down dock w/ down mango [6] (3.6e9) Up beacon on down long bookend; Cis- beacon down and long hook [6] (3.9e9) Block on griddle; Griddle and block; Singular flip- flop [12] (7.2e9) Spark coil tie boat; Boat on spark coil [5] (7.2e9) Pre- block on very long table w/ tail [11] (8.4e9) Fore and back; Complem- entary blinker [20] (8.4e9) Down beacon on up long bookend; Trans- beacon up and long hook [6] (1.0e10)
Beehive on griddle; Griddle and beehive [10] (1.3e10) Bipole tie ship; Bipole on ship [8] (1.7e10) Quad- pole tie boat; Quad- pole on boat [7] (1.7e10) Down beacon on up bookend siamese table [10] (1.7e10) Pre- block on very long table w/ tail and curl [10] (1.7e10) Down beacon on cap; Trans- beacon and cap [8] (2.5e10) Down beacon on down long bookend; Trans- beacon down and long hook [6] (2.5e10) Beacon w/ cover [9] (2.5e10) Cavity; Eater plug [8] (2.5e10)
Test tube baby w/ tub; Odd test tube baby [9] (2.5e10) Boat on griddle; Griddle and boat [13] (2.5e10) Pre- block on very long table w/ tail siamese tail [29] (2.5e10) Pre- block on very long table w/ tail and head [14] (2.5e10) Pre- block on very long table w/ feather and curl [9] (2.5e10)  


The top 7 naturally-occurring period 3 oscillators

natural period 3 oscillators

Pulsar; Pulsar CP 48-54-72 [3] (19584) Jam [7] (4.0e8) Block on up candel- frobra; Trans- block and long hook eating tub [9] (1.7e10) Caterer [11] (1.3e10) Block on down candel- frobra; Cis- block and long hook eating tub [12] (1.0e10) Up boat on down candel- frobra; Cis- boat and long hook eating tub [13] (2.5e10) Beehive on down candel- frobra; Beehive and long hook eating tub [12] (2.5e10)

The Caterer is the smallest oscillator that produces a period 3 finger spark.

Jam is the cheapest oscillator that produces a period 3 finger spark. It is one bit larger than the caterer, but much cheaper and easier to synthesize. Also, jam forms on most still-lifes that have a bonding surface like the long diagonal side of a loaf (from which its name was inspired), so it forms the basis for many larger period 3 oscillators (and many with periods that are multiples of 3, such as period 6).

The Pulsar consists of four inducting Traffic light predecessors. Its predecessors are used in many other oscillators (as described under Traffic light). Pulsars are also infinitely extensible, by arranging multiple quadrants in a closed loop. The Pulsar, consisting of four quadrants, is the smallest such arrangement. The Quasar, consisting of twelve quadrants, is the next largest.


The top 3 naturally-occurring period 4 oscillators

natural P4

Mold [5] (4.6e7) Mazing [5] (2.2e8) Cloverleaf; Dual 1-2-3-4; Flammen- kamp's P4 [7] (1.0e9)

Mold is the smallest oscillator that produces a period 4 diagonal bit spark. Also, mold forms on most still-lifes that have a bonding surface like the long diagonal side of a loaf (from which its name was inspired), so it forms the basis for many larger period 4 oscillators (and many with periods that are multiples of 4, such as period 12).


The top 1 naturally-occurring period 5 oscillator

natural P5

Octagon II [6] (1.7e9)

Octagon II has eight fingers that can sometimes be used to hassle other oscillators like the period 50 Traffic Jam.


The top 1 naturally-occurring period 6 oscillator

natural P6

Unix [6] (1.7e9)

The Unix is the smallest oscillator that produces a period 6 diagonal bit spark.


The top 3 naturally-occurring period 8 oscillators

natural P8

Figure-8; Big beacon [4] (3.3e7) Blocker [6] (3.7e8) Coe's P8; Tim Coe's P8 [8] (1.7e10)

Figure-8 is the smallest oscillator that produces a period 8 (delayed) domino spark.

The blocker is the smallest oscillator that produces a period 8 diagonal bit spark.


The top 1 naturally-occurring period 14 oscillator

natural P14

Tumbler [6] (2.3e9)


The top 1 naturally-occurring period 15 oscillator

natural P15

Penta- decathlon [3] (1631317)

The pentadecathlon consists of two forming Traffic light predecessors. It produces a useful domino spark, making it useful in hassler oscillators of many periods, including 15, 30, 45 and 60. Both its end and side sparks can eat gliders and the three simple spaceships in many different ways. Its end spark is also useful for reflecting gliders, and is used in glider shuttles of many periods, including 45, 60 and 75.

Its phase can also be altered (as described under the notes for Traffic light).


The top 2 naturally-occurring period 30 oscillators

natural period 30 oscillators

Queen bee shuttle between trans blocks [6] (5.7e8) Queen bee shuttle between cis blocks [6] (5.7e8)

The Queen bee is extremely versatile. It is a shuttle that flips over every 15 generations, leaving a beehive egg, which must be removed; in both cases above, by a block. The Queen bee forms the basis for the first glider gun ever discovered, as well as many oscillators with periods of 30n.

It can also eat gliders many different ways:



The top 7 naturally-occurring objects buildable from 2 gliders

2-glider natural objects

Blinker [2] (3.038) Block [2] (3.094) Beehive [2] (5.230) Loaf; Burloaf [2] (16.79) Boat [2] (18.27) Pond [2] (86.78) Eater; Eater-1; Fishhook [2] (5756)


The top 15 naturally-occurring objects buildable from 3 gliders

3-glider natural objects

Tub [3] (81.71) Ship [3] (132.9) Long boat [3] (279.7) Toad [3] (373.6) Beacon [3] (1221) Barge [3] (1234) 14.30; Half- bakery [3] (1943) 8.3; Mango; Cigar [3] (3148)
Long barge [3] (8116) Pulsar [3] (19584) 14.79; Paper clip [3] (20597) 16.1749; Bi-pond [3] (49455) 9.10; Hat [3] (90686) 9.1; Very long boat [3] (128043) Penta- decathlon [3] (1631317)


The top 113 naturally-occurring objects buildable from 4 gliders

4-glider natural objects

12.3; Half fleet; Ship tie ship [4] (730) Carrier; Aircraft carrier [4] (13077) Long ship [4] (24259) Shil- lelagh [4] (32987) 9.4; Integral [4] (35129) 10.24; Bowtie; Boat tie boat [4] (32688) Snake [4] (32880) 14.36; Bit S [4] (39770) 9.5; Up boat w/ tail [4] (87374)
11-30; Ship tie boat [4] (109739) Tub w/ tail; Twit [4] (139675) 10.2; Very long ship [4] (161862) 12.25; Cis table on table [4] (181444) 8.2; Canoe; Sinking ship [4] (219181) 14.55; Up bun on bun; Cis- mirrored R-bee [4] (346884) 15.243; Moose; Moose antlers [4] (382224) 10.25; Block on table [4] (414201) 14.89; Block on dock; [4] (422961)
16.737; Beehive on dock; [4] (629542) 10.7; Beehive w/ tail [4] (648130) 16.644; Scorpion [4] (810964) 10.4; Loop; Long hat [4] (832569) 14.39; Four- teener [4] (959835) 9.6; Down boat w/ tail [4] (1.2e6) Python; Long snake [4] (1.3e6) 14.13; Down bun on bun; Trans- mirrored R-bee [4] (1.4e6) 18.287; House on house; Dead spark coil; JC [4] (1.4e6)
14.590; Up bookend on bookend; Cis- mirrored hook; Bookends [4] (1.4e6) 11.38; Gull; Intens- ionless; Elevener [4] (1.4e6) 12.27; Block on cap [4] (1.5e6) 11.58; Down loaf w/ tail [4] (1.5e6) 14.87; Down bookend down on bookend; Cis- rotated hook [4] (1.5e6) 12.29; Block on up long bookend [4] (1.7e6) Clock [4] (1.7e6) 10.20; Cis shil- lelagh [4] (1.9e6) 20.5320; Dock on dock; Mirrored dock [4] (1.9e6)
14.589; Down bun on bookend; Trans- hook and R-bee [4] (2.1e6) 12.111; Block w/ cover [4] (2.2e6) 15.462; Up boat on dock [4] (2.3e6) 8.1; Very long snake [4] (2.4e6) 10.17; Integral w/ tub; Tub w/ nine [4] (2.6e6) 15.114; Down bun on wing; Trans- R-bee and R-loaf [4] (3.0e6) 14.591; Up bun on bookend; Cis- hook and R-bee [4] (3.2e6) 9.9; Tub w/ long tail [4] (3.4e6) 11.43; Loaf siamese loaf [4] (3.7e6)
8.4; Hook w/ tail; Snake eater [4] (3.7e6) 11.33; Very long hat; Eleven- loop [4] (3.9e6) 10.18; Claw w/ tail; Great snake eater [4] (4.6e6) 16.129; Sym- metric scorpion [4] (4.8e6) 11.53; Up loaf w/ tail [4] (4.8e6) 15.360; Bee hat [4] (5.1e6) 9.3; Long canoe [4] (5.1e6) 12.7; Boat tie eater [4] (5.9e6) 13.224; Down snake on bun; [4] (5.9e6)
11.37; Up boat on table [4] (6.2e6) 12.8; Beehive on table [4] (6.4e6) 10.5; Up barge w/ tail [4] (6.7e6) 11.11; Integral w/up boat; Trans- boat w/ nine [4] (7.9e6) 12.112; Beehive w/ hooked tail; Beehive bend tail [4] (8.3e6) 12.104; Bi- beehive; Beehive tie beehive [4] (8.8e6) Figure-8; Big beacon [4] (3.3e7) Spark coil [4] (3.6e7)  


The top 16 naturally-occurring objects buildable from 5 gliders

5-glider natural objects

17.242; Bi-hat [5] (460605) 10.9; Broken snake; Carrier siamese snake [5] (2.1e6) 12.85; Eater w/ nine [5] (2.3e6) 12.28 [5] (2.4e6) 9.7; Long shil- lelagh [5] (3.0e6) 10.23; Boat w/ long tail [5] (3.0e6) 13.154; Loaf tie beehive [5] (3.4e6) 10.19; Long integral; S-ten [5] (3.9e6)
14.15; Trans- rotated R-bee [5] (5.1e6) Bipole [5] (7.6e6) 14.50; Beehive on cap [5] (7.6e6) 13.27; Down loaf on table [5] (8.0e6) Great on-off [5] (1.2e7) Mold [5] (4.6e7) Mazing [5] (2.2e8) Spark coil tie boat; Boat on spark coil [5] (7.2e9)


The top 21 naturally-occurring objects buildable from 6 gliders

6-glider natural objects

15.472; Down boat on dock [6] (5.6e6) 12.113; Snorkel loop [6] (6.7e6) Quad- pole [6] (8.2e6) 12.73; Integral w/ beehive; Beehive w/ nine [6] (8.4e6) 15.8; Up bun on wing; Cis R-bee on and R-loaf [6] (8.5e6) 13.10; Long boat tie ship (8.6e6) Blocker [6] (3.7e8)  
Queen bee between trans blocks [6] (5.7e8) Queen bee between cis blocks [6] (5.7e8) Up beacon on table; Cis- beacon and table [6] (9.0e8) Down beacon on table; Trans- beacon and table [6] (9.3e8) Test tube baby [8] (1.3e9) Octagon II [6] (1.7e9)
Unix [6] (1.7e9) Tumbler [6] (2.3e9) Up beacon on up long bookend; Cis- beacon up and long hook [6] (3.0e9) Up beacon on cap; Cis- beacon and cap [6] (3.3e9) Up beacon on down dock w/ down mango [6] (3.6e9) Up beacon on down long bookend Cis- beacon down and long hook [6] (3.9e9) Down beacon on up long bookend; Trans- beacon down and long hook [6] (1.0e10) Down beacon on down long bookend; Trans- beacon up and long hook [6] (2.5e10)


The top 31 naturally-occurring objects buildable from 7 or more gliders

7+-glider natural objects

Quad- pole tie ship [7] (1.1e8) Tripole [7] (2.1e8) Jam [7] (4.0e8) Up beacon on dock; Cis- beacon and dock [7] (7.0e8) Clover- leaf [7] (1.0e9) Up beacon on up anvil; Cis- beacon and anvil [7] (1.1e9) Down beacon on dock; Trans- beacon and dock [7] (2.5e9) Quad- pole tie boat; Quad- pole on boat [7] (1.7e10)
Test tube baby w/ two tubs; Tub test tube baby [8] (2.4e9) Bipole tie ship; bipole on ship [8] (1.7e10) Coe's P8; Tim Coe's P8 [8] (1.7e10) Down beacon on cap [8]; Trans- beacon and cap (2.5e10) Cavity; Eater plug [8] (2.5e10) Block on griddle; Griddle and block [12]; Singular flip- flop (7.2e9) Block on down candel- frobra; Cis- block and long hook eating tub [12] (1.0e10) Beehive on down candel- frobra; Beehive and long hook eating tub [12] (2.5e10)
Block on up candel- frobra; Trans- block and long hook eating tub [9] (1.7e10) Beacon w/ cover [9] (2.5e10) Test tube baby w/ tub; Odd test tube baby [9] (2.5e10) Pre- block on very long table w/ feather and curl [9] (2.5e10) 1beacon [10] (3.3e9) Beehive on griddle; Griddle and beehive [10] (1.3e10) Down beacon on up bookend siamese table [10] (1.7e10) Pre- block on very long table w/ tail and curl [10] (1.7e10)
Pre- block on very long table w/ tail [11] (8.4e9) Caterer [11] (1.3e10) Up boat on down candel- frobra; Cis- boat and long hook eating tub [13] (2.5e10) Boat on griddle; Griddle and boat [13] (2.5e10) Pre- block on very long table w/ tail and head [14] (2.5e10) Fore and back; Complem- entary blinker [20] (8.4e9) Pre- block on very long table w/ tail siamese tail [29] (2.5e10)  


The top 1 naturally-occurring object costing >1 glider/bit

gt.1g/b nat.

Pre- block on very long table w/ tail siamese tail [29] (2.5e10)



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.