Grounded Life is a Life-like cellular automaton in which a cell survives from one generation to the next if it has 2 or 3 neighbors, and is born if it has 3 or 5 neighbors. Under this rule, patterns tend to stabilize much more quickly than in standard Life,[1] which is one of the reasons for its name.
Because Grounded Life adds one birth transition from Life, all still lives in Grounded Life are still lives in Conway's Game of Life, but the reverse is not true. For example, the boat fails in Grounded Life.
Many small still lifes under the standard Life rules have dead cells with five alive neighbours, so the list of still lifes for the two rules are extremely different for small and large cell counts. The smallest patterns that are still lifes in the standard Life rules but not in Grounded Life are boat (with 5 cells), beehive (with 6 cells) and loaf, long boat and fishhook (with 7 cells). Thus, the smallest asymmetric still life is hook with tail.
Also, any pattern using a house, bookend, or bun as an induction coil that is a still life under the standard rules, any extended forms of the ship or boat, or any still life in Life that contains a pre-blockmotif (that is not part of a hook) are not still lifes in Grounded Life.
All still lifes up to 10 bits have occurred naturally. Almost all still lifes with 11 bits have occured naturally, with the only exception being Hook line tub. Notably, barge and aircraft carrier are much more common than in Life.
Oscillators
Naturally occurring objects in this rule include oscillators of periods 2, 3, 4, 5, 8 and 26. There are also seminatural oscillators of periods 2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 16, 18, 21, 24, 26, 29, 33, 46, 82, and 142. Alien oscillators are also much more common than in similar rules, especially 8P8 (a mirrored short table) and 8P4 (a pre-pulsar predecessor in Life).
Notably, the washing machine is much more common in this rule, even in asymmetric soups.
It is the 56th most common object in asymmetric soups and the 21st most common object in D4_x4 soups. Toads and clocks are also significantly more common, and blinkers are more common than blocks.
Many alien oscillators exist in this rule, several of which are shown below:
A stamp collection of oscillators. From left to right, top to bottom, they are:
12P2 and Washing machine (rare examples of billiard tables in Grounded Life),
14P3 (a natural oscillator resembling the caterer),
8P4 (a pre-pulsar predecessor in Life, which resembles 8P8),
12P4 (dependent on the B5a transition; the pattern dies in Life due to the lack of it),
56P11 (resemblant of Achim's p11),
46P6 (Four rock toads hassling unknown active region),
14P8 (extensible, although only in discrete lengths or with proper induction coils),
8P8 (a mirrored short table),
32P33 (four blocks hassling four T-tetrominos),
60P21 (four blocks hassling 8 pi-heptominoes),
18P26 (the highest-period oscillator to have appeared naturally),
24P26 (an oscillator composed of interacting beehive sparks; appears in 1 in 1250 C4_4 soups),
48P46 (a shuttle of loaf and beehive sparks),
36P82,
and 104P142 (the highest period oscillator to have appeared semi-naturally).
104P142-based agar, which can be stabilised with ships. (click above to open LifeViewer)
Spaceships
Of particular note is the fact that neither the glider nor any of the xWSSes work in Grounded Life (all of them die off), giving the rule its alternate name. The most common spaceship according to Catagolue is the glider 3736.
Known spaceship speeds are c/2o, c/3o, c/4o, c/5o, c/6o, 2c/5o, c/4d and c/5d.
The three smallest spaceships in Pseudo Life work:
x = 7, y = 4, rule = B35/S23
2b3o$bo3bo$o2bo2bo$3ob3o!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBNAIL THUMBSIZE 4 ZOOM 24 HEIGHT 500 Y -4 THEME Book STARTFROM 10 ]]
13P5H2V0 (glider 3736) (Robert Wainwright, 1994) (click above to open LifeViewer) Catagolue: here
x = 7, y = 7, rule = B35/S23
2bo$b3o$o3bo$bo2bo$3b2obo$6bo$4bobo!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBNAIL THUMBSIZE 4 ZOOM 24 HEIGHT 500 Y -2 THEME Book STARTFROM 6 ]]
14P3H1V0 (glider 4793) (Nathan Thompson, 1994) (click above to open LifeViewer) Catagolue: here
x = 7, y = 7, rule = B35/S23
3bo$b2ob2o$o2bo2bo$obobobo$3bo$bo3bo$bobobo!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBNAIL THUMBSIZE 4 ZOOM 24 HEIGHT 500 Y -2 THEME Book STARTFROM 4 ]]
18P2H1V0 (glider 4716) (Nathan Thompson, 1994) (click above to open LifeViewer) Catagolue: here
x = 7, y = 7, rule = B35/S23
o3b2o6bo$2ob4o5bo$o5b2o2b5o$3bo3b3obo$3bob2ob2obo$5b3o$6b2o!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBNAIL THUMBSIZE 4 ZOOM 24 HEIGHT 500 Y -2 THEME Book STARTFROM 4 ]]
There is a naturally occurring orthogonal c/2 puffer with period 136, leaving three blinkers in a half-interchange formation and two blocks every 68 ticks. Combining two or more puffers can give other puffers and spaceships.[2][3] The puffer engine also works in B357/S238 (where it becomes a p248 puffer).
On September 10, 2021, FWKnightship posted a 24c/48 siderake emitting 2c/5 spaceships.[4]
The beehive/block fuse (click above to open LifeViewer)
Once the beehive reaches the end, it will reverse direction while shortening the chain, and will eventually annihilate it given enough time. This can be stopped with a pond:
A collection of beehive/block fuse reactions (click above to open LifeViewer)
These chains can interact in different ways to form logic gates.
Change in frequency, stabilisation time and evolutionary sequences
From the same random starting conditions, Grounded Life usually settles into much fewer objects than in Life due to the fact that many life evolutionary sequences are sparks in this rule. It also stabilises ten times faster than life on average.
The honey farm sequence, which evolves into 4 blinkers in a traffic light-like formation with a tub inside, is much rarer in Grounded Life due to the fact that the only 7-cell predecessor that still works is the line of seven, which is much rarer than the other predecessors.
The traffic light sequence is considerably rarer in Grounded Life due to the T-tetromino's disappearance, so the next most common predecessor that works is the X-pentomino, which is rarer.
On August 3, 2023, AlbertArmStain published a Rule 110 unit stripe based on the aforementioned beehive/block fuse, proving the rule's Turing-completeness.[5]
Soup search was performed using a modified version of apgsearch, yielding uncommon objects such as the c/3o spaceship (Glider 4793) as early as 2014.[6]
The b35s23/C1 census accumulated 375 million objects in April 2015,[c 2]
169 billion objects in October 2017,[c 3]
519 billion objects in July 2021,[c 4]
561 billion objects in October 2021,[c 5]
1690 billion objects in February 2023,[c 6]
1722 billion objects in August 2023.[c 7]
See also
Pseudo Life, a rule where many patterns from this rule also work, although with generally more chaotic evolution.
Eppstein, a rule only one transition away from grounded life, although it is explosive
References
↑ LumpsOfMuck (October 14, 2011). Re: B35/S23 (discussion thread) at the ConwayLife.com forums
↑ 2.02.1 Lewis (August 19, 2014). Re: B35/S23 (discussion thread) at the ConwayLife.com forums
↑ praosylen (February 27, 2015). Re: B35/S23 (discussion thread) at the ConwayLife.com forums
↑ FWKnightship (September 10, 2021). Re: B35/S23 (discussion thread) at the ConwayLife.com forums
↑ AlbertArmStain (August 3, 2023). Re: B35/S23 (discussion thread) at the ConwayLife.com forums