OCA:LeapLife
| LeapLife | |
| Rulestring | 23-q/2n3 B2n3/S23-q |
|---|---|
| Character | Chaotic |
LeapLife is an isotropic non-totalistic cellular automaton created by Hunting in January, 2020. It differs from Conway's Game of Life by two transitions, much like tlife, but is much more stable.
LeapLife ranked eighth in OCA Discovery of the Year 2020. LeapLife billiard tables ranked last in OCA Discovery of the Year 2021.
Patterns
Still lives
Because LeapLife added one birth transition and removed one survival transition from Life, all still lives in LeapLife are still lives in Conway's Game of Life, but the reverse is not true. For example, the snake with feather fails in LeapLife.
All still lives up to 12 bits have occured naturally. The last of them to occur, trans-very long fuse with two tails, appeared in November 2022, in a soup submitted by FWKnightship.
All still lives up to 11 bits have known syntheses. The following (probably outdated) table displays statistics about the costs for strict still lives up to 11 cells. Green indicates a cost lower than one glider per bit; yellow indicates a cost of equal to or more than one glider per bit. Max costs are linked to the corresponding still life.
| Live cells | Count | Max cost |
|---|---|---|
| 4 | 2 | 3 |
| 5 | 1 | 2 |
| 6 | 5 | 4 |
| 7 | 4 | 4 |
| 8 | 9 | 5 |
| 9 | 10 | 12 |
| 10 | 25 | 11 |
| 11 | 44 | 21 |
| 21-glider synthesis of the currently most expensive 11-bitter, cis-long^3 hook with tail, by Mark Niemiec (click above to open LifeViewer) |
Oscillators
A variety of oscillators are present in LeapLife, mostly discovered with apgsearch.
Of all alien oscillators, quite a few of them are especially common, shown below.
| From left to right: Row 1: The traffic-light p6, the interchange p6, and the "integral" p4. Row 2: The "two-blocks" p3, the "loaf-block" p4, and an unnamed p10 (click above to open LifeViewer) |
Most oscillators known before April 2020 can be found in a GitHub repository.
Spaceships
The gliders and xWSSes still work in LeapLife, and there's an additional (2,1)c/8 knightship called the "lepa".
As of October 2022, all spaceships discovered in LeapLife are elementary. The idea of building a Demonoid in LeapLife was brought up several times, but the spaceship itself is not yet completed. The currently known velocities are c/2, c/3, c/4, c/5, 2c/5, c/6, 2c/7, c/12 orthogonal, c/4, c/5 diagonal, and (2,1)c/6, (2,1)c/8 knightwise. A table of completed spaceship searches can be found here.
| Smallest example of all known simplified velocities. (2, 1)c/6 spaceship not shown for its size (click above to open LifeViewer) |
Very few spaceships in LeapLife have syntheses. Only the lepa, xWSSes and their combinations, and the c/12 have been synthesised.
Linear growth patterns
Guns
Very limited gun technologies are known in LeapLife. 2-engine p22-based and p24-based guns are discovered early on. p19-based guns are first constructed by FWKnightship in March 2021 using an XWSS salvo as an over-unity reaction. It was quickly superseded by a much smaller design by AbhpzTa, using a sparker-supported 2G-to-3G reaction.
Guns of period p19N, p22N, and p24N for all sufficiently large N are known as well.
| p22 and p24 glider guns (click above to open LifeViewer) |
Puffers
Puffers in LeapLife are discovered much later than guns, and very few puffers are known as of now.
The first puffer in LeapLife is the c/2 line puffer discovered by FWKnightship; It can be perturbed into rakes and others.
Some puffers of other velocities are known, including a 2c/5 orthogonal blinker puffer and a c/4 diagonal tubstretcher.
Unstable objects and evolutionary sequences
Methuselahs
Due to the nature of the rule, methuselahs in LeapLife are usually much shorter-lived than methuselahs in Life. The longest-lived methuselah currently known is one shown below, lasting 944 generations, found by User:Pzq_Alex.
| 944M. (click above to open LifeViewer) |
The longest-lived known diehard is the 710-tick diehard shown below:
| 710-tick diehard (click above to open LifeViewer) |
The following is a table of relatively long-lived methuselahs with historical significance.
The following is a table of long-lived methuselahs that were record-breaking at the time.
| Lifespan (L) | Pattern | Bounding box | MCPS | Initial population (I) | Final population (F) | L/I | F/I | F/L | L/MCPS |
|---|---|---|---|---|---|---|---|---|---|
| 395 | Big-R relative | 6 × 6 | 18 | 16 | 11 | 24.7 | 0.7 | 0.028 | 21.9 |
| 248 | Big-R relative | 3 × 5 | 9 | 8 | 11 | 31 | 1.4 | 0.044 | 27.6 |
| 247 | Big-R relative | 4 × 4 | 9 | 8 | 11 | 30.9 | 1.4 | 0.045 | 27.4 |
| 246 | Big-R | 4 × 4 | 7 | 7 | 11 | 35.1 | 1.6 | 0.045 | 35.1 |
| 235 | Nope | 4 × 4 | 9 | 9 | 10 | 26.1 | 1.1 | 0.043 | 26.1 |
(TODO)
Common evolutionary sequences
A few common evolutionary sequences in Life are common in LeapLife as well, like lumps of muck, bakery and a variant of pi-heptomino. There are also some other sequences known and investigated for a while that are not as common in Life, like the "butterfly sequence" (different from the butterfly sequence in Life).
A census of 8 × 8 soups in LeapLife has been done, similar to the method used in List of common evolutionary sequences. The following is the result:
(TODO)
Catalyses and other reactions
The simplest catalysis that exists in LeapLife and not Life is a block catalysis from the corner, due to the B2n transition. There are also some other catalysts, mostly discovered with a LeapLife hack of dr by wwei23.
| An example of the block corner catalysis, where only a single corner temporarily dies (click above to open LifeViewer) |
(TODO)
Variants
HighLeapLife (B2n36/S23-q)
HighLeapLife has a common p96 RRO:
| The RRO (click above to open LifeViewer) |
There is also a p72 oscillator, which was discovered in D4_+1.
| The p72 (click above to open LifeViewer) |
DryLeapLife (B2n37/S23-q)
DryleapLife is similar to LeapLife, with a natural c/7o and a gliderless c/4d, the latter of which was found in D8_1.
| c/7o and c/4d (click above to open LifeViewer) |
LispLife (B2n3/S23-q4e8)
LispLife is a more active variant of LeapLife. A natural p122 oscillator has been discovered.
| The p122 (click above to open LifeViewer) |
tDryLeapLife (B2n37/S2-i3-q4q)
tDryLeapLife has the glider, the c/5 orthogonal T, and an unnamed 3c/27o.
| Common spaceships in tDryLeapLife (click above to open LifeViewer) |
External links
- LeapLife (B2n3/S23-q) (discussion thread) at the ConwayLife.com forums
- LeapLife at Adam P. Goucher's Catagolue
- A LeapLife Status Report (NOW WITH LIFEVIEWER ANIMATION!) (discussion thread) at the ConwayLife.com forums
- LeapLife Relatives (discussion thread) at the ConwayLife.com forums
- LispLife (B2n3/S23-q4e8) (discussion thread) at the ConwayLife.com forums
- HighLeapLife at Adam P. Goucher's Catagolue
- DryLeapLife at Adam P. Goucher's Catagolue
- LispLife at Adam P. Goucher's Catagolue
- tDryLeapLife at Adam P. Goucher's Catagolue