Toad
| Toad | |||||||||
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| Pattern type | Oscillator | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Number of cells | 6 | ||||||||
| Bounding box | 4 × 4 | ||||||||
| Frequency class | 7.1 | ||||||||
| Period | 2 (mod: 2) | ||||||||
| Heat | 8 | ||||||||
| Volatility | 0.80 | 0.80 | ||||||||
| Kinetic symmetry | .k | ||||||||
| Rotor type | Toad | ||||||||
| Discovered by | Simon Norton | ||||||||
| Year of discovery | 1970 | ||||||||
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Toad is a 6-bit period-2 oscillator that was found by Simon Norton in May 1970.[1] It is one of very few known oscillators that is a polyomino in one of its phases. Its other phase consists of two banana sparks.
Toads often appear in large, complex patterns because of their ability of being catalysts. Additionally, toads are useful as building blocks for constructing large oscillators with an even period because of the various ways in which they can be hassled.
Applications
Toad hasslers
A toad flipper is a hassler that works by having two domino sparkers (pentadecathlons in the example shown below) apply their sparks to the toad in order to flip it over.[2] When the sparks are applied again, the toad is flipped back. Either or both domino sparkers can be moved down two cells from the position shown and the toad flipper will still work, but because of symmetry there are really only two different types of toad flippers. For another example of a toad flipper, see 186P24 and the period-4 turning toads wick. There are also other period-2 oscillators with a similar segment that can be flipped.[3]
A toad sucker is a toad hassler that works by having two domino sparkers (pentadecathlons in the example shown below) apply their sparks to the toad in order to shift it.[4] When the sparks are applied again, the toad is shifted back. Either or both domino sparkers can be moved down two cells from the position shown and the toad sucker will still work, but because of symmetry there are really only three different types of toad suckers. A p4 example is shown in the "subsequent improvement of the p44 gun" as a sparker in the p44 pi-heptomino hassler article.
These toad-hassling mechanisms were featured interchangeably in the first known period-36, period-48 and period-58 oscillators.
| Toads escorted at c/4 orthogonal with 46P4H1V0 (left) or c/6 orthogonal with dragons (right) (click above to open LifeViewer) RLE: here Plaintext: here |
| A toad escorted and flipped with two 2c/4 spaceships[5] (click above to open LifeViewer) RLE: here Plaintext: here |
Additionally, moving toad suckers have been created that use the domino sparks from two parallel spaceships to escort a toad, where the spaceships move one cell in an even period. It is also possible to shift and flip a toad simultaneously using one domino spark whose formation relies on the toad; in this case the two escorting spaceships move two cells in a period.
As an induction coil
| An example of toads being used as an induction coil (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here |
| Toads suppressing a line of four in a p36 oscillator[6] (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here |
Toads can be used as an induction coil where the number of cells in the row alternates between two numbers one apart. An example in Dean Hickerson's oscillator collection, where the row alternates between 5 and 6 cells, can be seen above to the left.
A second use is suppressing a line of four where a block would get destroyed, a recent example of which is shown to the right. The two outer cells in the line of four survive in the next generation, interfering the constant 2-cell surface of a block but not the 1-cell edge of the toad in banana spark phase. Blocked p4-5 is another example of this type.
On 2022-01-15, Charity Engine found a stabilisation of the queen bee shuttle with a boat and an induction coil toad in an asymmetric soup.
As a catalyst
- Main article: Toad reaction
A toad can act as a rock with the center of banana spark in certain situations. A singular toad serves as a catalyst in Achim's other p16, 52P44, 43P54, p16 century shuttle, the octomino II-to-glider converter in the hotcrystal0 reaction, and one of the period-120 pi-heptomino hasslers.[7] Catalysts containing a toad as a part appear in some patterns including 66P106, p82 lumps of muck hassler and 42P38.
Moreover, toads can be paired to form killer toads, which has been used in a small "p6 worker bee" period-6 oscillator (Catagolue: here) reminiscent of worker bee, period-60 twirling T-tetsons 2 and p2 version of L122 and 45-degree MWSS-to-G.
Starting in 2022, the term "toad" has been used more generically to refer to a reaction regardless of period that performs the same catalysis as a toad, such as candlefrobra and requests for "p7 toad"s.
As a one-time turner
In December 1971, Curt Gibson reported a reaction where a glider is reflected 90 degrees at the expense of a toad.[8] Unlike other small single-object turners like boat, fishhook and long boat, toad is color-preserving.
Occurrence
- See also: List of common oscillators
Toad is the second most common naturally-occurring oscillator in Achim Flammenkamp's census, although blinkers occur more than a hundred times as frequently.[9] It is also the eleventh most common object on Adam P. Goucher's Catagolue.[10]
Toads have a tendency to be destroyed after being created, which happens in both the century and two-glider octomino sequences, while frequency lists typically include only surviving objects.
Glider synthesis
A 3-glider synthesis of toad can be made by suppressing extraneous junk with another glider from the two-glider octomino after dropping the toad. Coincidentally, one of the octomino-making gliders is on the same lane as a glider reflected by a toad at the same location.[11] Other 3-glider recipes of a toad are also known.
| Glider syntheses of toad from Mark Niemiec's database (click above to open LifeViewer) RLE: here Plaintext: here |
See also
References
- ↑ Dean Hickerson's oscillator stamp collection. Retrieved on March 14, 2020.
- ↑ "Toad-flipper". The Life Lexicon. Stephen Silver. Retrieved on May 16, 2009.
- ↑ Matthias Merzenich (January 2, 2021). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ "Toad-sucker". The Life Lexicon. Stephen Silver. Retrieved on May 16, 2009.
- ↑ praosylen (December 18, 2020). Re: Thread for your Trolls (discussion thread) at the ConwayLife.com forums
- ↑ David Raucci (April 25, 2022). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ iNoMed (February 10, 2022). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ Robert Wainwright (December 1971). Lifeline, vol 4, page 6.
- ↑ Achim Flammenkamp (September 7, 2004). "Most seen natural occurring ash objects in Game of Life". Retrieved on January 15, 2009.
- ↑ Adam P. Goucher. "Statistics". Catagolue. Retrieved on June 24, 2016.
- ↑ GUYTU6J (May 3, 2022). Re: Thread For Your Useless Discoveries (discussion thread) at the ConwayLife.com forums
External links
- The 3 six-bit oscillators at Mark D. Niemiec's Life Page (download pattern file: 0/6td.rle)
- Toad at the Life Lexicon
- Toad at Adam P. Goucher's Catagolue
- 6P2.1 at Heinrich Koenig's Game of Life Object Catalogs
- Patterns
- Patterns with Catagolue frequency class 7
- Natural periodic objects
- Oscillators with 6 cells
- Periodic objects with minimum population 6
- Patterns with 6 cells
- Patterns found by Simon Norton
- Patterns found in 1970
- Patterns that can be constructed with 3 gliders
- Oscillators
- Oscillators with period 2
- Oscillators with mod 2
- Oscillators with heat 8
- Oscillators with volatility 0.80
- Oscillators with strict volatility 0.80
- Oscillators with .k symmetry
- Oscillators with rotor Toad
- Catalysts
- Polyominoes