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'''Toad''' is a {{cells|6}}-[[cell]] {{period|2}} [[oscillator]] that was found by [[Simon Norton]] in May {{year|1970}}.<ref>{{CiteHickersonOscillators|accessdate=March 14, 2020}}</ref> It is one of very few known oscillators that is a [[polyomino]] in one of its [[phase]]s. Its other phase consists of two [[banana spark]]s. | '''Toad''' is a {{cells|6}}-[[cell]] {{period|2}} [[oscillator]] that was found by [[Simon Norton]] in May {{year|1970}}.<ref>{{CiteHickersonOscillators|accessdate=March 14, 2020}}</ref> It is one of very few known oscillators that is a [[polyomino]] in one of its [[phase]]s. Its other phase consists of two [[banana spark]]s. | ||
Toads often appear in large, complex patterns because of their ability to eat things. Additionally, toads are useful as building blocks for constructing large oscillators with | Toads often appear in large, complex patterns because of their ability to eat things. 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 [[hassle]]d. | ||
== Applications == | == Applications == | ||
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A '''toad flipper''' is a hassler that works by having two [[domino | A '''toad flipper''' is a hassler that works by having two [[domino spark]]ers ([[pentadecathlon]]s in the example shown above) apply their sparks to the toad in order to flip it over.<ref>{{CiteLexicon|file=lex_t.htm#toadflipper|name=Toad-flipper|accessdate=May 16, 2009}}</ref> When the sparks are applied again, the toad is flipped back. Either or both domino sparkers can be moved down two [[cell]]s 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.<ref name="post117782" /> | ||
A '''toad sucker''' is a toad hassler that works by having two domino sparkers (pentadecathlons in the example shown above) apply their sparks to the toad in order to shift it.<ref>{{CiteLexicon|file=lex_t.htm#toadsucker|name=Toad-sucker|accessdate=May 16, 2009}}</ref> 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. | A '''toad sucker''' is a toad hassler that works by having two domino sparkers (pentadecathlons in the example shown above) apply their sparks to the toad in order to shift it.<ref>{{CiteLexicon|file=lex_t.htm#toadsucker|name=Toad-sucker|accessdate=May 16, 2009}}</ref> 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. | ||
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These toad-hassling mechanisms were featured interchangeably in the first known period-[[p36 toad hassler|36]], [[p48 toad hassler|48]] and [[p58 toadsucker|58]] oscillators. | These toad-hassling mechanisms were featured interchangeably in the first known period-[[p36 toad hassler|36]], [[p48 toad hassler|48]] and [[p58 toadsucker|58]] oscillators. | ||
Additionally, moving toad suckers have been created that use the domino sparks from two parallel [[spaceship]]s 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. | Additionally, moving toad suckers have been created that use the domino sparks from two parallel [[spaceship]]s 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 === | ||
{| | {| | ||
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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. | 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. | ||
=== | === As a catalyst === | ||
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]], the [[octomino II]]-to-glider converter in the [[hotcrystal0 reaction]], and a recent period-120 pi-heptomino hassler.<ref name="post141451" /> | 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]], the [[octomino II]]-to-glider converter in the [[hotcrystal0 reaction]], and a recent period-120 pi-heptomino hassler.<ref name="post141451" /> | ||
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Moreover, toads can be paired to form [[killer toads]], which has been used in {{LinkCatagolue|xp6_7exe7z01ici1zotxtoz1y11|style=raw|patternname=a small period-6 oscillator}} reminiscent of [[worker bee]], period-60 [[twirling T-tetsons 2]] and p2 version of [[L122]]. | Moreover, toads can be paired to form [[killer toads]], which has been used in {{LinkCatagolue|xp6_7exe7z01ici1zotxtoz1y11|style=raw|patternname=a small period-6 oscillator}} reminiscent of [[worker bee]], period-60 [[twirling T-tetsons 2]] and p2 version of [[L122]]. | ||
=== | === As a one-time reflector === | ||
In December 1971, Curt Gibson reported a reaction where a [[glider]] is reflected 90 degrees at the expense of a toad.<ref>{{CiteLifeline|vol=4|pages=page 6}}</ref> Unlike other small single-object [[turner]]s like [[boat]], [[fishhook]] and [[long boat]], toad is [[color-preserving]]. | In December 1971, Curt Gibson reported a reaction where a [[glider]] is reflected 90 degrees at the expense of a toad.<ref>{{CiteLifeline|vol=4|pages=page 6}}</ref> Unlike other small single-object [[turner]]s like [[boat]], [[fishhook]] and [[long boat]], toad is [[color-preserving]]. | ||
== | == Commonness == | ||
Toad is the second | Toad is the second [[List of common oscillators|most common naturally-occurring oscillator]] in [[Achim Flammenkamp's census]], although [[blinker]]s occur more than a hundred times as frequently.<ref>{{citeAchim|accessdate=January 15, 2009}}</ref> It is also the eleventh most common object on [[Adam P. Goucher]]'s [[Catagolue]].<ref>{{citeCatagolueStats|June 24, 2016}}</ref> | ||
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. | 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 {{gliders|3}} 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.<ref name="post145011" /> Other 3-glider recipes of a toad are also known. | A {{gliders|3}} [[Glider synthesis|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.<ref name="post145011" /> Other 3-glider recipes of a toad are also known. | ||
== See also == | == See also == | ||
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== External links == | == External links == | ||
{{LinkNiemiec|0/6td.rle}} | * {{LinkNiemiec|0/6td.rle}} | ||
{{LinkLexicon|lex_t.htm#toad}} | * {{LinkLexicon|lex_t.htm#toad}} | ||
{{LinkCatagolue|xp2_7e}} | * {{LinkCatagolue|xp2_7e}} | ||
{{LinkPentadecathlonObject|6P2.1}} | * {{LinkPentadecathlonObject|6P2.1}} | ||
[[Category:Polyominoes]] | [[Category:Polyominoes]] | ||
{{Symmetry|180degree}} | {{Symmetry|180degree}} | ||
Revision as of 22:15, 9 July 2022
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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 | Unspecified | ||||||||
| Rotor type | Toad | ||||||||
| Discovered by | Simon Norton | ||||||||
| Year of discovery | 1970 | ||||||||
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Toad is a 6-cell 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 to eat things. 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
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A toad flipper is a hassler that works by having two domino sparkers (pentadecathlons in the example shown above) apply their sparks to the toad in order to flip it over.[3] 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.[4]
A toad sucker is a toad hassler that works by having two domino sparkers (pentadecathlons in the example shown above) apply their sparks to the toad in order to shift it.[5] 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, 48 and 58 oscillators.
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
|
|
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.
As a catalyst
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, the octomino II-to-glider converter in the hotcrystal0 reaction, and a recent period-120 pi-heptomino hassler.[7]
Moreover, toads can be paired to form killer toads, which has been used in a small period-6 oscillator reminiscent of worker bee, period-60 twirling T-tetsons 2 and p2 version of L122.
As a one-time reflector
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.
Commonness
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.
See also
References
- ↑ Dean Hickerson's oscillator stamp collection. Retrieved on March 14, 2020.
- ↑ praosylen (December 18, 2020). Re: Thread for your Trolls (discussion thread) at the ConwayLife.com forums
- ↑ "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.
- ↑ 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
- Toad at Mark D. Niemiec's Life Page
- 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 rotor Toad
- Polyominoes
- Patterns with 180-degree rotation symmetry