Toad: Difference between revisions
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'''Toad''' is a {{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. Toads often appear in large, complex patterns because of their ability to eat things when paired together (as in [[killer toads]]). Additionally, toads are useful as building blocks for constructing large oscillators with periods that are a multiple of two because of the various ways in which they can be [[hassle | '''Toad''' is a {{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. Toads often appear in large, complex patterns because of their ability to eat things when paired together (as in [[killer toads]]). Additionally, toads are useful as building blocks for constructing large oscillators with periods that are a multiple of two because of the various ways in which they can be [[hassle]]d. | ||
== Toad hasslers == | |||
==Toad hasslers== | |||
A '''toad flipper''' is a hassler that works by having two [[domino]] [[spark]]ers ([[pentadecathlon]]s in the example shown below) 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]]. | A '''toad flipper''' is a hassler that works by having two [[domino]] [[spark]]ers ([[pentadecathlon]]s in the example shown below) 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]]. | ||
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It is also possible to simultaneously shift and flip a toad using one domino spark. However, the domino spark must be inserted in a special way that would not result in a domino spark without the toad. Two spaceships that are suitable sparkers, one on each side, can escort a toad similarly to the moving toad suckers mentioned earlier except that the amalgamation moves two squares orthogonal per period instead of one square orthogonal per period.<ref>{{LinkForumThread | format = ref | title = Re: Thread for your Trolls | p = 116330 | author = praosylen | date = December 18, 2020 }}</ref> | It is also possible to simultaneously shift and flip a toad using one domino spark. However, the domino spark must be inserted in a special way that would not result in a domino spark without the toad. Two spaceships that are suitable sparkers, one on each side, can escort a toad similarly to the moving toad suckers mentioned earlier except that the amalgamation moves two squares orthogonal per period instead of one square orthogonal per period.<ref>{{LinkForumThread | format = ref | title = Re: Thread for your Trolls | p = 116330 | author = praosylen | date = December 18, 2020 }}</ref> | ||
== | == Use 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 in the gallery below. | 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 in the gallery below. | ||
==Gallery== | == [[List of common oscillators|Commonness]] == | ||
Toad is the second 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; this happens in both the [[century]] and [[two-glider octomino]] sequences. Frequency lists typically include only surviving objects. | |||
== [[Glider synthesis]] == | |||
{{Small constructible periodic object}} | |||
== Gallery == | |||
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==See also== | == See also == | ||
*[[Pentoad]] | * [[Pentoad]] | ||
*[[Tritoad]] | * [[Tritoad]] | ||
*[[Turning toads]] | * [[Turning toads]] | ||
==References== | == References == | ||
<references /> | <references /> | ||
==External links== | == External links == | ||
{{LinkNiemiec|p2osc.htm#6-bit%20p2|patternname=Life Period-2 Oscillators (six-bit)}} | {{LinkNiemiec|p2osc.htm#6-bit%20p2|patternname=Life Period-2 Oscillators (six-bit)}} | ||
{{LinkLexicon|lex_t.htm#toad}} | {{LinkLexicon|lex_t.htm#toad}} | ||
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{{Symmetry|180degree}} | {{Symmetry|180degree}} | ||
Revision as of 04:36, 24 December 2021
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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 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. Toads often appear in large, complex patterns because of their ability to eat things when paired together (as in killer toads). Additionally, toads are useful as building blocks for constructing large oscillators with periods that are a multiple of two because of the various ways in which they can be hassled.
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.
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.[3] 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. Additionally, moving toad suckers have been created that use the domino sparks from two parallel even-period spaceships to escort a toad.
It is also possible to simultaneously shift and flip a toad using one domino spark. However, the domino spark must be inserted in a special way that would not result in a domino spark without the toad. Two spaceships that are suitable sparkers, one on each side, can escort a toad similarly to the moving toad suckers mentioned earlier except that the amalgamation moves two squares orthogonal per period instead of one square orthogonal per period.[4]
Use 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 in the gallery below.
Toad is the second most common naturally-occurring oscillator in Achim Flammenkamp's census, although blinkers occur more than a hundred times as frequently.[5] It is also the eleventh most common object on Adam P. Goucher's Catagolue.[6]
Toads have a tendency to be destroyed after being created; this happens in both the century and two-glider octomino sequences. Frequency lists typically include only surviving objects.
All strict still lifes with a population of 23 or fewer cells, all oscillators with 16 or fewer cells, and all spaceships with 35 or fewer cells are known to be glider-constructible. A glider synthesis of this object can be found in the infobox to the right.
Gallery
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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.
- ↑ "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
- ↑ 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.
External links
- Life Period-2 Oscillators (six-bit) 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
- Patterns with 180-degree rotation symmetry