Toad

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Toad
b2o$o$3bo$b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ]] #C [[ LOOP 2 GPS 2 THUMBSIZE 2 ]]
Pattern type Oscillator
Number of cells 6
Bounding box 4×4
Frequency class 7.1
Period 2
Mod 2
Heat 8
Volatility 0.80
Strict volatility 0.80
Rotor type Toad
Discovered by Simon Norton
Year of discovery 1970

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 periods that are a multiple of two because of the various ways in which they can be hassled.

Applications

Toad hasslers

x = 18, y = 10, rule = B3/S23 bo14bo$bo14bo$obo12bobo$bo14bo$bo6bo7bo$bo6b2o6bo$bo6b2o6bo$obo6bo5bob o$bo14bo$bo14bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART GPS 5 LOOP 60 ]]
p60 toad flipper
(click above to open LifeViewer)
RLE: here Plaintext: here
Catagoluehere
x = 18, y = 11, rule = B3/S23 bo$bo14bo$obo13bo$bo13bobo$bo6bo7bo$bo6b2o6bo$bo6b2o6bo$obo6bo6bo$bo 13bobo$bo14bo$16bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART GPS 5 LOOP 60 ]]
p60 toad sucker
(click above to open LifeViewer)
RLE: here Plaintext: here
Catagoluehere
x = 111, y = 30, rule = B3/S23 78bo6bo$54bo6bo15bobo4bobo11bo6bo$53bobo4bobo14bobo4bobo10bobo4bobo$ 53bobo4bobo15bo6bo11bobo4bobo$54bo6bo36bo6bo$77b3o4b3o$53b3o4b3o14b4o 2b4o10b3o4b3o$53b4o2b4o17bo2bo13b4o2b4o$56bo2bo17b3ob2ob3o13bo2bo$53b 3ob2ob3o14b2o6b2o10b3ob2ob3o$53b2o6b2o13b2o8b2o9b2o6b2o$52b2o8b2o32b2o 8b2o$75bo12bo$51bo12bo8bo2bo10bo2bo4bo12bo$49bo2bo10bo2bo2b2o2bo2bo10b o2bo2bo2bo10bo2bo$49bo2bo10bo2bo4bo21bo2bo10bo2bo$68bo7b3o6b3o$52b3o6b 3o5b2o5bo10bo8b3o6b3o$52bo10bo14bo6bo10bo10bo$30bo11bo11bo6bo14b3o6b3o 10bo6bo$3bo11bo14bo11bo9b3o6b3o32b3o6b3o$3bo11bo13bobo9bobo35bob2obo4b obo$2bobo9bobo38bob2obo19bo2bo7b2obo4bob2obo$28bo3bo7bo3bo11bo2bo16bob 2ob2ob2obo3b2o7bo2bo$bo3bo7bo3bo10bob6ob6obo7bob2ob2ob2obo12b3o6b3o4bo 3bob2ob2ob2obo$bob6ob6obo9bo7bobo7bo6b3o6b3o32b3o6b3o$o7bobo7bo3b3o2bo 7bobo7bo30bobo6bobo$o7bobo7bo2bo5bo17bo6bobo6bobo12bobo6bobo8bobo6bobo $o17bo9bob2ob2o3b2ob2obo7bobo6bobo10b3ob3o2b3ob3o6bobo6bobo$bob2ob2o3b 2ob2obo4b2o26b3ob3o2b3ob3o28b3ob3o2b3ob3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 4 ]]
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
#C RLE taken from https://www.conwaylife.com/forums/viewtopic.php?p=116324#p116324 x = 47, y = 10, rule = B3/S23 2bo15bo10bo15bo$b3o6bo6b3o8b3o6bo6b3o$2obo5b3o4b2obo7b2obo5b3o4b2obo$ 3o5b2o2bo3b3o8b3o5b2o2bo3b3o$3o5bo2bobo2b3o3b3o2b3o5bo2bobo2b3o$b2o2b 3obo7b2o6bo2b2o2b3obo7b2o$b2o3b2o6b2o12b2o3b2o6b2o$2b2o3bo6bo2bo5b2o4b 2o3bo6bo2bo$6bo11bo14bo11bo$18bo26bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 12 ]]
A toad escorted and flipped with two 2c/4 spaceships[2]
(click above to open LifeViewer)
RLE: here Plaintext: here

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.

Use as an induction coil

x = 20, y = 20, rule = B3/S23 4b2o$3bobo$5bob3o7bo$2b2obo2b3o4bobo$5bo13bo$4bo9b6o$6bo5bo$7bo4bo3b2o $7bo3bo6bo$2b2o5bo5bo$4bo5bo5b2o$bo6bo3bo$2b2o3bo4bo$7bo5bo$6o9bo$o13b o$2bobo4b3o2bob2o$2bo7b3obo$14bobo$14b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 8 GPS 2 AUTOSTART ]]
An example of toads being used as an induction coil
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 40, y = 19, rule = B3/S23 10bo18bo$9bobo6b2o8bobo$6bo2bobo5bo10bobo2bo$5bobobob2o7bo6b2obobobo$ 4bobobobo7b2o9bobobobo$4bo3bo2b3o12b3o2bo3bo$2bobobobob2o16b2obobobobo $bobobob2o4bo5b2o5bo4b2obobobo$bobobobo2bo3bo4b2o4bo3bo2bobobobo$2ob2o b2obo4bo4b2o4bo4bob2ob2ob2o$bobobobo2bo3bo3b4o3bo3bo2bobobobo$bobobob 2o4bo4b4o4bo4b2obobobo$2bobobobob2o6b4o6b2obobobobo$4bo3bo2b3o12b3o2bo 3bo$4bobobobo9b2o7bobobobo$5bobobob2o6bo7b2obobobo$6bo2bobo10bo5bobo2b o$9bobo8b2o6bobo$10bo18bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 8 GPS 6 ]]
Toads suppressing a line of four in a p36 oscillator[6]
(click above to open LifeViewer)
RLE: here Plaintext: 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.

Use 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.

Use 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

  1. Dean Hickerson's oscillator stamp collection. Retrieved on March 14, 2020.
  2. praosylen (December 18, 2020). Re: Thread for your Trolls (discussion thread) at the ConwayLife.com forums
  3. "Toad-flipper". The Life Lexicon. Stephen Silver. Retrieved on May 16, 2009.
  4. Matthias Merzenich (January 2, 2021). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  5. "Toad-sucker". The Life Lexicon. Stephen Silver. Retrieved on May 16, 2009.
  6. David Raucci (April 25, 2022). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  7. iNoMed (February 10, 2022). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  8. Robert Wainwright (December 1971). Lifeline, vol 4, page 6.
  9. Achim Flammenkamp (September 7, 2004). "Most seen natural occurring ash objects in Game of Life". Retrieved on January 15, 2009.
  10. Adam P. Goucher. "Statistics". Catagolue. Retrieved on June 24, 2016.
  11. GUYTU6J (May 3, 2022). Re: Thread For Your Useless Discoveries (discussion thread) at the ConwayLife.com forums

External links

  • 6P2.1 at Heinrich Koenig's Game of Life Object Catalogs