Sombreros

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Sombreros
x = 18, y = 11, rule = B3/S23 3b2o8b2o$3bobo6bobo$5bo6bo$3bob2o4b2obo$b3o10b3o$o3bobo4bobo3bo$b3o10b 3o$3bob2o4b2obo$5bo6bo$3bobo6bobo$3b2o8b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ]] #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 24 GPS 3 LOOP 6 ]]
Pattern type Oscillator
Number of cells 50
Bounding box 18 × 11
Period 6
Mod 6
Heat 5.3
Volatility 0.25
Strict volatility 0.25
Discovered by David Buckingham
Year of discovery 1972
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Sombreros is a period-6 oscillator that was found by David Buckingham in December 1972.[1][2] Each half by itself is called a sombrero.

If the two sombreros are moved three cells closer to one another, the oscillator's period drops to 4 ticks and the result is just a less compact form of Achim's p4:

x = 15, y = 11, rule = B3/S23 3b2o5b2o$3bobo3bobo$5bo3bo$3bob2ob2obo$b3o7b3o$o3bobobobo3bo$b3o7b3o$ 3bob2ob2obo$5bo3bo$3bobo3bobo$3b2o5b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 GPS 3 AUTOSTART ]]
Period 4 variant
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RLE: here Plaintext: here

Two sombreros moved two spaces closer and staggered by one space forms a period 5 oscillator called Siesta.

x = 16, y = 12, rule = B3/S23 11b2o$3b2o5bobo$3bobo4bo$5bo3b2obo$3bob2o5b3o$b3o5bobo3bo$o3bobo5b3o$b 3o5b2obo$3bob2o3bo$5bo4bobo$3bobo5b2o$3b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 GPS 3 AUTOSTART ]]
Siesta
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RLE: here Plaintext: here

goldenratio found a 36-glider synthesis of a sombreros variant[c 1] in October 2020.[3]

One sombrero can be supported by two eater 1s.[4] The resulting oscillator is shown below, with a stator variant[5] that is thinner but taller:

x = 12, y = 11, rule = B3/S23 2o6b2o$bo5bo2bo$bobo3bob2o$2b2o2b2o$6bo2b2o$8b2obo$6bo4bo$2b2o2b2ob2o$ bobo3bobo$bo5bobo$2o6bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 GPS 3 AUTOSTART ]]
Stator variant of sombrero supported by two eaters[4][5]
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Catagoluehere

One period-6 stabilisation of scrubber halves involves them each mutually stabilising with a single sombrero, and can be extended to a glide-symmetric wick.

x = 75, y = 21, rule = B3/S23 19bo11bo11bo$18bobo9bobo9bobo$18bobo9bobo9bobo$13bo3b2ob2o7b2ob2o7b2ob2o$8b2o2bobo4bo4bobo4bo4bobo4bo4bo$7bobo2bob4obob4ob4obob4ob4obob4o$6bo3b2o5b2ob2o7b2ob2o7b2ob2o$5bob3o2b3o9b3o9b3o9b3o$5bo4bobo2bo7bobobo7bobobo7bobobo18b2o$ob2ob5ob2ob2o7b2ob2o7b2ob2o7b2ob2o19bo$2obo5bob2o43b2obo3bob2o4bob2o$3bo13b2ob2o7b2ob2o7b2ob2o7b2ob2ob5ob2ob2obo2bo$3b2o12bobobo7bobobo7bobobo7bo2bobo5bobo2bob2o$18b3o9b3o9b3o9b3o2b5o2b3o$23b2ob2o7b2ob2o7b2ob2o5b2o5b2o$20b4obob4ob4obob4ob4obob4o2bo2bo2bo2bo$20bo4bo4bobo4bo4bobo4bo4bo4b2o3b2o$23b2ob2o7b2ob2o7b2ob2o$24bobo9bobo9bobo$24bobo9bobo9bobo$25bo11bo11bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 HEIGHT 585 ZOOM 8 GPS 2 STARTFROM 6 AUTOSTART ]]
Showing two different end stabilisations
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Catagoluehere

Oscillators sharing its stator

A 37-cell glide-symmetric period-16 oscillator bearing all stator cells of a lone sombrero except the two at the ends of the eaters' tails was found by Dean Hickerson in 1997 or 1998.[6]

x = 11, y = 13, rule = B3/S23 2o$o5b2o$b3obobo$3bobo$5bobo$4b2ob3o$4b2o4bo$4bo2b3o$5bobo$3bobo$b3obobo$o5b2o$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 HEIGHT 560 ZOOM 36 GPS 3 AUTOSTART ]]
(click above to open LifeViewer)
Catagoluehere

In other rules

A lone sombrero[7] would function as a period-6 pipsquirter if not for the births triggered by the b3q and b3y transitions when the edges have not receded in the phase of the domino's appearance. However, interestingly, when only b3q is removed (for the rule called qlife), it becomes a period-9 pipsquirter[c 2] with a single cell of additional clearance.

x = 8, y = 11, rule = B3-q/S23 3b2o$2bobo$2bo$b2obo$o3b3o$ob2o3bo$o3b3o$b2obo$2bo$2bobo$3b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 600 THUMBSIZE 3 ZOOM 36 X -3/2 GPS 3 AUTOSTART ]]
qlife p9 sombrero
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Catagoluehere

References

  1. Robert Wainwright (March 1973). Lifeline, vol 9, page 3.
  2. Dean Hickerson's oscillator stamp collection. Retrieved on March 14, 2020.
  3. goldenratio (October 3, 2020). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  4. 4.0 4.1 toroidalet (November 19th, 2016). Re: Oscillator Discoveries Thread (discussion thread) at the ConwayLife.com forums
  5. 5.0 5.1 BlinkerSpawn (November 19th, 2016). Re: Oscillator Discoveries Thread (discussion thread) at the ConwayLife.com forums
  6. Dean Hickerson's "New billiard tables" oscillator collection
  7. Headerless RLE: 3b2ob2o$b3o3b3o$o4bo4bo$2ob2ob2ob2o$4bobo$4bobo$5bo!
Adam P. Goucher's Catagolue

External links