Regenerative loop

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The regenerative loop is a loop-like motif found in some stable catalysts that, when perturbed in a certain way, hits a block to produce a grin and then restores itself.

Pi splitter

Pi splitter is a representative elementary converter with a regenerative loop motif. It was originally found by Ivan Fomichev with Bellman in August 2013[1] and subsequently reduced by Martin Grant. It is a constellation consisting of a block and an unnamed 27-cell still life. Its name originates from the fact that a pi-heptomino can be split into two gliders in a reaction shown to the left, with systematic label PNE−6T40_SE−6T40.

Later this catalyst is generalized to a replacement catalyst for the tub when it is turned into a certain block predecessor. Shown to the right below are two example catalyses; the first was used in both a period-36 honey farm hassler and an alternative G4 receiver, while the second was used in a variant of p124 lumps of muck hassler. However, both oscillators can be reduced with other catalysts.

x = 20, y = 14, rule = B3/S23 15bo$14bobo$14bobo$13b2ob2o$12bo2bo2bo$3o8bobobobobo$2bo9bobobobo$3o 11bobo$14bo2bo$15b2o3$14b2o$14b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 16 HEIGHT 600 GPS 8 LOOP 61 AUTOSTART PAUSE 2 T 60 PAUSE 2 ]]
Original pi-splitting reaction

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RLE: here Plaintext: here
x = 34, y = 39, rule = B3/S23 27b2o$26b2o$25b2o$bo5bo2$2b2ob2o$4bo3$5bo19bo$4bobo17bobo$5bo19bo10$27b2o$26b2o$25b2o$bo5bo2$2b2ob2o$4bo3$5bo19bo$4bobo17bobo$3bobo17bobo$b3o2b3o3b2o7b3o2b3o3b2o$o3b2o3bo2b2o6bo3b2o3bo2b2o$b3o2b2obo11b3o2b2obo$3bobo2bo14bobo2bo$4bobo17bobo$5bo19bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 12 Y -4 HEIGHT 600 GPS 8 LOOP 30 AUTOSTART PAUSE 2 ]]
Tub replacement catalyses

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RLE: here Plaintext: here

xs14_31egm93 and block

The regenerative loop can also be activated by other reactions not starting from a (failed) tub reaction, and in this case, the smallest working object with the motif is an unnamed 14-cell still life. By inducing the birth of a cell, the nine becomes a bookend and proceeds.

The first panel below shows how the catalyst can be hassled by a spark, the second shows a random active region perturbed by the catalyst, and the third shows a glider eater that is recorded in Dean Hickerson's 1998 eater stamp collection and has a recovery time of 10 ticks.[2]

x = 19, y = 22, rule = B3/S23 6b2o$6bobo3b2o3b2o$8bo3bobobobo$3bo2bob2o4bobo$3b4o7bo2bo$7b2o2b2o2b2o $3b4o$obo3bob2o$2ob2obobo5b2o$3bo4bo5b2o$3bobobob2o$2obobobobo$obo4bob o$2bob2obo2b2o$2bobo3bobo$b2o2bob2obo$2bobo4bo$2bo3b3o$3b2obo$8b3o$b7o 2bo$bo2bo2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 16 HEIGHT 600 AUTOSTART GPS 7 PAUSE 2 LOOP 28 ]]
p7 pipsquirter interacting with a regenerative loop

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RLE: here Plaintext: here
x = 14, y = 14, rule = B3/S23 2bo$o$2b3o$3b3o$o4bo$2b2o3b2o3b2o$2bo4bobobobo$9bobo$9bo2bo$10b2o3$9b2o$9b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 16 HEIGHT 600 ]]
A complex regenerative loop catalysis

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RLE: here Plaintext: here
x = 17, y = 18, rule = B3/S23 bo$2bo$3o2$5bo$3bobo$4b2o$8bo$9bo2b2o$7b3o3bo$13bob2o$10b2obo2bo$11bob 2o$3b2o3b3o$3b2o2bo$7bob2o$8bo2bo$10b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 32 HEIGHT 600 AUTOSTART GPS 7 PAUSE 2 T 4 PAUSE 2 LOOP 42 ]]
A regenerative loop in a glider eater

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RLE: here Plaintext: here

References

  1. Ivan Fomichev (August 7, 2013). Pi splitter (discussion thread) at the ConwayLife.com forums
  2. Dean Hickerson. "Glider eaters". Dean Hickerson's Game of Life page. Retrieved on February 20, 2022.

External links