p5760 unit Life cell

p5760 unit Life cell
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Pattern type	Unit cell
Number of cells	4761
Bounding box	499 × 499
Cell size	500 × 500
Period	5760
Discovered by	David Bell
Year of discovery	1996
Rules Outer-totalistic rules B3/S23 only # of rules 20 = 1 Isotropic rules B3/S23 only
Pattern files Plaintext p5760unitlifecell.cells RLE p5760unitlifecell.rle

The p5760 unit Life cell is the first unit Life cell that was explicitly constructed, and it was finished on January 18, 1996 by David Bell. It is a 500 × 500 square that takes 5760 generations to emulate the behavior of one Life cell.

The existence of this unit cell implies the existence of an infinite number of unit cells, of period 5760ⁿ and size 500ⁿ × 500ⁿ (here n = 1, of course). In practice, this cell is terribly slow, and would still be just an interesting curiosity even if it were fast.

The state is determined by the presence or absence of a glider at every multiple of 5760 generations, in a space in the upper left quadrant that is marked by two long boats. Long boats are also pointing at the corners of the pattern, to aid alignment with other unit cells.

The presence or absence of a glider at the green circle determines whether or not the unit Life cell is considered "dead" or "alive".

In November 2020, Peter Naszvadi created a custom 10-state ruletable to visualize this unit cell. Besides the state-1 cells that act as in normal Life, each unit cell in this rule has a state-4 cell lying between the two long boats mentioned above. When the glider that represents state passes by, it triggers an explosion cloud in state 6 and 7 that grows quickly, thus visualizing the emulated pattern at a larger, more observable scale.

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3bo290b3o$111b3o291b3o$109b2o3b2o288bo3bo$403bo5bo2b2o$79b2o294b2o27bo 3bo3b2o$79b2o294b2o28b3o$378b2o$66b2o31b2o277b3o5b2o$66b2o14bo14bo3bo 276b2o6b2o$81bo9b2o3bo5bo265b2o5b2o$81bo9b2o2b2obo3bo264bobo5b2o35b3o$ 96bo5bo264bo14b2o27b2ob2o$97bo3bo264b2o12bo3bo11bo14b2ob2o$77b2o3b2o2b o12b2o273b2o3bo5bo9bobo13b5o$80bo5b3o285b2o2b2obo3bo10b2o12b2o3b2o$77b o5bo5bo23b2o264bo5bo20b2o$78b2ob2o5b2o23b2o265bo3bo21b2o$65b3o11bobo 300b2o42bo$64bo3bo11bo344bobo$63bo5bo10bo344b2obo4b2o$63bo5bo355b2ob2o 3b2o$66bo358b2obo$64bo3bo21b3o27bobo267b3o32bobo$65b3o21bo3bo26bo3bo 264bo3bo32bo$66bo21bo5bo29bo287bo$76bobo9b2obob2o15b2o8bo4bo262bo5bo 16bobo$76b2o32b2o12bo263b2o3b2o17b2o$63b3o11bo3b3o36bo3bo3b2o$63b3o14b o3bo6bo28bobo5bobo$62bo3bo12bo5bo4bobo18b2o17bo260bo26b2o$70bobo6b2obo b2o4bobo9b2o7bo2bo15b2o258bobo25bobo$61b2o3b2o3b2o18bo9b3o11bo6b2o266b obo25bo$71bo30bob2o9bo6b2o268bo12b2o5bo$90b2o23bo276bo11b3o3bo3bo$90b 2o13bo5bo2bo274bo2bo8bob2o5bo$111b2o182bo94b2o9bo2bo4bo5bo$84b2o18bo 188b3o105bob2o9b2o$84bo20bo186bo103b2o6b3o11bo$85b3o17bo186b2o101bobo 7b2o11b3o$66b2o19bo307bo25bo$66bo327b2o24b2o$67b3o$69bo33b2o3b2o179b3o $104b5o179b2ob2o$104b2ob2o179b2ob2o16bo$73bo2b2o15bobo8b2ob2o179b5o14b 3o$72bo3b2o2b2o11bo2bo8b3o179b2o3b2o12bo114b2o$72bo7b2o14b2o208b2o109b 2o2b2o$73b4o17bo3b2o187b2o15b3o110b2o$96b2o190b2o13bobo$85b2o6bo2bo5b 2o4b2o175b2ob2o12bo3bo$84bobo6bobo6bobo3bo193b5o145b2o$84bo19bo4b3o 180b2o7b2o3b2o112b2o18b3o2bo5bo3bo$83b2o19b2o5bo173bo8bo7b5o114b2o13bo 3bo9bo5bo3b2o$287b2obobo10b3o104bo9bo13bobo4bo8bo3bob2o2b2o$304bo105bo bo19b2o16bo5bo$398b2o11bobo9b2o7b2o17bo3bo$299b2o97b2o11bo2bo7b3o7b2o 18b2o$299bobo109bobo5bob2o5b2o4bobo$299bo110bobo6bo2bo4bo2bo5bo$287b3o 120bo8bob2o5b2o$208bo77bo3bo131b3o$203bo4b4o73bo5bo131b2o$203bo5b4o73b o3bo$198b2o9bo2bo74b3o$198b2o9b4o74b3o$208b4o5b2o82b3o$208bo8bobo70b2o 8bo3bo$219bo70bo$219b2o70b3o5bo5bo$293bo5b2o3b2o3$302bo$301bobo$301bob o$303bo$303bo$300bo2bo$301b2o10$2bo493bo$bobo491bobo$obo493bobo$2o495b 2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 1100 WIDTH 1100 THUMBSIZE 2 ZOOM 2 ]]

The pattern (click above to open LifeViewer) RLE: here Plaintext: here

Videos

Click to load content The ON unit cell evolving for 5760 generations into the OFF unit cell

See also

• Deep cell
• OTCA metapixel

External links

• David Bell's Unit Life Cell at Paul Callahan's Page of Conway's Life Miscellany