Total aperiodic

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Total aperiodic
x = 59, y = 57, rule = B3/S23 41bo$40b3o$39b2obo5bo$39b3o5b3o$40b2o4bo2b2o3b3o$46b3o4bo2bo$56bo$56bo $56bo$40b3o12bo$40bo2bo$40bo$40bo$41bo7$38b3o$38bo2bo11bo$38bo13b3o$ 38bo12b2obo$38bo12b3o$39bo12b2o3$35b3o$34b5o$34b3ob2o7b2o5bo2bo$37b2o 7b4o8bo$46b2ob2o3bo3bo$48b2o5b4o3$20bo$21bo$b2o13bo4bo32b3o$4o13b5o34b o$2ob2o51bo$2b2o51bo$36bo$37bo$21b2o10bo3bo$22b2o10b4o15b2o$21b2o27b3o b2o$21bo28b5o$51b3o2$22b2o$13b4o4b4o$12bo3bo4b2ob2o$b5o10bo6b2o$o4bo9b o$5bo$4bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 8 WIDTH 500 HEIGHT 500 ]]
Pattern type Miscellaneous
Number of cells 182
Bounding box 59 × 57
Discovered by Bill Gosper
Year of discovery 1997

A finite pattern is total aperiodic if it evolves in such a way that no cell in the plane is eventually periodic.

The first example was found by Bill Gosper on November 16, 1997. A few days later, on November 19, he found the much smaller example that consists of three copies of backrake 2 (by David Buckingham),[1] shown in the infobox. Two of the rakes release southwestbound gliders, which perform 90-degree kickbacks to the northwestbound outputs from the third rake. As each kickback happens farther away from the last one and shifts the central glider by one half-diagonal southwestwards, any cell in the plane will be covered by infinitely many gliders on their aperiodic lanes.

On June 24, 2004, Gosper found that a block can be added to the pattern to make the total periodic pattern shown below, in which every cell in the plane will eventually die and stay dead, albeit incredibly slowly. The block remains untouched for about 363 generations. It deletes the nth glider (and is shifted) at about generation 357.5+5.5n.[2]

x = 60, y = 59, rule = b3/s23 40b3o17b$39bo2bo17b$42bo4b3o10b$42bo4bo2bo4bo4b$39bobo4bo3bo3b3o3b$46b 4o4bob2o2b$47bo7b3o2b$55b3o2b$41bo13b2o3b$40b3o17b$39b2obo17b$39b3o18b $40b2o18b7$39bo20b$38b3o19b$37b2obo11b3o5b$37b3o11bo2bo5b$37b3o14bo5b$ 38b2o14bo5b$51bobo6b3$38bo21b$39bo20b$34bo4bo9bo10b$35b5o10bo6b2ob$46b o3bo4b2ob2o$47b4o4b4ob$56b2o2b3$55bo4b$55b2o3b$56b2o2b$23b2o30b2o3b$3b o2bo13b3ob2o34b$7bo12b5o35b$3bo3bo13b3o12b2o22b$4b4o26b2ob2o21b$34b4o 13b5o4b$35b2o13bo4bo4b$24b3o28bo4b$26bo27bo5b$24bobo33b$24b2o34b3$17b 2o5bo2bo32b$16b4o8bo31b$5b3o8b2ob2o3bo3bo31b$2o2b5o9b2o5b4o31b$2o2b3ob 2o50b$7b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 WIDTH 500 HEIGHT 500 ]]
Total periodic
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RLE: here Plaintext: here

A space nonfiller is also capable of touching every cell in the plane at least once and making them eventually OFF.


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