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), 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 eventually becomes periodic (specifically period-1 vacuum, albeit incredibly slowly). The block remains untouched for about 363 generations. It deletes its nth glider (and is shifted) at about generation 357.5+5.5n.[1]

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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A space nonfiller is also capable of touching every cell in the plane at least once and making them eventually OFF (period-1 vacuum)

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External links