Octohash database

The octohash function is a hash function that returns the same value for any of the eight orientations of a pattern -- in other words, the octohash of any rotation or reflection of a pattern will always be the same as the octohash of the original pattern.

Several databases implemented using the octohash function can be used to search for active reactions that produce a given pattern (which may be active or settled). The databases are designed to work with Golly and Python, without other dependencies.

x = 79, y = 25, rule = B3/S23 10bo$9bobo$8bo2bo$9b2o6$74bo$75b2o$29bo24bo19b2o$28bobo22bobo$29bobo 22bobo$24b2o4b2o17b2o4b2o17b2o$23bo2bo21bo2bo21bobo$24b2o23b2o24bo$2b 3o2$o5bo$o5bo31bo$o5bo30b2o23b2o$37bobo21b2o13b3o$2b3o58bo14bo$77bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME Book ZOOM 6 X 4 Y 0 AUTOSTART GPS 12 T 0 PAUSE 5 T 22 PAUSE 3 T 119 PAUSE 2 LOOP 120 ]] For a TL+loaf constellation (left), the octohash database has two matches (middle), the octo3g database has one match (right), and the octo3obj database has 56 matches (not shown) (click above to open LifeViewer)

x = 27, y = 22, rule = B3/S23 7$10b2o$10b2o2$5b2o$4bobo3b2o6b2o$6bo3b2o2b2o2b2o$14b2o2$11b2o$11b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME Book ZOOM 16 X 2 Y 4 AUTOSTART GPS 12 T 0 PAUSE 3 T 22 PAUSE 3 T 44 PAUSE 2 LOOP 45 ]] For a pattern consisting of a Herschel and a block, the octo3obj database has one match, with a glider hitting a constellation made of two half blockades and one other block (click above to open LifeViewer)

The octohash database, published in August 2020, catalogues generations of 455380 collisions between a single glider and all possible constellations of up to two well-separated objects (excluding pseudo still lifes) fitting inside a 12 × 12 bounding box; the included objects are block, tub, boat, beehive, ship, loaf, eater, pond, long boat, and blinker.

The octo3obj database, finished in June 2022, catalogues generations of 3421907 collisions between a single glider and all possible constellations of up to three well-separated patterns fitting inside an 11 × 11 bounding box; the included objects and constellations are blinker, block, beehive, bi-block, half blockade, and teardrop ash (two beehives).

The octo3g database, completed in August 2022, catalogues generations of 464746 collisions in a subset of three-glider collisions, making it possible to search 3G collisions in the same way as active patterns in the previous octo3obj and octohash databases.

See also

• Tutorials/Glider syntheses
• Tutorials/Catagolue stdin symmetry