OCA:FireWorld

FireWorld
x=64, y = 64, rule =03ajkr/2ak/3 ! #C [[ THEME Generations ]] #C [[ RANDOMIZE2 RANDSEED 1729 THUMBLAUNCH THUMBNAIL THUMBSIZE 2 GRID ZOOM 6 WIDTH 600 HEIGHT 600 LABEL 90 -20 2 "#G" AUTOSTART PAUSE 2 GPS 8 LOOP 256 ]] LifeViewer-generated pseudorandom soup
Rulestring	03ajkr/2ak/3 B2ak/S03ajkr/C3 B2ak/S03ajkr/G3
Character	Chaotic

FireWorld is a rule created in 2020 by Yoel Matveyev. Fireworld operates in the Moore neighborhood. Cells may have 4 states: empty, alive, dead and wire.

It's based on the older rule, which Matveyev discovered and started researching in 2001 and which he later nicknamed, somewhat confusingly, Fireworld with the small "w". Its rulestring is "03ajkr/2ak/3". That means the following:

• An empty cell becomes alive only if it is surrounded by one live cell horizontally or vertically adjacent to it, while one other cell is adjacent to it diagonally.
• A live cell survives either if there are no other live cells in its neighborhood or there are exactly three live cells adjacent to it in a particular way: two adjacent orthogonally (horizontally or vertically), while the third one is adjacent diagonally.
• Dead cells count as empty and do not interfere with birth or survival if they are present in the neighborhood. However, they do prevent a cell being born in their place, as usual in the "Generations" rules.
• A dead cell becomes empty in the next generation.

Due to a simple reaction that allows to use single dots as stable data bits and photons as data carriers, this rule allows relatively easy logic circuitry construction and was proven by Matveyev in 2020 to be Turing-complete .

For more concise and faster logic circuitry, Matveyev invented a backward compatible superset of the original rule called FireWorld with the capital "W". It has the fourth state of immutable wires. Unlike the well known WireWorld, signals in FireWorld can be carried on the wires' surface, according to the following additional definition:

• A live cell is born, if surrounded by 1 live cell or two live cells in either "2a" or "2k" position, and 2 or 3 wire cells. Dead cells are allowed in the neighborhood.

That means that in in order for 2 live cells to give birth next to 2 or 3 wire cells, one live cell must be in an orthogonal and the another one in a diagonal position. That matches the original pattern of "03ajkr/2ak/3".

Unlike WireWorld, which can only use unstable logic, FireWorld can use dots as stable data, which turned out to be very useful for registers and data manipulation, largely eliminating synchronization issues and thus allowing scalable modular "hardware" architecture. Within a year after inventing the rule, Yoel Matveyev had built a large computer in it, called Izhora .

See also

• Izhora