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Neutronium, in the context of multi-state Life-like cellular automata, refers to an additional cell state that is permanently live. A cell in the "neutronium" state is also said to be neutronic. Informally, the term may also be used to refer to anti-neutronium: a cell that is permanently dead.

The Neutronium rule

Neutronium was first considered by Mike Turniansky for a rule of the same name[1]. In this rule, cells can exist in three states, dead, live and neutronium, the last of which is considered "live"; evolution happens as in Conway's Game of Life, except that a live cell surrounded by eight live neighbors (including neutronic neighbors) will itself turn into neutronium.

More precisely, patterns in this CA evolve according to the following rules:

  1. A dead cell:
    1. is born if it has precisely 5 dead neighbors (i.e. precisely 3 neighbors each of which is either live or neutronic).
  2. A live cell:
    1. turns into neutronium if it has precisely 0 dead neighbors;
    2. survives (remains live) if it otherwise has has precisely 5 or 6 dead neighbors;
    3. dies otherwise.
  3. A neutronic cell:
    1. remains neutronic.

Many small patterns evolve the same in Neutronium as they do in Conway's Game of Life; however, the HWSS is unstable, due to a neutronium cell forming, and the R-pentomino explodes:

Generalizations and variants

Neutronium can be generalized in a straightforward manner to outer-totalistic rules other than Conway's Game of Life (B3/S23). Variants of the rule were created by 'c0b0p0' and Alexey Nigin.

Also see


  1. Mike Turniansky (March 10, 2014). R-pentomino neutronium (discussion thread) at the forums