User:Haycat2009/Incubator/Durnak notation
- Not to be confused with Durnak-Cole notation
Durnak notation is a system for encoding anisotropic cellular automata in a manner that is more intuitive and concise than MAP strings.
Durnak notation is an extension of Hensel notation that assigns additional letters depending on the direction. For conditions involving 1-4 cells, this chart is used. For those involving 5-7 cells, the black/white reversal of each condition is used. Note that 0, 4c, 4e and 8 have no directions.
Letter List
Letters used in asymmetric conditions:
- u, where the heavy part is pointing up and in the clockwise direction (Up)
- d, where the heavy part is pointing down and in the clockwise direction (Down)
- L, where the heavy part is pointing left and in the clockwise direction (Left)
- s, where the heavy part is pointing right and in the clockwise direction (Starboard, r is already used)
- v, where the heavy part is pointing left and in the anticlockwise direction (Vanster)
- h, where the heavy part is pointing right and in the anticlockwise direction (Hoger)
- b, where the heavy part is pointing down and in the anticlockwise direction (Backwards)
- x, where the heavy part is pointing up and in the anticlockwise direction (Flip, as in Fx)
Letters used in bilaterally symmetrical conditions: (1c, 1e, 2c, 2e, 3c, 3e, 3k, 3a, 3y, 4i, 4q, 4w, 4t)
- u, where the heavy part is pointing up/up and left (Up)
- d, where the heavy part is pointing down/down and right (Down)
- L, where the heavy part is pointing left/down and left (Left)
- s, where the heavy part is pointing right/up and right (Starboard, r is already used)
Letters used in 2-way rotational symmetrical conditions: (4z only, prove me wrong)
- u, where the heavy parts are pointing up and in the clockwise direction, as well as pointing right and in the clockwise direction (Up)
- x, where the heavy parts are pointing up and in the anticlockwise direction, as well as pointing down and in the anticlockwise direction (Flip, as in Fx)
- L, where the heavy parts are pointing left and in the clockwise direction, as well as pointing right and in the clockwise direction (Left)
- v, where the heavy parts are pointing left and in the anticlockwise direction as well as pointing right and in the anticlockwise direction (Vanster)
Letters used in 4-way symmetrical conditions: (2i, 2n)
- u, where the heavy part is pointing up/up and left as well as down and right (Up)
- L, where the heavy part is pointing left/down and left as well as right/up and right (Left)
Note that nonexistent letters are simply ignored.
Negation
Conditions can also be negated with the - sign, as in Hensel notation. For instance, the transition B2a-u means all B2a except where the heavy part is pointing up and in the clockwise direction. (a-u is parsed first).
B3-u means all B3 conditions except where the heavy part is pointing up and in the clockwise direction.
As a-u is parsed first, B2-a-u can be converted to and intepreted as B2au.
In B3aiu for instance, it means the transitions B3a in any direction, and B3i only in the u direction.
Comparison to MAP strings
Durnak notation rulestrings are, on average, considerable shorter than the MAP strings describing the same cellular automata, and can be understood, created and read much more easily than MAP strings by humans.
Example
| Gallery of transitions of various types. (click above to open LifeViewer) |
See also
Notes
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