User:Apple Bottom/Incubator/Swedish notation: Difference between revisions
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'''Swedish notation'''{{refn|group=note|The name "Swedish notation" refers to the use of "vänster" and "höger" for the backward diagonal compass directions, but is also a pun on "Polish notation".}} is a system for encoding [[non-isotropic Life-like cellular automaton|non-isotropic Life-like cellular automata]] in a manner that is more intuitive than [[MAP string]]s.<ref name="post51158" /> | '''Swedish notation'''{{refn|group=note|The name "Swedish notation" refers to the use of "vänster" and "höger" for the backward diagonal compass directions, but is also a pun on "Polish notation" and "Hungarian notation".}} is a system for encoding [[non-isotropic Life-like cellular automaton|non-isotropic Life-like cellular automata]] in a manner that is more intuitive than [[MAP string]]s.<ref name="post51158" /> | ||
Swedish notation assigns a single letter to each of the eight major compass directions, as follows; "vänster" and "höger" are Swedish for "left" and "right": | Swedish notation assigns a single letter to each of the eight major compass directions, as follows; "vänster" and "höger" are Swedish for "left" and "right": | ||
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|} | |} | ||
Each possible neighborhood configuration with ''n'' < 5 live cells is represented as a group of letters indicating which cells are live (in any order); for ''n'' ≥ 5 live cells, the dead cells | Each possible neighborhood configuration with ''n'' < 5 live cells is represented as a group of letters indicating which cells are live (in any order); for ''n'' ≥ 5 live cells, the letters instead represent the dead cells, to keep the overall notation shorter and more intuitively understood. For example: | ||
{| style="margin-left: auto; margin-right: auto;" | {| style="margin-left: auto; margin-right: auto;" | ||
|- | |- | ||
| [[File: | | [[File:INT Moore R1 2a.png]] | ||
| [[File: | | [[File:INT Moore R1 2a rotated.png]] | ||
| [[File: | | [[File:INT Moore R1 3k.png]] | ||
| [[File: | | [[File:INT Moore R1 5a.png]] | ||
| [[File: | | [[File:INT Moore R1 6c.png]] | ||
| [[File: | | [[File:INT Moore R1 7c.png]] | ||
|- | |- | ||
| align="center" | 2(ln) | | align="center" | 2(ln) | ||
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{| style="margin-left: auto; margin-right: auto;" | {| style="margin-left: auto; margin-right: auto;" | ||
|- | |- | ||
| [[File: | | [[File:INT Moore R1 2a.png]] | ||
| [[File: | | [[File:INT Moore R1 2a rotated.png]] | ||
| [[File: | | [[File:INT Moore R1 3k.png]] | ||
| [[File: | | [[File:INT Moore R1 5a.png]] | ||
| [[File: | | [[File:INT Moore R1 6c.png]] | ||
| [[File: | | [[File:INT Moore R1 7c.png]] | ||
|- | |- | ||
| align="center" colspan="6" | B2(ln,re)3(wnh)5(lnw)7(l) | | align="center" colspan="6" | B2(ln,re)3(wnh)5(lnw)6(lr)7(l) | ||
|} | |} | ||
As with [[Hensel notation]] for isotropic [[non-totalistic Life-like cellular automaton|non-totalistic Life-like cellular automata]], conditions can be negated by prefixing them with a minus sign. For example, a cellular automaton in which dead cells get born if they have two live neighbors, ''unless'' those neighbors happen to be located southeast (h) and north (n) of a cell, would include "B2(-hn)" as part of its rulestring in Swedish notation. | As with [[Hensel notation]] for isotropic [[non-totalistic Life-like cellular automaton|non-totalistic Life-like cellular automata]], conditions can be negated by prefixing them with a minus sign. For example, a cellular automaton in which dead cells get born if they have two live neighbors, ''unless'' those neighbors happen to be located southeast (h) and north (n) of a cell, would include "B2(-hn)" as part of its rulestring in Swedish notation. | ||
==Comparison to MAP strings== | If ''all'' possible neighborhood configurations lead to the birth or survival of a cell, they do need to be listed individually; for example, "B1" is equivalent to "B1(l,n,r,w,e,v,s,h)". | ||
== Comparison to MAP strings == | |||
Swedish notation rulestrings are, on average, longer than the MAP strings describing the same cellular automata, but can be understood, created and read more easily than MAP strings by humans. | Swedish notation rulestrings are, on average, longer than the MAP strings describing the same cellular automata, but can be understood, created and read more easily than MAP strings by humans. | ||
== | == See also == | ||
* [[Rulestring]] | * [[Rulestring]] | ||
==Notes== | == Notes == | ||
<references group="note" /> | <references group="note" /> | ||
==References== | == References == | ||
<references> | <references> | ||
<ref name="post51158">{{LinkForumThread | <ref name="post51158">{{LinkForumThread | ||
Latest revision as of 08:33, 8 January 2022
Swedish notation[note 1] is a system for encoding non-isotropic Life-like cellular automata in a manner that is more intuitive than MAP strings.[1]
Swedish notation assigns a single letter to each of the eight major compass directions, as follows; "vänster" and "höger" are Swedish for "left" and "right":
| l (left) |
n (north) |
r (right) |
| w (west) |
— | e (east) |
| v (vänster) |
s (south) |
h (höger) |
Each possible neighborhood configuration with n < 5 live cells is represented as a group of letters indicating which cells are live (in any order); for n ≥ 5 live cells, the letters instead represent the dead cells, to keep the overall notation shorter and more intuitively understood. For example:
|
|
|
|
|
|
| 2(ln) | 2(re) | 3(wnh) | 5(lnw) | 6(lr) | 7(l) |
Different neighborhood configurations with the same number n of live cells are separated with commas and grouped along with the respective birth (Bn) or survival (Sn) condition:
|
|
|
|
|
|
|
| B2(ln,re)3(wnh)5(lnw)6(lr)7(l) | |||||
As with Hensel notation for isotropic non-totalistic Life-like cellular automata, conditions can be negated by prefixing them with a minus sign. For example, a cellular automaton in which dead cells get born if they have two live neighbors, unless those neighbors happen to be located southeast (h) and north (n) of a cell, would include "B2(-hn)" as part of its rulestring in Swedish notation.
If all possible neighborhood configurations lead to the birth or survival of a cell, they do need to be listed individually; for example, "B1" is equivalent to "B1(l,n,r,w,e,v,s,h)".
Comparison to MAP strings
Swedish notation rulestrings are, on average, longer than the MAP strings describing the same cellular automata, but can be understood, created and read more easily than MAP strings by humans.
See also
Notes
- ↑ The name "Swedish notation" refers to the use of "vänster" and "höger" for the backward diagonal compass directions, but is also a pun on "Polish notation" and "Hungarian notation".
References
- ↑ Apple Bottom. Re: Thread for basic questions (discussion thread) at the ConwayLife.com forums