Object: Difference between revisions
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* A [[cluster]] of adjacent living [[cell]]s (e.g. [[block]], [[tub]], [[beacon]], [[glider]]) | * A [[cluster]] of adjacent living [[cell]]s (e.g. [[block]], [[tub]], [[beacon]], [[glider]]) | ||
* Two objects close to each other in such a way that they suppress one or more births that would occur if they were separated (e.g. [[aircraft carrier]]) | * Two objects close to each other in such a way that they suppress one or more births that would occur if they were separated (e.g. [[aircraft carrier]]) | ||
* [[Still-life]]s are non-moving objects with a period of one. [[Oscillators]] are non-moving objects with a period greater than one. [[Spaceships]] are moving periodic objects. | * Two periodic objects that interact as described above in at least one of their phases (e.g. beacon, two [[pentadecathlon]]s [[shuttle|shuttling]] a glider) | ||
[[Still-life]]s are non-moving objects with a period of one. [[Oscillators]] are non-moving objects with a period greater than one. [[Spaceships]] are moving periodic objects. | |||
Note that the word ''object'' is often use informally to mean a generic ''thing''. The above formal definition is most useful when distinguishing among objects, pseudo-objects and quasi-objects. | Note that the word ''object'' is often use informally to mean a generic ''thing''. The above formal definition is most useful when distinguishing among objects, pseudo-objects and quasi-objects. | ||
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A pseudo object is formed when two or more objects and/or pseudo-objects are close to each other in such a way that adjacent empty cells do not change their behaviors, but the reason births do not form is due to over-population rather than under-population, and there is at least one way that the clusters can be partitioned into disjoint sets that operate the same way (e.g. bi-block that can be partitioned into two blocks). | A pseudo object is formed when two or more objects and/or pseudo-objects are close to each other in such a way that adjacent empty cells do not change their behaviors, but the reason births do not form is due to over-population rather than under-population, and there is at least one way that the clusters can be partitioned into disjoint sets that operate the same way (e.g. bi-block that can be partitioned into two blocks). | ||
In most cases, this partitioning can be done into two sets, but there have been examples found that require three or even four sets (four is the maximum, given the 4-color map theorem). | In most cases, this partitioning can be done into two sets, but there have been examples found that require [[Triple pseudo still life|three]] or even [[Quad pseudo still life|four]] sets (four is the maximum, given the 4-color map theorem). | ||
Note that objects can fit this definition, but they are generally classed separately, in the same way that still-lifes are technically trivial period-1 oscillators but are not generally classified as such. | Note that objects can fit this definition, but they are generally classed separately, in the same way that still-lifes are technically trivial period-1 oscillators but are not generally classified as such. | ||
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|position = center | |position = center | ||
|viewerconfig = #C [[ THUMBSIZE 2 ]] | |viewerconfig = #C [[ THUMBSIZE 2 ]] | ||
|caption = The two [[pre-block]]s that form an aircraft carrier<br/>suppress the birth of the | |caption = The two [[pre-block]]s that form an aircraft carrier<br/>suppress the birth of the cells between them<br/> | ||
|apgcode = xs6_39c | |||
}} | }} | ||
|{{EmbedViewer | |{{EmbedViewer | ||
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|viewerconfig = #C [[ THUMBSIZE 2 AUTOSTART GPS 2 ]] | |viewerconfig = #C [[ THUMBSIZE 2 AUTOSTART GPS 2 ]] | ||
|caption = The two parts of a beacon suppress the birth<br/>of the cells between them every other tick<br/> | |caption = The two parts of a beacon suppress the birth<br/>of the cells between them every other tick<br/> | ||
|apgcode = xp2_318c | |||
}} | }} | ||
|{{EmbedViewer | |{{EmbedViewer | ||
| Line 42: | Line 46: | ||
|position = center | |position = center | ||
|viewerconfig = #C [[ THUMBSIZE 2 AUTOSTART GPS 2 ]] | |viewerconfig = #C [[ THUMBSIZE 2 AUTOSTART GPS 2 ]] | ||
|caption = Two pentadecathlons<br/>shuttling a glider<br/> | |caption = [[p60 glider shuttle|Two pentadecathlons<br/>shuttling a glider]]<br/> | ||
|apgcode = xp60_vtvz757zac4zzzy0vtvzy0757 | |||
}} | }} | ||
|} | |} | ||
===Pseudo-objects=== | ===Pseudo-objects=== | ||
{| | {| | ||
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|viewerconfig = #C [[ THUMBSIZE 2 ]] | |viewerconfig = #C [[ THUMBSIZE 2 ]] | ||
|caption = A bi-block is a pseudo-still-life that<br/>can be partitioned into two block objects<br/> | |caption = A bi-block is a pseudo-still-life that<br/>can be partitioned into two block objects<br/> | ||
|apgcode = xs8_rr | |||
}} | }} | ||
|{{EmbedViewer | |{{EmbedViewer | ||
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|viewerconfig = #C [[ THUMBSIZE 2 AUTOSTART GPS 2 ]] | |viewerconfig = #C [[ THUMBSIZE 2 AUTOSTART GPS 2 ]] | ||
|caption = Beacon on block is a pseudo-oscillator that<br/>can be partitioned into a beacon and a block<br/> | |caption = Beacon on block is a pseudo-oscillator that<br/>can be partitioned into a beacon and a block<br/> | ||
|apgcode = xp2_rbzw23 | |||
}} | }} | ||
|{{EmbedViewer | |{{EmbedViewer | ||
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|viewerconfig = #C [[ THUMBSIZE 2 ]] | |viewerconfig = #C [[ THUMBSIZE 2 ]] | ||
|caption = LWSS on LWSS is a pseudo-spaceship<br/>that can be partitioned into two LWSSes<br/> | |caption = LWSS on LWSS is a pseudo-spaceship<br/>that can be partitioned into two LWSSes<br/> | ||
|apgcode = xq4_6frcxcrf6 | |||
}} | }} | ||
|} | |} | ||
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===Quasi-objects=== | ===Quasi-objects=== | ||
{| class="wikitable" | {| class="wikitable" | ||
| style="text-align:center" | [[File:Quasistilllife.png|200px]]<br>Quasi-still-life: 2 blocks sharing a dead cell<br>(yellow) that remains dead after separation | | style="text-align:center" | [[File:Quasistilllife.png|200px]]<br>Quasi-still-life: 2 blocks sharing a dead cell<br>(yellow) that remains dead after separation<br>'''[[Catagolue]]''': [https://catagolue.hatsya.com/object/xs8_330oo/b3s23 here] | ||
| {{EmbedViewer|pname=trafficlight||position=center|viewerconfig=#C [[ THUMBSIZE 2 AUTOSTART GPS 2 ]]|caption = [[Traffic light]] is a quasi-oscillator<br/>composed of four blinkers<br/> | | {{EmbedViewer|pname=trafficlight||position=center|viewerconfig=#C [[ THUMBSIZE 2 AUTOSTART GPS 2 ]]|caption = [[Traffic light]] is a quasi-oscillator<br/>composed of four blinkers<br/> | ||
|apgcode = xp2_s01110szw222 | |||
}} | }} | ||
|} | |} | ||
Latest revision as of 02:01, 1 August 2024
An object is formally defined as follows:[1]
- A cluster of adjacent living cells (e.g. block, tub, beacon, glider)
- Two objects close to each other in such a way that they suppress one or more births that would occur if they were separated (e.g. aircraft carrier)
- Two periodic objects that interact as described above in at least one of their phases (e.g. beacon, two pentadecathlons shuttling a glider)
Still-lifes are non-moving objects with a period of one. Oscillators are non-moving objects with a period greater than one. Spaceships are moving periodic objects.
Note that the word object is often use informally to mean a generic thing. The above formal definition is most useful when distinguishing among objects, pseudo-objects and quasi-objects.
Pseudo-object
A pseudo object is formed when two or more objects and/or pseudo-objects are close to each other in such a way that adjacent empty cells do not change their behaviors, but the reason births do not form is due to over-population rather than under-population, and there is at least one way that the clusters can be partitioned into disjoint sets that operate the same way (e.g. bi-block that can be partitioned into two blocks).
In most cases, this partitioning can be done into two sets, but there have been examples found that require three or even four sets (four is the maximum, given the 4-color map theorem).
Note that objects can fit this definition, but they are generally classed separately, in the same way that still-lifes are technically trivial period-1 oscillators but are not generally classified as such.
Pseudo-still-lifes, pseudo-oscillators, and pseudo-spaceships are pseudo-objects similar to the above (e.g. bi-block, beacon on block, LWSS-on-LWSS).
Quasi-object
A quasi-object is formed when two or more objects and/or pseudo-objects and/or or quasi-objects are close to each other in such a way that they share adjacent empty cells that remain empty when the parts are separated (e.g. two diagonally adjacent blocks).
Note that objects and pseudo-objects can fit this definition but are generally classed separately.
Quasi-still-lifes, quasi-oscillators and quasi-spaceships are quasi-objects similar to the above.
Gallery
Objects
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Pseudo-objects
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Quasi-objects
 Quasi-still-life: 2 blocks sharing a dead cell (yellow) that remains dead after separation Catagolue: here |
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References
- ↑ mniemiec (January 4, 2022). Re: Thread for Basic Questions (discussion thread) at the ConwayLife.com forums
External links
- Four color theorem at Wikipedia