Possible new type of category to define ships/oscillators?

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Gamedziner
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Possible new type of category to define ships/oscillators?

Post by Gamedziner » June 2nd, 2016, 1:03 pm

My idea is something I'd like to call periodic density.

Periodic density would be the ratio of the number of cells in an oscillator or spaceship to its period.
For example, a glider has 5 cells and a period of 4. The periodic density, then, would be 5/4, or 1.25.

The reason I want to define such a thing is that, as far as I can tell, people tend to get more excited over ships and oscillators that have a smaller periodic density. By making such a definition formalized, it could make communication of what is desired much easier.

Code: Select all

x = 81, y = 96, rule = LifeHistory
58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27.
A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A
$4.2A18$4.2A$4.2A2.2A$8.2A!

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Nathaniel
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Re: Possible new type of category to define ships/oscillators?

Post by Nathaniel » June 2nd, 2016, 3:49 pm

There are (reasonably) small oscillators with extremely high period. The following oscillator by Dave Greene has periodic density 1618/103079214841 = 0.0000000157, but isn't *that* interesting:

Code: Select all

x = 297, y = 227, rule = B3/S23
193b2o72b2o$193bo73bo$194bo73bo$182bo10b2o61bo10b2o$182b3o71b3o$185bo
73bo$172bo11b2o60bo11b2o$170b3o71b3o$169bo40bo32bo40bo$169b2o19b2o16b
3o32b2o37b3o$155b2o33b2o15bo21b2o50bo$156bo50b2o21bo50b2o$156bobo71bob
o$157b2o72b2o2$176b2o72b2o$176b2o72b2o6$173b2o36b2o34b2o36b2o$77b2o94b
o19b2o16bobo33bo19b2o16bobo$77b2o5b2o88b3o15bobo18bo34b3o15bobo18bo$
84b2o90bo15bo20b2o35bo15bo20b2o$48b2o97bob2o19b2o19b2o4b2o22bob2o19b2o
19b2o4b2o$49bo97b2obo19bo25bobo22b2obo19bo25bobo$36bo11bo14b2o17b2o87b
3o22bo48b3o22bo$36b3o9b2o14bo17b2o89bo21b2o7b2o41bo21b2o7b2o$39bo24bob
o21b2o114b2o72b2o$26b2o10b2o25b2o21b2o$27bo$27bobo$13b2o13b2o$13b2o36b
2o$51b2o$195bo18b2o53bo18b2o$7b2o140b2o43bobo17bo8b2o43bobo17bo$7b2o
139bobo44bo16bobo7bobo44bo16bobo$11b2o135bo63b2o8bo63b2o$11b2o134b2o
44b5o23b2o44b5o$192bo4bo68bo4bo$61b2o99b2o27bo2bo41b2o27bo2bo$42b2o18b
o28b2o69b2o24bo2bob2o41b2o24bo2bob2o$6b2o34bo16b3o29bo95bobobo5bo63bob
obo5bo$6b2o35b3o13bo29bobo77bob2o15bo2bo4bobo44bob2o15bo2bo4bobo$45bo
43b2o78b2obo18b2o2bo2bo44b2obo18b2o2bo2bo$26bo3b2o120b2o42b2o28b2o42b
2o$25bobo3bo120b2o72b2o$25b2o3bo111b2o72b2o$29bo113bo73bo$25b5obo111bo
bo71bobo$25bo4b2o112b2o72b2o$26b3o$9bo18bob2o$7b3o19bobo$6bo$6b2o186b
2o16b2o54b2o16b2o$9b2o77b2o104b2o16b2o54b2o16b2o$4b5obo61b2o14b2o$4bo
21b2o45bo22b2o$6bob2o16bobo41b3o23bo51b2o72b2o$5b2ob2o18bo41bo23bobo
50bobo39b2o30bobo39b2o$28b2o64b2o51bo42bo30bo42bo$20b2o124b2o42bobo27b
2o42bobo$20b2o169b2o72b2o$200b2o72b2o$4b2o70bo123b2o72b2o$4b2o70b3o$
79bo$78b2o83b2o72b2o$163b2o72b2o$154b2o72b2o$153bobo27b2o42bobo27b2o$
153bo30bo42bo30bo$152b2o30bobo39b2o30bobo$96b2o87b2o72b2o$21b2o73bo$
21bobo70bobo$23bo70b2o61b2o16b2o54b2o16b2o$23b2o132b2o16b2o54b2o16b2o
2$77b2o$77b2o15b2o$94bobo$5b2o89bo84b2o72b2o$4bobo23bo65b2o82bobo71bob
o$4bo23b3o149bo73bo$3b2o22bo151b2o72b2o$11b2o14b2o160b2o72b2o$11b2o64b
2o80b2o28b2o42b2o28b2o$77bo76b2o2bo2bo7bo36b2obo18b2o2bo2bo44b2obo$75b
obo73bo2bo4bobo6bobo35bob2o15bo2bo4bobo44bob2o$75b2o73bobobo5bo6b2ob2o
52bobobo5bo$151bo2bob2o9bo2bo28b2o24bo2bob2o41b2o$154bo2bo8bo3bo28b2o
27bo2bo41b2o$155bo4bo9bo58bo4bo$92b2obo60b5o23b2o44b5o$92bob2o79b2o8bo
63b2o$158bo16bobo7bobo44bo16bobo$85b2o70bobo17bo8b2o43bobo17bo$85b2o
71bo18b2o53bo18b2o$10b2o13b2o236b2o18bo$9bobo13b2o237bo17bobo$9bo254bo
bo16bo$8b2o255b2o$27bo253b5o$26bobo252bo4bo$27bo47b2o91bo72b2o41bo2bo$
28b3o45bo81b2o7b2o41bo21b2o7b2o41b2obo2bo$30bo45bobo80bo48b3o22bo47bo
5bobobo$77b2o80bobo22b2obo19bo25bobo44bobo4bo2bo$154b2o4b2o22bob2o19b
2o19b2o4b2o44bo2bo2b2o$136b2o17bo20b2o35bo15bo20b2o29b2o$20b2o115bo17b
obo18bo34b3o15bobo18bo$20b2o74bo27bo11bo19b2o16bobo33bo19b2o16bobo$94b
3o27b3o9b2o36b2o34b2o36b2o$93bo33bo$11b2o80b2o19b2o10b2o$11b2o84b2o16b
o$46b2o50bo16bobo$46b2o48bo19b2o$96b2o41b2o72b2o$139b2o72b2o50b2o16b2o
$12b2o152b2o97b2o16b2o$13bo152b2o26b2o$10b3o3b2o175bobo$10bo4bobo152b
2o21bo50b2o43b2o$15bo83b2o69bo21b2o50bo44bo$14b2o64b2o17b2o70b3o32b2o
37b3o39bobo$13bo66b2o91bo32bo40bo39b2o$13b3o25b2o87b2o75b3o$16bo24bo
88bo16b2o60bo11b2o14b2o38b2o$15b2o25b3o34b2o50b3o14bo73bo15bo38b2o$44b
o35bo52bo11b3o71b3o15bo$77b3o12b2o51bo10b2o61bo10b2o5b2o10bo$16b2o19b
2o38bo14bo64bo73bo15b3o$16b2o19b2o54b3o60bo73bo15bo$89b2o4bo60b2o72b2o
14b2o13b2o$89bobo170bo$91b3o127bo39bo31bo$90bo3bob2o123b3o37b2o28b3o$
90b2o2b2obo126bo65bo$223b2o65b2o4$254b2o$29b2o223b2o$29bo$30b3o260b2o$
32bo260bobo$295bo$295b2o$162b2o55b2o36b2o$8b2o3b2o103b2o42b2o54bobo16b
2o19bo$9bo2bobo103bo99bo18bobo15b3o25b2o3b2o$8bo3bo106bo97b2o20bo15bo
6bo11b2o7b2o3b2o$8b5o105b2o48b2o63b2o4b2o19b3o11bo$168b2o63bobo23bo15b
3o$6b5o153b2o69bo23b2o16bo$5bo4bo153b2o60b2o7b2o$4bo2bo218b2o$bo2bob2o
135b2o$obobo5bo63b2o39b2o26b2o$bo2bo4bobo9b2o51b2o39b2o52b2o$4b2o2bo2b
o9b2o146b2o$9b2o19b2o37b2o$28bo2bo37b2o$28b2o186b2o$33b2o182bo$33bo
111b2o70bobo$31bobo71b2o38bobo70b2o$30bobo72bo41bo$26b2o3bo20bo53b3o
11b2o25b2o$26b2o23bobo54bo11b2o$50bo2bo$8b2o41b2o183b2o$8b2o56bo67b2o
100bo$62b2o2bobo65bo99bobo$62b2o2b2o67b3o96b2o$137bo11b2o$124b2o22bobo
23bo$125bo22bo23b3o$122b3o22b2o22bo$122bo32b2o14b2o$155b2o$75b2o$9b2o
64b2o$8bobo60b2o$8bo62bobo$7b2o64bo$73b2o158b2o$60b2o155b2o14b2o$60b2o
156bo22b2o$215b3o23bo$12b2o3b2obo194bo23bobo$13bo3b2ob3o35b2o109b2o2b
2ob2o61b2o$10b3o10bo34b2o94b2o13bobo2bobo$10bo6b2ob3o130bobo16b2o3bo7b
o$18bobo132bo19bob2o6b3o$18bobo131b2o16bo2bobo6bo38bo$19bo149bobobobo
6b2o37b3o$170b2ob2o49bo$202bo20b2o$200b3o16b2o$199bo19bo$186b2o11b2o
20bo$186b2o32b2o6$155b2o60b2o$155b2o60b2o17b2o$161b2o73b2o$161b2o$180b
2o$176b2o2bo2b2o52b2o$159b2o16bo3bob2o52bo$159b2o5b2o9bobobo42b2o12b3o
$166b2o10b2obob2o22b2o16bo14bo$181bo2bo4b2o16bo14b3o$181b2o6b2o17b3o
11bo$210bo!

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simsim314
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Joined: February 10th, 2014, 1:27 pm

Re: Possible new type of category to define ships/oscillators?

Post by simsim314 » June 2nd, 2016, 4:01 pm

There is something similar called Heat.

And although heat does seems to be interesting property, it's pretty minor one - for example I don't know of an attempt to optimize glider guns for Heat. Such properties are usually less important than the "bigger picture" of the specific spaceship or oscillator.

Gamedziner
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Re: Possible new type of category to define ships/oscillators?

Post by Gamedziner » June 2nd, 2016, 4:40 pm

Got it.

Code: Select all

x = 81, y = 96, rule = LifeHistory
58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27.
A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A
$4.2A18$4.2A$4.2A2.2A$8.2A!

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pcallahan
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Joined: April 26th, 2013, 1:04 pm

Re: Possible new type of category to define ships/oscillators?

Post by pcallahan » June 7th, 2016, 2:16 pm

I would not expect any aggregate value to tell you much about large constructions such as a Herschel-based oscillator, but I agree that it might be interesting to optimize various metrics in small-oscillator searches. I would think of these more as heuristics than as mathematically interesting properties. It might be worthwhile to try to infer the metric from actual data on which oscillators people find most appealing, though it would be hard to gather that data.

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