Patterns with unusual growth rates

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Rhombicubocta
Posts: 81
Joined: May 27th, 2026, 9:44 am

Re: Patterns with unusual growth rates

Post by Rhombicubocta »

While trying to tame a rule with a superstring puffing replicator I found a pattern whose maximum populations seems to go up about linearly but the minimum populations that go up logarithmically.
The pattern itself is a wave puffing replicator interacting with debris to form a temporary puffer at the back that is repeatedly destroyed and recreated at different intervals.
The population plot looks like bizzare.
Can someone help me figure out the growth rate of this?

Code: Select all

x = 28, y = 50, rule = B3aeijn/S2-n3-ck5en6ck8
3$12b3o$12bobo$13bo$12bobo$13bo3$13bo$12bobo$13bo$12bobo$12b3o5$12b3o$
12bobo$13bo$12bobo$13bo3$13bo$12bobo$13bo$12bobo$12b3o5$12b3o$12bobo$
13bo$12bobo$13bo3$13bo$12bobo$13bo$12bobo$8bo3b3o3bo$7bobo7bobo$7bobo
7bobo$8bo9bo!
edit: here it is later on to make the pattern more apparent.

Code: Select all

x = 2531, y = 1599, rule = B3aeijn/S2-n3-ck5en6ck8
1265bo$1264bobo$1264bobo$1264b3o$1264b3o$1264bobo$1264bobo$1264b3o$1264b
3o$1264bobo$1264bobo$1264b3o$1264b3o$1264bobo$1264bobo$1264b3o$1264b3o
$1264bobo$1264bobo$1264b3o$1264b3o$1264bobo$1264bobo$1264b3o$1264b3o$
1264bobo$1264bobo$1264b3o$1264b3o$1264bobo$1264bobo$1265bo33$1216bo97b
o$1217bo95bo$1216bo97bo2$1213b2o101b2o$1212bo105bo$1212bo105bo$1212b2o
103b2o$1212b2o103b2o$1212bo105bo$1212bo105bo$1212b2o103b2o$1212b2o103b
2o$1212bo105bo$1212bo105bo$1212b2o103b2o$1212b2o103b2o$1212bo105bo$1212b
o105bo$1212b2o103b2o$1212b2o103b2o$1212bo105bo$1212bo105bo$1212b2o103b
2o$1212b2o103b2o$1212bo105bo$1212bo105bo$1213b2o101b2o2$1216bo97bo$1217b
o95bo$1216bo97bo33$1265bo$1264bobo$1264bobo$1264b3o$1264b3o$1264bobo$
1264bobo$1264b3o$1264b3o$1264bobo$1264bobo$1264b3o$1264b3o$1264bobo$1264b
obo$1264b3o$1264b3o$1264bobo$1264bobo$1264b3o$1264b3o$1264bobo$1264bo
bo$1264b3o$1264b3o$1264bobo$1264bobo$1264b3o$1264b3o$1264bobo$1264bob
o$1265bo177$1008bo513bo$1009bo511bo$bo1006bo513bo1006bo$2o2527b2o$obo
1002b2o517b2o1002bobo$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b
2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004b
o521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b
2o$1004b2o519b2o$1004bo521bo$53bo950bo521bo950bo$52b2o950b2o519b2o950b
2o$52bobo949b2o519b2o949bobo$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b
2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521b
o$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b
2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b
2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004b
o521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b
2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$
1004bo521bo$157bo846bo521bo846bo$156b2o846b2o519b2o846b2o$156bobo845b
2o519b2o845bobo$1004bo521bo$1004bo521bo$1004b2o519b2o$131bo872b2o519b
2o872bo$130b2o872bo521bo872b2o$130bobo871bo521bo871bobo$1004b2o519b2o
$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004b
o521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521b
o$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b
2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521b
o$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b
2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b
2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004b
o521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b
2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$
1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004b
o521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b
2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$
1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$365bo
638bo521bo638bo$364b2o638b2o519b2o638b2o$364bobo637b2o519b2o637bobo$1004b
o521bo$1004bo521bo$1004b2o519b2o$339bo664b2o519b2o664bo$338b2o664bo521b
o664b2o$338bobo663bo521bo663bobo$1004b2o519b2o$1004b2o519b2o$1004bo521b
o$313bo690bo521bo690bo$312b2o690b2o519b2o690b2o$312bobo689b2o519b2o689b
obo$1004bo521bo$1004bo521bo$1004b2o519b2o$287bo716b2o519b2o716bo$286b
2o716bo521bo716b2o$286bobo715bo521bo715bobo$1004b2o519b2o$1004b2o519b
2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004b
o521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b
2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$
1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004b
o521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b
2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$
1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004b
o521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b
2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$
1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004b
o521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b
2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$
1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004b
o521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b
2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$
1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004b
o521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b
2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$
1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004b
o521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b
2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$
1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004b
o521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b
2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$
1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004b
o521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$781bo222bo521bo222bo$780b
2o222b2o519b2o222b2o$780bobo221b2o519b2o221bobo$1004bo521bo$1004bo521b
o$1004b2o519b2o$755bo248b2o519b2o248bo$754b2o248bo521bo248b2o$754bobo
247bo521bo247bobo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$729bo274bo521b
o274bo$728b2o274b2o519b2o274b2o$728bobo273b2o519b2o273bobo$1004bo521b
o$1004bo521bo$1004b2o519b2o$703bo300b2o519b2o300bo$702b2o300bo521bo300b
2o$702bobo299bo521bo299bobo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$677b
o326bo521bo326bo$676b2o326b2o519b2o326b2o$676bobo325b2o519b2o325bobo$
1004bo521bo$1004bo521bo$1004b2o519b2o$651bo352b2o519b2o352bo$650b2o352b
o521bo352b2o$650bobo351bo521bo351bobo$1004b2o519b2o$1004b2o519b2o$1004b
o521bo$625bo378bo521bo378bo$624b2o378b2o519b2o378b2o$624bobo377b2o519b
2o377bobo$1004bo521bo$1004bo521bo$1004b2o519b2o$599bo404b2o519b2o404b
o$598b2o404bo521bo404b2o$598bobo403bo521bo403bobo$1004b2o519b2o$1004b
2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521b
o$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b
2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b
2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004b
o521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b
2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$
1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004b
o521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b
2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$
1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004b
o521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b
2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$
1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004b
o521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b
2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$
1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004b
o521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b
2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$
1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004b
o521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b
2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$
1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004b
o521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b
2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$
1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004b
o521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b
2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$
1004bo521bo$1004bo521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004b
o521bo$1004b2o519b2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1004b2o519b
2o$1004b2o519b2o$1004bo521bo$1004bo521bo$1005b2o517b2o2$1008bo513bo$1009b
o511bo$1008bo513bo177$1265bo$1264bobo$1264bobo$1264b3o$1264b3o$1264bo
bo$1264bobo$1264b3o$1264b3o$1264bobo$1264bobo$1264b3o$1264b3o$1264bob
o$1264bobo$1265bo3$1249bo31bo$1248b2o31b2o$1248bobo14bo14bobo$1264bob
o$1264bobo$1265bo$1223bo83bo$1222b2o41bo41b2o$1222bobo39bobo39bobo$1264b
obo$1265bo31$1265bo$1264bobo$1264bobo$1265bo29$1265bo$1264bobo$1264bo
bo$1265bo29$1265bo$1264bobo$1264bobo$1265bo29$1265bo$1264bobo$1264bob
o$1265bo29$1265bo$1264bobo$1264bobo$1265bo29$1265bo$1264bobo$1264bobo
$1265bo29$1265bo$1264bobo$1264bobo$1265bo29$1265bo$1264bobo$1264bobo$
1265bo29$1265bo$1264bobo$1264bobo$1265bo29$1265bo$1264bobo$1264bobo$1265b
o29$1265bo$1264bobo$1264bobo$1265bo29$1265bo$1264bobo$1264bobo$1265bo
29$1265bo$1264bobo$1264bobo$1265bo29$1265bo$1264bobo$1264bobo$1265bo29$
1265bo$1264bobo$1264bobo$1265bo29$1265bo$1264bobo$1264bobo$1265bo29$1265b
o$1264bobo$1264bobo$1265bo!
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User avatar
muzik
Posts: 6604
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Re: Patterns with unusual growth rates

Post by muzik »

Katrina wrote: April 1st, 2026, 8:50 pm Woah
Time dilation?

Code: Select all

x = 1, y = 1, rule = 11622909951
!
[[ PASTET EVERY 1 PASTEDELTA 0 -1 PASTE B! 0 4094 AUTOFIT ]]
@RULE 11622909951
@TABLE
n_states:3
neighborhood:oneDimensional
symmetries:none
var a = {0 1 2}
var b = a
var c = a
1,0,2,0
0,2,2,0
1,1,0,0
2,0,2,0
2,2,1,0
0,1,1,0
2,1,1,0
0,1,1,1
0,0,2,1
0,0,1,2
0,1,2,1
2,1,0,0
1,0,0,0
1,2,1,0
0,2,1,0
0,2,0,2
0,1,0,0
1,2,0,0
1,1,2,0
2,0,1,0
2,1,2,0
0,0,1,1
0,2,1,2
0,2,1,1
0,0,2,2
0,0,2,0
0,1,0,2
0,2,0,0
0,2,0,1
0,2,2,2
0,1,2,0
0,1,0,1
a,b,c,0
Parity Replicator Collection v1.6 is now live - please send all relevant discoveries here.
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User avatar
CARuler
Posts: 1350
Joined: July 30th, 2024, 5:38 pm
Location: A rule-verse in floor rule-verse of the CGOL skyscraper

Re: Patterns with unusual growth rates

Post by CARuler »

superlog growth rate

Code: Select all

x = 8, y = 1, rule = superlogGrowth
A.C.E2.J!

@RULE superlogGrowth
@COLORS
0   0   0   0
1 255 255   0
2 128   0 255
3 255 255 255
4 128 128 128
5   0 255   0
6   0 255 255
7 255   0   0
8 255   0 255
9   0   0 255
10 255 128   0
11   0 128 255
12   0 255 128
@TABLE
n_states:13
neighborhood:oneDimensional
symmetries:none
var a = {0,1,2,3,4,5,6,7,8,9,10,11,12}
var b = a
0,1,3,4
0,0,3,3
0,4,0,4
0,0,7,2
0,0,2,2
0,5,0,6
0,10,0,11
0,4,5,4
0,4,6,4
5,4,0,3
6,3,0,8
0,8,0,5
0,5,10,6
0,5,11,6
0,8,10,5
0,8,11,5
6,3,10,8
6,3,11,8
10,5,0,6
10,8,0,5
5,0,11,9
0,0,9,9
9,4,0,5
4,0,9,12
5,4,10,3
0,0,12,12
0,1,12,12
1,0,12,7
12,1,0,4
#defaults
3,a,b,0
4,a,b,0
2,a,b,0
7,a,b,1
8,a,b,0
5,a,b,0
9,a,b,0
10,a,b,0
6,a,b,5
11,a,b,10
12,a,b,0
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