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Highest-period objects with smallest bounding boxes
Posted: July 6th, 2024, 7:59 am
by muzik
Another discussion in the vein of threads like these:
viewtopic.php?f=11&t=3089
viewtopic.php?f=11&t=3097
I want to see what the highest period object we can get is that remains in the smallest possible bounding box throughout its entire evolution. Can be an oscillator, spaceship or bounded grid.
Here's a period-64 from OmniOsci which remains in a 4x4 box at all times:
Code: Select all
x = 4, y = 4, rule = B2ikn3ajnr4aijk5eir6ek7c/S012-ce3cen4iy5ei6ak
o$3bo2$2bo!
p269532480 by Brian Prentice, remains in a 7x7 box:
Code: Select all
x = 5, y = 5, rule = PCA_10
GNGNK$5G$GKMNG$5G$KMKMG!
7x6, unknown period:
Code: Select all
x = 5, y = 4, rule = 2PCA4,0,1,2,3,4,5,6,13,8,9,10,14,12,7,11,15
GNGNK$GO3G$GKMNG$G3OG!
7x8, unknown period:
Code: Select all
x = 8, y = 7, rule = M0,1,2,3,4,10,6,11,8,9,5,13,12,14,7,15
5bo$5b2o$4bo2bo$5bobo$bob3obo$5bobo$4bo!
What's the maximum we can get for each small bounding box size? Rule tables permitted.
Re: Highest-period objects with smallest bounding boxes
Posted: July 6th, 2024, 8:35 am
by H. H. P. M. P. Cole
muzik wrote: July 6th, 2024, 7:59 am
What's the maximum we can get for each small bounding box size? Rule tables permitted.
One must also specify the state count as well as bounding box for this challenge to be nontrivial. Even at a 1x1 bounding box we can make a period-(n-1) oscillator with n states, like so (shown for n = 4, period = 3):
Code: Select all
x = 1, y = 1, rule = P3
A!
@RULE P3
@TABLE
n_states: 4
neighborhood: Moore
symmetries: rotate4reflect
1,0,0,0,0,0,0,0,0,2
2,0,0,0,0,0,0,0,0,3
3,0,0,0,0,0,0,0,0,1
For oscillators, does this challenge require the bounding box to stay stationary or can it move around?
Re: Highest-period objects with smallest bounding boxes
Posted: July 6th, 2024, 9:37 am
by muzik
H. H. P. M. P. Cole wrote: July 6th, 2024, 8:35 am
For oscillators, does this challenge require the bounding box to stay stationary or can it move around?
The bounded box displayed in Identify, so the stationary bounding box containing every cell that comes alive throughout the entire evolution.
10x6, period unknown:
Code: Select all
x = 7, y = 6, rule = M0,1,2,3,4,10,6,11,8,9,5,13,12,14,7,15
b3o$2bo$bob2o$3b3o$bo2b3o$bob2obo!
Re: Highest-period objects with smallest bounding boxes
Posted: July 7th, 2024, 3:27 am
by muzik
52x2, period 16777214:
Code: Select all
x = 52, y = 2, rule = B2ae/S
bo46bobo$o47bo2bo!
58x2, period 134217726:
Code: Select all
x = 58, y = 2, rule = B2ae/S
bo52bobo$o53bo2bo!
64x2, period 1073741822:
Code: Select all
x = 64, y = 2, rule = B2ae/S
bo58bobo$o59bo2bo!
Re: Highest-period objects with smallest bounding boxes
Posted: August 4th, 2024, 8:30 am
by muzik
I somehow overlooked this amazing period-560 oscillator that fits within a 4x4 bounding box in all phases. Perhaps this was a recent addition to OmniOsci? I don't remember it being there earlier.
Code: Select all
x = 4, y = 4, rule = B2ek3ajnq4ainrz5-enq6-en8/S02eik3ajqry4aiqrty5-qr7e8
obo2$2b2o$3bo!
Re: Highest-period objects with smallest bounding boxes
Posted: August 4th, 2024, 8:35 am
by confocaloid
muzik wrote: August 4th, 2024, 8:30 am
I somehow overlooked this amazing period-560 oscillator that fits within a 4x4 bounding box in all phases. Perhaps this was a recent addition to OmniOsci? I don't remember it being there earlier.
Code: Select all
x = 4, y = 4, rule = B2ek3ajnq4ainrz5-enq6-en8/S02eik3ajqry4aiqrty5-qr7e8
obo2$2b2o$3bo!
Source for that p560 oscillator:
carsoncheng wrote: October 7th, 2023, 7:00 am
p560 in 4x4:
Code: Select all
x = 4, y = 4, rule = B2ek3ajnq4ainrz5-enq6-en8/S02eik3ajqry4aiqrty5-qr7e8
bo2$o$3bo!
Check
that forum thread for more examples.
Re: Highest-period objects with smallest bounding boxes
Posted: August 4th, 2024, 8:36 am
by pifricted
P450000+
Code: Select all
x = 11, y = 12, rule = M0,2,4,3,1,5,6,7,0,2,4,3,1,5,6,7|M0,0,8,8,2,2,6,6,4,4,10,10,12,12,14,14
9bo4$6bo$8bo$3bo$6bo$2bo2$9bo!
Who can tell me its bounding box?
Re: Highest-period objects with smallest bounding boxes
Posted: August 4th, 2024, 6:42 pm
by muzik
pifricted wrote: August 4th, 2024, 8:36 am
Who can tell me its bounding box?
91x91, which is obviously huge and something we can get far, far,
far higher periods than this from.