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"Banks" equivalent

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"Banks" equivalent

Posted: September 20th, 2016, 12:32 am
by PHPBB12345

Code: Select all

x = 75, y = 123, rule = B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78
o18bo$5ob14o$4ob15o$20o6b5o2b5o2b5o2b5o$o18bo7b3o4b3o4b3o4b3o$27b3o4b
3o4b3o4b3o$27b3o4b3o4b3o4b3o$o18bo7b3o4bobo4b3o4bobo$15ob4o7b3o5b2o4b
3o4b2o$16ob3o7b3o4b3o4b3o4b3o$20o7b3o4b3o4b3o4b3o$o18bo7b3o4b3o4b3o4b
3o$27b3o4b3o4b3o4b3o$27b3o4b3o4b3o4b3o$o18bo7b3o4b3o4b3o4b3o$20o7b3o4b
3o4b3o4b3o$4ob15o7b3o4b3o4b3o4b3o$5ob14o7b3o4b3o4b3o4b3o$o18bo7b3o4b3o
4b2o5b3o$28b2o4b3o4bobo4b3o$27bobo4b3o4b3o4b3o$o18bo7b3o4b3o4b3o4b3o$
20o6b5o2b5o2b5o2b5o$17ob2o$16ob3o$o18bo5$o13bo4bo$5ob14o$4ob15o$20o6b
5o2b5o2b5o2b5o$o18bo7b3o4b3o4b3o4b3o$27b3o4b3o4b3o4b3o$27b3o4b3o4b3o4b
3o$o6bo11bo7b3o4bobo4b3o4bobo$15ob4o7b3o5b2o4b4o3b2o$16ob3o7b3o4b3o4b
3o4b3o$20o6b4o4b3o4b3o4b3o$o18bo7b3o4b3o4b3o4b3o$27b3o4b3o4b3o4b3o$27b
3o4b3o4b3o4b3o$o18bo7b3o4b3o4b3o4b3o$20o7b3o4b3o4b3o4b3o$4ob15o7b3o3b
4o4b3o4b4o$5ob14o7b3o4b3o4b3o4b3o$o12bo5bo7b3o4b3o4b2o5b3o$28b2o4b3o4b
obo4b3o$27bobo4b3o4b3o4b3o$o18bo7b3o4b3o4b3o4b3o$20o6b5o2b5o2b5o2b5o$
17ob2o$16ob3o$o5bo12bo7$14b5o30b5o$15b3o32b3o$15b3o32bobo$15b3o32b2o$
15b3o32b3o$15b3o32b3o$15b3o32b3o$15b3o32b3o$15b3o32b3o$15b3o32b3o$o14b
3o32b3o$3ob14o15bo16b3o$2ob31o16b3o$15o3b16o15b4o$o12b2o3b16o16b3o$13b
2o3b3o12bo16b3o$12b4o2b3o28b4o4bo$18b3o30b7o16bo$18b3o30b24o$18b3o30bo
6b17o$18b3o37b17o$18b3o37bo15bo$18b3o$18b3o$18b3o$18b3o$18b3o$17b5o8$
9bo25bo$9b27o$bo8b26o$b9ob25o$7obo26bo$8bo3$16b5o$17b3o$17b3o$17b3o$
17b3o$17b3o$17bobo$18b2o$17b3o$17b4o$17b3o$o16b3o$3ob8ob7o19bo$2ob8ob
28o$17o3b20o$o14b2o3b20o$15b2o3bo18bo$14b4o!

Code: Select all

x = 89, y = 54, rule = B2ce3e4jr5cin6-en7c8/S012-ac3-cn4-eikny5-kr67c8
30bo35bo$52bo$6b2ob26o14b4ob30o$5b4ob23o16b5ob30o$6b2ob23o17b4ob30o$
31bo$31bo34bo5$6b2ob23o$5b4ob23o$6b2ob23o6$6b3ob22o$5b5ob22o$6b3ob22o
4$14b3o$14b3o34b3o23b3o$14b3o34b3o23b3o$15bo36bo25bo$14bobo34bobo23bob
o$14b3o34b3o23b3o$14b3o34b3o23b3o$14b3o34b3o23b3o$3bo8bob3obo8bo21bob
3obo19bob3obo$3bo10b3o10bo23b3o23b3o$3b25o14b2ob18o5b2ob18o$2b27o13b3o
b17o5b3ob17o$31o11b2ob18o5b2ob18o$14b3o34b3o23b3o$4bo7bob3obo7bo22bob
3obo19bob3obo$14b3o34b3o23b3o$14b3o34b3o23b3o$14b3o34b3o23b3o$14b3o34b
3o23bobo$14b3o34b3o24bo$14b3o34b3o23b3o$14b3o34b3o23b3o$14b3o$14b3o$
14b3obo$12b5o$15b2o$16bo$16bo!

Re: "Banks" equivalent

Posted: December 20th, 2016, 10:41 am
by Naszvadi
Cool. Is there a tool where /B01?2?3?4?\/S0?1?2?3?V/ ruleSTRINGS can be converted to equivalent nontotalistic life-like two-state Moore-ruleSTRINGS?

Q.: Why? For *.* purpose?

A.: Yes, I would like to use existing glider searching tools for inspecting B0*V spaces :)

Re: "Banks" equivalent

Posted: December 20th, 2016, 3:59 pm
by _zM
Naszvadi wrote:Cool. Is there a tool where /B01?2?3?4?\/S0?1?2?3?V/ ruleSTRINGS can be converted to equivalent nontotalistic life-like two-state Moore-ruleSTRINGS?

Q.: Why? For *.* purpose?

A.: Yes, I would like to use existing glider searching tools for inspecting B0*V spaces :)
Quick and dirty Python script for use in Golly:

Code: Select all

import golly as g

oldrule = g.getrule()
newrule = ""
dict = {
	"0":"01c2cn3c4c",
	"1":"1e2ak3inqy4ny5e",
	"2":"2ei3kajr4kaiqtwz5kajr6ei",
	"3":"7e6ak5inqy4jr3e",
	"4":"87c6cn5c4e",
	"B":"B",
	"S":"S",
	"/":"/",
	"V":""
}

for char in oldrule:
	newrule = newrule + dict[char]

g.setrule(newrule)

Re: "Banks" equivalent

Posted: December 20th, 2016, 7:30 pm
by Naszvadi
_zM wrote:
Naszvadi wrote:Cool. Is there a tool where /B01?2?3?4?\/S0?1?2?3?V/ ruleSTRINGS can be converted to equivalent nontotalistic life-like two-state Moore-ruleSTRINGS?
...
Quick and dirty Python script for use in Golly:

...
Now, I made my version, this is a CLI utility in order to use it with command line glider search programs that support BOTH B0 and nontotalistic Moore rulestrings.

Here you are:

Code: Select all

#!/usr/bin/env python
#
# Neumann to Moore rulestring converter utility.
# Idea from _zM's golly script stub and recreated using this:
# http://golly.sourceforge.net/Help/Algorithms/QuickLife.html#nontotal
#
# NASZVADI, P. 2016.12.*, don't violate the law of the author
#
# Usage:
# run with the following parameters:
#
# APPLICATION [-d|-diag|--diag] <Neumann rulestring>
#
# It prints the equivalent 2D nontotalistic Moore rule
# Using the -d/-diag/--diag switch, only the same colours
# of used on the infinite checkerboard on the cellspace,
# so a diagonal rule is created, which is useful for
# glider searching programs that can perform hunting for
# orthogonal gliders.

import sys

myarglist = sys.argv[1:]
for oldrule in myarglist:
  if oldrule[0] != '-':
    break
newrule = ""
if ('-diag' in myarglist) or \
   ('--diag' in myarglist) or \
   ('-d' in myarglist):
  dict = {
    "0":"01e2ei3e4e",
    "1":"1c2ak3kajr4jr5c",
    "2":"2cn3inqy4kaiqtwz5inqy6cn",
    "3":"3c4ny5kajr6ak7c",
    "4":"4c5e6ei7e8",
    "B":"B",
    "S":"S",
    "b":"B",
    "s":"S",
    "/":"/",
    "_":"/",
    "V":""
  }
else:
  dict = {
    "0":"01c2cn3c4c",
    "1":"1e2ak3inqy4ny5e",
    "2":"2ei3kajr4kaiqtwz5kajr6ei",
    "3":"3e4jr5inqy6ak7e",
    "4":"4e5c6cn7c8",
    "B":"B",
    "S":"S",
    "b":"B",
    "s":"S",
    "/":"/",
    "_":"/",
    "V":""
  }

for char in oldrule:
  newrule = newrule + dict[char]

print newrule
A link to these scripts is needed from a new topic here: http://conwaylife.com/forums/viewforum.php?f=9

Re: "Banks" equivalent

Posted: March 15th, 2020, 12:59 pm
by Naszvadi
PHPBB12345 wrote: September 20th, 2016, 12:32 am

Code: Select all

x = 89, y = 54, rule = B2ce3e4jr5cin6-en7c8/S012-ac3-cn4-eikny5-kr67c8
30bo35bo$52bo$6b2ob26o14b4ob30o$5b4ob23o16b5ob30o$6b2ob23o17b4ob30o$
31bo$31bo34bo5$6b2ob23o$5b4ob23o$6b2ob23o6$6b3ob22o$5b5ob22o$6b3ob22o
4$14b3o$14b3o34b3o23b3o$14b3o34b3o23b3o$15bo36bo25bo$14bobo34bobo23bob
o$14b3o34b3o23b3o$14b3o34b3o23b3o$14b3o34b3o23b3o$3bo8bob3obo8bo21bob
3obo19bob3obo$3bo10b3o10bo23b3o23b3o$3b25o14b2ob18o5b2ob18o$2b27o13b3o
b17o5b3ob17o$31o11b2ob18o5b2ob18o$14b3o34b3o23b3o$4bo7bob3obo7bo22bob
3obo19bob3obo$14b3o34b3o23b3o$14b3o34b3o23b3o$14b3o34b3o23b3o$14b3o34b
3o23bobo$14b3o34b3o24bo$14b3o34b3o23b3o$14b3o34b3o23b3o$14b3o$14b3o$
14b3obo$12b5o$15b2o$16bo$16bo!
Banks-III rule - the referred pattern works between these rules:
B2ce3e4jr5cin6acik7c8/S012ei3aijr4acjqrt5aceijnqy67c8 - B2cein3ejk4ijkrwz5cinry6acikn78/S012eikn3aeijkqry4acjqrtwz5aceijnqy67c8

Simplified (same) rulestrings:
B2ce3e4jr5cin6-en7c8/S012ei3aijr4acjqrt5-kr67c8 - B2-ak3ejk4ijkrwz5cinry6-e78/S012-ac3-cn4-eikny5-kr67c8

Is there a spaceship in any of such rules?

Re: "Banks" equivalent

Posted: March 16th, 2020, 12:31 am
by Saka
Naszvadi wrote: March 15th, 2020, 12:59 pm (Banks)
Is there a spaceship in any of such rules?
A while back I tried using ntzfind on Banks. I didnt get any spaceships but I did get quite a few long and somewhat interesting partials.
Unfortunately I only posted 2 (on Discord) so here they are

Code: Select all

x = 13, y = 41, rule = B2ce3e4jr5cin6-en7c8/S012-ac3-cn4-eikny5-kr67c8
6bo$5b3o$3bo2bo2bo$2bobobobobo$2bo2bobo2bo$2b9o$2bob5obo$2bob2ob2obo$b
3obobob3o$2o2b2ob2o2b2o$b3obobob3o$b5ob5o$2ob3ob3ob2o$b5ob5o$bob7obo$b
ob7obo$b3obobob3o$bobobobobobo$bob3ob3obo$bob7obo$2b4ob4o$3b7o$b2ob5ob
2o$b4obob4o$b5ob5o$bobob3obobo$2b4ob4o$bo2b5o2bo$4b5o$4b5o$4b2ob2o$3b
3ob3o$4b5o$3b3ob3o$5bobo$4b5o$5b3o$5b3o$4bo3bo$3bobobobo$2bob2ob2obo!

Code: Select all

x = 246, y = 15, rule = B2ce3e4jr5cin6-en7c8/S012-ac3-cn4-eikny5-kr67c8
2o6bo6bo39bo11bo7bo5bo5bo4bo74bo36bo14bo$2bob3ob8obob2o2bo4b3o20b2o2b
2o2bob7ob2o5bo8b2o4b77o4bo2b29o2b2o4bob4ob2o5bo2bo10bo$b3obob5o2b5obo
2b6obobob2obo7b2o5b3ob2ob3o4b2ob3ob2o11bob4ob86o2b4o2b2o6b2o2b2o2b6ob
11o6bob7o3b6o$obob7ob9o4b2ob4ob15ob2ob5ob3ob7ob3ob5obobo2b4ob5o2b5o2b
2o2b2o8b4o2b4o2b6o2b8o2b4o6b2o2b6ob3obobob26o2b2o2bob2obo2b4ob6ob2ob2o
b2o2bo3b3o$ob13ob2ob11o2b2ob2obo6b9ob3ob3ob5ob7ob6ob2obob2obo4b65o2b2o
2b9ob3ob4o8b2o2b15ob8ob9ob2obo3b5o$5o2b2ob3o2bo2b4ob5obo5b6ob3obob2ob
5o4bob4ob6o2b3ob3obo2b6obobobo2b2o6b2o2b2o4b12o2b36ob3obob5ob24obob3o
2b2ob5ob4ob3ob3ob4o$b7obobob10o4b2obobo2b2ob3ob2ob6o2bob2o3b6ob4o2bob
7o2b2ob7ob37o2b2o2b4o2b2o6b2o2b2o4b7ob7obobo21bo4bob4ob2ob2ob3ob2ob3o
2b3ob2o$b3o4b3o5bobob6ob4o2bobobo2b2ob2obobob4ob2o5bob4ob2obo3b2ob3o3b
o2b3ob8o2b8o2b4o6b2o4b2o2b38ob6o2bo22b8o2bo3b6obo4b4o2bob2o$b7obobob
10o4b2obobo2b2ob3ob2ob6o2bob2o3b6ob4o2bob7o2b2ob7ob37o2b2o2b4o2b2o6b2o
2b2o4b7ob7obobo21bo4bob4ob2ob2ob3ob2ob3o2b3ob2o$5o2b2ob3o2bo2b4ob5obo
5b6ob3obob2ob5o4bob4ob6o2b3ob3obo2b6obobobo2b2o6b2o2b2o4b12o2b36ob3obo
b5ob24obob3o2b2ob5ob4ob3ob3ob4o$ob13ob2ob11o2b2ob2obo6b9ob3ob3ob5ob7ob
6ob2obob2obo4b65o2b2o2b9ob3ob4o8b2o2b15ob8ob9ob2obo3b5o$obob7ob9o4b2ob
4ob15ob2ob5ob3ob7ob3ob5obobo2b4ob5o2b5o2b2o2b2o8b4o2b4o2b6o2b8o2b4o6b
2o2b6ob3obobob26o2b2o2bob2obo2b4ob6ob2ob2ob2o2bo3b3o$b3obob5o2b5obo2b
6obobob2obo7b2o5b3ob2ob3o4b2ob3ob2o11bob4ob86o2b4o2b2o6b2o2b2o2b6ob11o
6bob7o3b6o$2bob3ob8obob2o2bo4b3o20b2o2b2o2bob7ob2o5bo8b2o4b77o4bo2b29o
2b2o4bob4ob2o5bo2bo10bo$2o6bo6bo39bo11bo7bo5bo5bo4bo74bo36bo14bo!
EDIT:
Max rule - partials

Code: Select all

x = 129, y = 76, rule = B2-ak3ejk4ijkrwz5cinry6-e78/S012-ac3-cn4-eikny5-kr67c8
6bo43bo2bo35bo31bo$4b5o40b6o33b3o29b3o$5bobo41b6o32b2ob2o27b2ob2o$4b5o
38bob6obo30b5o27b5o$4b5o39b3o2b3o31b5o27b5o$4b5o38b10o29b7o25b7o$2b9o
36b2obo2bob2o31b3o29b3o$2b3obob3o36bobob2obobo30bobobo27bobobo$b3ob3ob
3o36bob4obo32bobo29bobo$2bob2ob2obo36bobob2obobo30b5o27b5o$2b2ob3ob2o
36b10o30b2ob2o27b2ob2o$2bob5obo35b2ob6ob2o29b5o27b5o$2b9o36b10o29b7o
25b7o$2b4ob4o36b10o29b7o25b7o$2b4ob4o36b10o30b5o27b5o$b4obob4o35b10o
29bob3obo25bob3obo$b2ob5ob2o35bob6obo30b5o27b5o$b4obob4o35b10o30b2ob2o
27b2ob2o$2bob5obo36b2ob4ob2o28bob5obo23bob5obo$2ob2obob2ob2o34bob6obo
27b3ob3ob3o21b3ob3ob3o$b5ob5o35b10o26b3ob5ob3o19b3ob5ob3o$2b9o35b12o
27bob5obo23bob5obo$2bob5obo37b8o28b11o21b11o$b3ob3ob3o35b10o27b11o21b
11o$b2obobobob2o35b3ob2ob3o27bobob3obobo21bobob3obobo$b11o37b6o29b2ob
5ob2o21b2ob5ob2o$b2ob2ob2ob2o36b8o27b13o19b13o$bobob3obobo36b8o27b13o
19b13o$b2ob5ob2o36b8o27b2obobobobob2o19b2obobobobob2o$b11o35b3ob2ob3o
28b9o23b9o$2b9o35b2ob6ob2o26b3ob3ob3o21b3ob3ob3o$3b2obob2o37b4o2b4o27b
ob7obo21bob7obo$2b3obob3o36b10o27b11o21b11o$2b9o37b8o29b3obob3o23b3obo
b3o$2b3obob3o38bob2obo29bobob3obobo21bobob3obobo$2b9o36b2ob4ob2o27b3o
5b3o21b3o5b3o$b4obob4o34b2ob6ob2o26b4obob4o21b4obob4o$2b9o36b2ob4ob2o
27b11o21b11o$2bob5obo37b2ob2ob2o29b3obob3o23b3obob3o$2b2obobob2o35b12o
27b9o23b9o$bobob3obobo34b4ob2ob4o26b11o21b11o$2bo2b3o2bo35b12o27b9o23b
2ob3ob2o$bob2o3b2obo34b12o27b9o23b4ob4o$b2o2b3o2b2o35b3ob2ob3o28b4ob4o
24b7o$bo2bobobo2bo34bobobo2bobobo28b7o26bobobo$b11o34b4ob2ob4o25b13o
19b13o$b11o33b14o25b11o22bobobobobo$2b2ob3ob2o35b12o27bob5obo23b2ob3ob
2o$b5ob5o34b3ob4ob3o25b2ob2obob2ob2o20b11o$b4obob4o34bob8obo25b4ob3ob
4o21bo2bobo2bo$bob7obo34b5o2b5o25b6ob6o22bo2bo2bo$b3ob3ob3o34bob8obo
25b3ob5ob3o25bo$b4o3b4o35bo2bo2bo2bo25b6obob6o19bob2o3b2obo$b2o2b3o2b
2o34b4ob2ob4o25b3obobobob3o19bobob5obobo$46b2obob2obob2o25b2ob7ob2o20b
3ob3ob3o$46bob3o2b3obo24b3ob7ob3o17b4obobobob4o$83bob4ob4obo19b4ob3ob
4o$83b13o19bob9obo$83bobob2ob2obobo20b3o5b3o$84bob7obo20b13o$83bobob5o
bobo18b4ob5ob4o$83b13o20b11o$84b11o21b3obobob3o$84b2ob5ob2o21b2ob5ob2o
$83b13o19bobob2ob2obobo$84bob7obo19b15o$85bob5obo21b13o$83bob4ob4obo
19bobob5obobo$84b3o2bo2b3o20b2ob2o3b2ob2o$83bo2b3ob3o2bo19b13o$84bobob
3obobo21b5ob5o$115bobo2b3o2bobo$117b2ob3ob2o$114b6obob6o$116bob3ob3obo
$115bo2bo2bo2bo2bo!
Min rule: Wickstretcher and cool partial (please some do p7 k1 w10 a)

Code: Select all

x = 42, y = 28, rule = B2ce3e4jr5cin6-en7c8/S012ei3aijr4acjqrt5-kr67c8
5bo32bo$4b3o30b3o$4bobo30b4o$3bo3bo29b3o$2b3ob3o28b4o$3b2ob2o26bo4b2o$
3b5o25bo2bo2b2o$3b2ob2o27bobob2o$obo5bobo25bo2b2o$3bo3bo26b2ob4o$2b7o
24b2ob6o$3b5o26b5obo$4b3o28bo$3bobobo$3bobobo29bob2o$2b7o26b2obo$4b3o
29b6o$4b3o29b4obo$4b3o30bo2b2o$4b3o26b2obo4bo$4b3o26bobobo$4b3o28b2obo
bo$4b3o30bobobo$4b3o$4b3o$4b3o$4b3o$4b3o!

Re: "Banks" equivalent

Posted: March 16th, 2020, 10:46 am
by Hunting
A bit off-topic, diagonal equivalent:

Code: Select all

x = 72, y = 102, rule = B3c4c/S01c2n3c4c
4bo$3bo$2bobo$bobobo$obobobo$3bobobo$4bobobo$5bo$6bobobo$7bobobo$8bobo
bo$9bobobo$10bobobo$11bobobo$12bobobo$13bobobo$14bobobo$15bobobo$16bob
obo$17bobobo$18bobobo$19bobobo$20bobobo$21bobobo$22bobobo$23bobobobo$
24bobobo$25bobo$26bo$25bo44$43bo$40bobo$41bobo$42bobo$43bobo$44bobo$
45bobo5bo$46bobo3bo$49bo3bo$48bobobobo$47bo5bobo$52bobobo$53bobobo$54b
obobo$55bobobo$56bobobo$57bobobo$58bobobo$59bobobo$60bobobo$61bobobo$
62bobobo$63bobobo$64bobobo$65bobobobo$66bobobo$67bobo$68bo$67bo!

Re: "Banks" equivalent

Posted: December 13th, 2020, 5:19 am
by GUYTU6J
Last night I wrote an article about Banks-I on LifeWiki: OCA:Banks-I
Now I'd like to ask, what's the black-white reversal of the rule B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78? I can only figure out the reversal of Hunting's diagonal equivalent above:

Code: Select all

x = 50, y = 50, rule = B2c/S2cn3c4c
42bo$41bobo$40bobobo$39bo3bobo$38bobo3bobo$37bobo5bobo$36bobo7bobo$35b
obo9bobo$34bobo7bobobo$33bobo7bobobo$32bobo7bobobo$31bobo7bobobo$30bob
o7bobobo$29bobo7bobobo$28bobo7bobobo$27bobo7bobobo$26bobo7bobobo$25bob
o7bobobo$24bobo7bobobo$23bobo7bobobo$22bobo7bobobo$21bobo7bobobo$20bob
o7bobobo$19bobo7bobobo$18bobo7bobobo$17bobo7bobobo$16bobo7bobobo$15bob
o7bobobo$14bobo7bobobo$13bobo7bobobo$12bobo7bobobo$11bobo7bobobo$10bo
9bobobo$9bobo7bobobo$8bobobobobobobobo$7bobobobo3bobobo$6bobobobo3bobo
bo$5bobobobo5bobo$4bobobobo3bo3bo$3bobobobo5bobo$2bobobobo5bobo$bobobo
bo5bobo$obobo7bobo$bobobo5bobo$2bobobo3bobo$3bobo3bobo$4bobobobo$5bobo
bo$6bobo$7bo!
Said reversal must has some connection to these Margolus-emulating rules, as the signal in Banks-I is extensible in width and those square oscillators exist on a dense agar:

Code: Select all

x = 31, y = 36, rule = B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78
9bo19bo$9b21o$bo7b21o$b29o$obobobobo20bo$8bo4$9bo19bo$9b21o$9b21o$bo7b
21o$b29o$obobobobo20bo$8bo3$9bo20bo$9b22o$9b22o$9b22o$bo7b22o$b30o$obo
bobobo21bo$8bo2$9bo19bo$9b21o$9b21o$9b21o$9b21o$bo7b21o$b29o$obobobobo
20bo$8bo!

Code: Select all

x = 513, y = 259, rule = B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78
bo510bo$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b
512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o
$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b
512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o
$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b
512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o
$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b
512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o
$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b
512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o
$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b
512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o
$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b
512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o
$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b
512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o
$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b
512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o
$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b
512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o
$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b
512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o$b512o
$b512o$b512o$b512o$2b511o$2ob510o$bo510bo!

Re: "Banks" equivalent

Posted: December 13th, 2020, 2:49 pm
by bubblegum
GUYTU6J wrote: December 13th, 2020, 5:19 am Now I'd like to ask, what's the black-white reversal of the rule B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78?
B2e3ajk4akqw5ajk6e/S0123-e4-ejr5aejkr6ei

Re: "Banks" equivalent

Posted: December 14th, 2020, 3:19 am
by GUYTU6J
bubblegum wrote: December 13th, 2020, 2:49 pm
GUYTU6J wrote: December 13th, 2020, 5:19 am Now I'd like to ask, what's the black-white reversal of the rule B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78?
B2e3ajk4akqw5ajk6e/S0123-e4-ejr5aejkr6ei
Mmm... That is c̶o̶r̶r̶e̶c̶t̶ ̶i̶n̶ ̶t̶h̶e̶ ̶u̶s̶u̶a̶l̶ ̶s̶e̶n̶s̶e̶ ̶b̶u̶t̶ ̶n̶o̶t̶ ̶w̶o̶r̶k̶i̶n̶g̶ ̶f̶o̶r̶ ̶m̶y̶ ̶p̶u̶r̶p̶o̶s̶e̶. (EDIT: wrong, as the survival condition should be subtracted from 8.) The negation should actually be taken on the von Neumann neighbourhood instead of the Moore neighbourhood. (EDIT: nope, after correction the Moore reversal is fine)

Anyway, given an INT rule on the von Neumann neighbourhood, it is easy to write the diagonal equivalent INT Moore rule by appending c's to the 1,3 and 4's, putting 2c if two neighbours are near/cis or 2n if two neighbours are opposite/trans, and deleting the V. Then the orthogonal equivalent INT Moore rule follows from the dictionary adapted from _zM:

Code: Select all

dict = {
	"0":"01c2cn3c4c",
	"1c":"1e2ak3inqy4ny5e",
	"2c":"2e3ajk4akqw5ajk6e",
	"2n":"2i3r4itz5r6i",
	"3c":"7e6ak5inqy4jr3e",
	"4c":"87c6cn5c4e",
	"B":"B",
	"S":"S",
	"/":"/"
These two steps will map Banks-I to B3c4c/S01c2n3c4c and then B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78, verifying PHPBB12345's result. Meanwhile, the anti-Banks-I, the black-white reversal on the von Neumann neighbourhood, maps to B2c/S2cn3c4c and then B2e3ajk4akqw5ajk6e/S2ei3aejkr4-cny5-e678, as you can see:

Code: Select all

x = 154, y = 110, rule = B2e3ajk4akqw5ajk6e/S2ei3aejkr4-cny5-e678
44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b
3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$
44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b
3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$
44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b
3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$44b3o$
44b3o$34o10b3o$34o10b3o$11ob19ob2o10b3o$11o21b2o10b3o$3ob7o21b2o10b3o$
3o29b2o10b3o$2obobobobob20ob2o10b3o$10ob23o10b3o$34o10b3o$34o10b3o$34o
10b3o$11ob19ob2o10b3o$11o21b2o10b3o$11o21b2o10b3o$3ob7o21b2o10b3o$3o
29b2o10b3o$2obobobobob20ob2o10b3o$10ob23o10b3o$34o10b3o$34o10b3o$11ob
20obo10b3o$11o22bo10b3o$11o22bo10b3o$11o22bo10b3o$3ob7o22bo10b3o$3o30b
o10b3o$2obobobobob21obo10b3o$10ob23o10b3o$34o10b3o$11ob19ob2o10b3o$11o
21b2o10b3o$11o21b2o10b3o$11o21b2o10b3o$11o21b2o10b3o$3ob7o21b2o10b3o$
3o29b2o10b4o$2obobobobob20ob2o10b2o2bo$10ob23o10b3ob106o$34o10b110o$
34o10b110o!
EDIT: p4 "clocks" (signal emitters), one or two barrelled

Code: Select all

x = 46, y = 6, rule = B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78
o39bo$41o$2ob3ob3ob3ob3ob3ob18o4bo$ob3ob3ob3ob3obob3ob17ob4o$o18bo21b
5o$41bo3bo!
A one-dimensional replicator loop/shuttle can also serve as a source, but the bounding box is twice as large.

Code: Select all

x = 24, y = 16, rule = B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78
11bo11bo$11b13o$7bo3b13o$7bob15o$6b5o12bo$10bo5$11bo11bo$11b13o$o10b
13o$8ob15o$11o12bo$o9bo!
Soup-searching in the black/white reversal may result in some high-period oscillator interactions:

Code: Select all

x = 57, y = 17, rule = B2e3ajk4akqw5ajk6e/S2ei3aejkr4-cny5-e678
12bo2bo35bo2bo$6b3o2bo3b2o28b3o2bo3b2o$5b4obobo2bobo26b4obobo2bobo$7bo
4b2o32bo4b2o$4b4o6b3o26b4o6b3o$6bo7bo30bo7bo$4b2o7bo29b2o7bo$5b2o4bobo
30b2o4bobo$2o3b4obo2bo25b2o3b4obo2bo$bobo3bo3bo2bo25bobo3bo3bo2bo$o2b
2ob2o6bo24bo2b2ob2o6bo$2bo6b3o29bo6b3o$o4b3ob2o28bo4b3ob2o$b3ob3o4b2ob
o24b3ob3o4b2o$ob4o4bob2o25bob4o4bob2o$7bobob4obo29bobob3o$8bob2o2b2o
31bob2o!
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