OCA:Banks-I - Revision history

Confocal: links, formatting

2023-05-24T05:40:54Z

links, formatting

← Older revision		Revision as of 05:40, 24 May 2023
Line 15:		Line 15:
	* Any dead cell with three or four orthogonally adjacent live neighbours comes to life; otherwise it remains dead.		* Any dead cell with three or four orthogonally adjacent live neighbours comes to life; otherwise it remains dead.

	In current terminology, what he specified is an [[isotropic non-totalistic cellular automaton]] on the range-1 [[von Neumann neighbourhood]]. Since the neighbourhood is a subset of the [[Moore neighbourhood]], the rule can also be written in Hensel notation. However, the resulted rulestring (B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78)<ref name="post35944" /> is very bulky due to reflecting all of the possible configurations of a cell's diagonally adjacent neighbour.		In current terminology, what he specified is an [[isotropic non-totalistic cellular automaton]] on the range-1 [[von Neumann neighbourhood]]. Since the neighbourhood is a subset of the [[Moore neighbourhood]], the rule can also be written in [[Hensel notation]]. However, the resulted [[rulestring]] ({{nowrap\|B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78}})<ref name="post35944" /> is very bulky due to reflecting all of the possible configurations of a cell's diagonally adjacent neighbour.

	A way to get around the issue is to consider the diagonal neighbours of a cell only and leave orthogonal ones dead, leading to an equivalent rule B3c4c/S01c2n3c4c where patterns are rotated 45 degrees.<ref name="post91281" />		A way to get around the issue is to consider the diagonal neighbours of a cell only and leave orthogonal ones dead, leading to an equivalent rule {{nowrap\|B3c4c/S01c2n3c4c}} where patterns are rotated 45 degrees.<ref name="post91281" />

	Banks-I is a built-in "general binary" rule in [[Mirek's Cellebration]], and also a rule table in [[Golly]] that can be loaded via [[RuleLoader]] even before supporting non-totalistic rules.		Banks-I is a built-in "general binary" rule in [[Mirek's Cellebration]], and also a rule table in [[Golly]] that can be loaded via [[RuleLoader]] even before supporting non-totalistic rules.
Line 25:		Line 25:

	{{EmbedViewer		{{EmbedViewer
	\|rle = x = 52, y = 56, rule = B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78		\|rle = x = 52, y = 56, rule = B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78
	o18bo$5ob14o$4ob15o$20o6b5o2b5o2b5o2b5o$o18bo7b3o4b3o4b3o4b3o$27b3o4b		o18bo$5ob14o$4ob15o$20o6b5o2b5o2b5o2b5o$o18bo7b3o4b3o4b3o4b3o$27b3o4b
	3o4b3o4b3o$27b3o4b3o4b3o4b3o$o18bo7b3o4bobo4b3o4bobo$15ob4o7b3o5b2o4b		3o4b3o4b3o$27b3o4b3o4b3o4b3o$o18bo7b3o4bobo4b3o4bobo$15ob4o7b3o5b2o4b
Line 40:		Line 40:
	obo4b3o$27bobo4b3o4b3o4b3o$o18bo7b3o4b3o4b3o4b3o$20o6b5o2b5o2b5o2b5o$		obo4b3o$27bobo4b3o4b3o4b3o$o18bo7b3o4b3o4b3o4b3o$20o6b5o2b5o2b5o2b5o$
	17ob2o$16ob3o$o5bo12bo!		17ob2o$16ob3o$o5bo12bo!
	~~\|position = center~~		\|viewerconfig = #C [[ WIDTH 600 HEIGHT 600 THUMBSIZE 2 ZOOM 8 ]]
	\|viewerconfig = #C [[ ~~ZOOM 8~~ WIDTH 600 HEIGHT 600 ]]		\|position = center
	\|caption = The wire, signal and "dead-end" in all orientations~~<br>~~		\|caption = The wire, signal and "dead-end" in all orientations
			\|style = width:300px;
	}}		}}

	Signals can be emitted at regular intervals with a "clock". These devices are essentially [[period]]-2<sup>n~~</sup>~~ signal [[factory\|factories]] driven by [[Rule 90]] [[replicator]] loops.		Signals can be emitted at regular intervals with a "clock". These devices are essentially [[period]]-2{{sup\|''n''}} signal [[factory\|factories]] driven by [[Rule 90]] [[replicator]] loops.

	{{EmbedViewer		{{EmbedViewer
	\|rle = x = 30, y = 16, rule = B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78		\|rle = x = 30, y = 16, rule = B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78
	5bo11bo$5b13o$bo3b13o$b17o$3obo12bo$4bo5$9bo19bo$9b21o$bo7b21o$b29o$7o		5bo11bo$5b13o$bo3b13o$b17o$3obo12bo$4bo5$9bo19bo$9b21o$bo7b21o$b29o$7o
	bo20bo$8bo!		bo20bo$8bo!
	~~\|position = center~~		\|viewerconfig = #C [[ WIDTH 600 HEIGHT 360 THUMBSIZE 2 ZOOM 8 ]]
	\|viewerconfig = #C [[ ZOOM 8 ]]		\|position = center
	\|caption = Clocks at period 8 and 16 respectively~~<br>~~		\|caption = Clocks at period 8 and 16 respectively
			\|style = width:300px;
	}}		}}

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	{{EmbedViewer		{{EmbedViewer
	\|rle = x = 75, y = 28, rule = B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78		\|rle = x = 75, y = 28, rule = B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78
	14b5o30b5o$15b3o32b3o$15b3o32bobo$15b3o32b2o$15b3o32b3o$15b3o32b3o$15b		14b5o30b5o$15b3o32b3o$15b3o32bobo$15b3o32b2o$15b3o32b3o$15b3o32b3o$15b
	3o32b3o$15b3o32b3o$15b3o32b3o$15b3o32b3o$o14b3o32b3o$3ob14o15bo16b3o$		3o32b3o$15b3o32b3o$15b3o32b3o$15b3o32b3o$o14b3o32b3o$3ob14o15bo16b3o$
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	3o28b4o4bo$18b3o30b7o16bo$18b3o30b24o$18b3o30bo6b17o$18b3o37b17o$18b3o		3o28b4o4bo$18b3o30b7o16bo$18b3o30b24o$18b3o30bo6b17o$18b3o37b17o$18b3o
	37bo15bo$18b3o$18b3o$18b3o$18b3o$18b3o$17b5o!		37bo15bo$18b3o$18b3o$18b3o$18b3o$18b3o$17b5o!
	~~\|position = center~~		\|viewerconfig = #C [[ WIDTH 800 HEIGHT 400 THUMBSIZE 2 ZOOM 8 ]]
	\|viewerconfig = #C [[ ~~ZOOM 8~~ WIDTH 800 HEIGHT 400 ]]		\|position = center
	\|caption = The signal duplicator (left) and reflector (right)~~<br>~~		\|caption = The signal duplicator (left) and reflector (right)
			\|style = width:300px;
	}}		}}

	Following these, Boolean logic elements including ANDNOT, NOT and NOR gates have been built, which are sufficient to construct a general purpose computer based on the universal [https://en.wikipedia.org/wiki/NOR_logic NOR logic].		Following these, Boolean logic elements including ANDNOT, NOT and NOR gates have been built, which are sufficient to construct a general purpose computer based on the universal NOR logic.{{refn\|group=note\|See also [https://en.wikipedia.org/wiki/NOR_logic NOR logic] on Wikipedia}}

	With some new observations in {{year\|2017}}, [[Peter Naszvadi]] constructed a [[Rule 110]] [[unit cell]] in Banks-I, proving the rule Turing-complete.<ref name="post52584" />		With some new observations in {{year\|2017}}, [[Peter Naszvadi]] constructed a [[Rule 110]] [[unit cell]] in Banks-I, proving the rule Turing-complete.<ref name="post52584" />

	== Related rules ==		== Related rules ==
	The [[black/white reversal]] of Banks-I is B2e3ajk4akqw5ajk6e/S2ei3aejkr4-cny5-e678, which has a slightly shorter rulestring and corresponds to the diagonal equivalent B2c/S2cn3c4c with patterns rotated 45 degrees. They are related to the [[Life-like cellular automaton]] [[2×2]] due to an infinite family of rectangular oscillators that oscillates according to a [[block cellular automaton]] on the [[Margolus neighbourhood]]. For any oscillator with a 2×(4n) box of alive cells in B36/S125 (2×2), the corresponding oscillator is an [[long\|extended]] [[barge]] with 2×(4n) alive cells in B2e3ajk4akqw5ajk6e/S2ei3aejkr4-cny5-e678, or a rectangle of 2×(4n) dots with every coordinate even in B2c/S2cn3c4c.		The [[black/white reversal]] of Banks-I is {{nowrap\|B2e3ajk4akqw5ajk6e/S2ei3aejkr4-cny5-e678}}, which has a slightly shorter rulestring and corresponds to the diagonal equivalent {{nowrap\|B2c/S2cn3c4c}} with patterns rotated 45 degrees.
			They are related to the [[Life-like cellular automaton]] {{rl\|2×2}} due to an infinite family of rectangular oscillators that oscillates according to a [[block cellular automaton]] on the [[Margolus neighbourhood]].
			For any oscillator with a {{times\|2\|(4''n'')}} box of alive cells in {{nowrap\|B36/S125}} (2×2), the corresponding oscillator is an [[long\|extended]] [[barge]] with {{times\|2\|(4''n'')}} alive cells in {{nowrap\|B2e3ajk4akqw5ajk6e/S2ei3aejkr4-cny5-e678}}, or a rectangle of {{times\|2\|(4''n'')}} dots with every coordinate even in {{nowrap\|B2c/S2cn3c4c}}.

			== Notes ==
			<references group=note>
			</references>

	== References ==		== References ==
	<references>		<references>
	<ref name="post35944">{{LinkForumThread		<ref name="post35944">{{LinkForumThread
	\|p = ~~35944~~		\|format = ref
	\|~~format~~ = ~~ref~~		\|p = 35944
	\|title = "Banks" equivalent		\|title = "Banks" equivalent
	\|author = PHPBB12345		\|author = PHPBB12345
	\|date = September 20, 2016		\|date = September 20, 2016
			}}</ref>
			<ref name="post52584">{{LinkForumThread
			\|format = ref
			\|p = 52584
			\|title = Re: List of the Turing-complete totalistic life-like CA
			\|author = Peter Naszvadi
			\|date = November 1, 2017
	}}</ref>		}}</ref>
	<ref name="post91281">{{LinkForumThread		<ref name="post91281">{{LinkForumThread
	\|p = ~~91281~~		\|format = ref
	\|~~format~~ = ~~ref~~		\|p = 91281
	\|title = Re: "Banks" equivalent		\|title = Re: "Banks" equivalent
	\|author = Hunting		\|author = Hunting
	\|date = March 16, 2020		\|date = March 16, 2020
	~~}}</ref>~~
	~~<ref name="post52584">{{LinkForumThread~~
	~~\|p = 52584~~
	~~\|format = ref~~
	~~\|title = Re: List of the Turing-complete totalistic life-like CA~~
	~~\|author = Peter Naszvadi~~
	~~\|date = November 1, 2017~~
	}}</ref>		}}</ref>
	</references>		</references>

Book: linkify

2022-11-28T21:36:06Z

linkify

← Older revision		Revision as of 21:36, 28 November 2022
Line 7:		Line 7:
	\|reversal = B2e3ajk4akqw5ajk6e/S2ei3aejkr4-cny5-e678		\|reversal = B2e3ajk4akqw5ajk6e/S2ei3aejkr4-cny5-e678
	}}		}}
	'''Banks-I''' is an two-state [[cellular automaton]] devised by [[Roger Banks]] in his {{year\|1971}} PhD thesis as a simulated model of a universal computer.		'''Banks-I''' is an two-state [[cellular automaton]] devised by [[Roger Banks]] in his {{year\|1971}} PhD thesis as a simulated model of a [[universal computer]].

	== Rule definition and simulation ==		== Rule definition and simulation ==

Confocal: Category:Isotropic non-totalistic rules

2022-08-10T17:19:00Z

Category:Isotropic non-totalistic rules

← Older revision		Revision as of 17:19, 10 August 2022
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	* {{LinkCatagolueRule\|b3e4ejr5cinqy6-ei78s012-e3-ajk4-akqw5-ajk6-e78\|rulename=Banks-I}}		* {{LinkCatagolueRule\|b3e4ejr5cinqy6-ei78s012-e3-ajk4-akqw5-ajk6-e78\|rulename=Banks-I}}
	* {{LinkMirek\|rullex_gebi.html#Banks\|title=MCell built-in Life rules: Banks}}		* {{LinkMirek\|rullex_gebi.html#Banks\|title=MCell built-in Life rules: Banks}}

			[[Category:Isotropic non-totalistic rules]]

Confocal: LifeWiki:Tiki bar/Archive/2020#"Non-Lifelike" CAs -- cleanup suggested

2022-08-10T05:54:50Z

LifeWiki:Tiki bar/Archive/2020#"Non-Lifelike" CAs -- cleanup suggested

← Older revision		Revision as of 05:54, 10 August 2022
Line 15:		Line 15:
	* Any dead cell with three or four orthogonally adjacent live neighbours comes to life; otherwise it remains dead.		* Any dead cell with three or four orthogonally adjacent live neighbours comes to life; otherwise it remains dead.

	In current terminology, what he specified is an [[isotropic non-totalistic ~~Life-like~~ cellular automaton]] on the range-1 [[von Neumann neighbourhood]]. Since the neighbourhood is a subset of the [[Moore neighbourhood]], the rule can also be written in Hensel notation. However, the resulted rulestring (B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78)<ref name="post35944" /> is very bulky due to reflecting all of the possible configurations of a cell's diagonally adjacent neighbour.		In current terminology, what he specified is an [[isotropic non-totalistic cellular automaton]] on the range-1 [[von Neumann neighbourhood]]. Since the neighbourhood is a subset of the [[Moore neighbourhood]], the rule can also be written in Hensel notation. However, the resulted rulestring (B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78)<ref name="post35944" /> is very bulky due to reflecting all of the possible configurations of a cell's diagonally adjacent neighbour.

	A way to get around the issue is to consider the diagonal neighbours of a cell only and leave orthogonal ones dead, leading to an equivalent rule B3c4c/S01c2n3c4c where patterns are rotated 45 degrees.<ref name="post91281" />		A way to get around the issue is to consider the diagonal neighbours of a cell only and leave orthogonal ones dead, leading to an equivalent rule B3c4c/S01c2n3c4c where patterns are rotated 45 degrees.<ref name="post91281" />

Confocal: /* External links */ consistent formatting for bulleted lists

2022-06-03T08:23:45Z

External links: consistent formatting for bulleted lists

← Older revision		Revision as of 08:23, 3 June 2022
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	== External links ==		== External links ==
	* <span id="Banks_1971">Banks, E. R. (1971) [http://www.bottomlayer.com/bottom/banks/banks_thesis_1971.pdf ''Information processing and transmission in cellular automata''].</span>		* <span id="Banks_1971">Banks, E. R. (1971) [http://www.bottomlayer.com/bottom/banks/banks_thesis_1971.pdf ''Information processing and transmission in cellular automata''].</span>
	{{LinkCatagolueRule\|b3e4ejr5cinqy6-ei78s012-e3-ajk4-akqw5-ajk6-e78\|rulename=Banks-I}}		* {{LinkCatagolueRule\|b3e4ejr5cinqy6-ei78s012-e3-ajk4-akqw5-ajk6-e78\|rulename=Banks-I}}
	{{LinkMirek\|rullex_gebi.html#Banks\|title=MCell built-in Life rules: Banks}}		* {{LinkMirek\|rullex_gebi.html#Banks\|title=MCell built-in Life rules: Banks}}

Muzik at 09:43, 15 February 2022

2022-02-15T09:43:16Z

← Older revision		Revision as of 09:43, 15 February 2022
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	{{stub}}		{{stub}}
	{{Rule		{{Rule
	\|name = Banks-I		\|name = Banks-I
	\|b = 3e4ejr5cinqy6-ei78		\|b = 3e4ejr5cinqy6-ei78
	\|s = 012-e3-ajk4-akqw5-ajk6-e78		\|s = 012-e3-ajk4-akqw5-ajk6-e78
	\|char = Stable		\|char = Stable
	\|reversal = B2e3ajk4akqw5ajk6e/S2ei3aejkr4-cny5-e678		\|reversal = B2e3ajk4akqw5ajk6e/S2ei3aejkr4-cny5-e678
	}}		}}
	'''Banks-I''' is an two-state [[cellular automaton]] devised by [[Roger Banks]] in his {{year\|1971}} PhD thesis as a simulated model of a universal computer.		'''Banks-I''' is an two-state [[cellular automaton]] devised by [[Roger Banks]] in his {{year\|1971}} PhD thesis as a simulated model of a universal computer.

	==Rule definition and simulation==		== Rule definition and simulation ==

	The original definition of Banks-I by Banks was written in a checkerboard manner and had three rotationally symmetric transition rules, namely:		The original definition of Banks-I by Banks was written in a checkerboard manner and had three rotationally symmetric transition rules, namely:

Line 22:		Line 21:
	Banks-I is a built-in "general binary" rule in [[Mirek's Cellebration]], and also a rule table in [[Golly]] that can be loaded via [[RuleLoader]] even before supporting non-totalistic rules.		Banks-I is a built-in "general binary" rule in [[Mirek's Cellebration]], and also a rule table in [[Golly]] that can be loaded via [[RuleLoader]] even before supporting non-totalistic rules.

	==Constructions==		== Constructions ==

	In the PhD thesis, Banks demonstrated how [[signal]] [[circuitry]] can be built in Banks-I. A "wire" consists of a three-cell-thick block of live cells, and a "signal" is carried by a [[duoplet]]-shaped perturbation travelling at [[lightspeed]] along the edge of a wire. A five-cell bump extension and an additional cell on the edge can kill a signal.		In the PhD thesis, Banks demonstrated how [[signal]] [[circuitry]] can be built in Banks-I. A "wire" consists of a three-cell-thick block of live cells, and a "signal" is carried by a [[duoplet]]-shaped perturbation travelling at [[lightspeed]] along the edge of a wire. A five-cell bump extension and an additional cell on the edge can kill a signal.

Line 76:		Line 74:
	With some new observations in {{year\|2017}}, [[Peter Naszvadi]] constructed a [[Rule 110]] [[unit cell]] in Banks-I, proving the rule Turing-complete.<ref name="post52584" />		With some new observations in {{year\|2017}}, [[Peter Naszvadi]] constructed a [[Rule 110]] [[unit cell]] in Banks-I, proving the rule Turing-complete.<ref name="post52584" />

	==Related rules==		== Related rules ==

	The [[black/white reversal]] of Banks-I is B2e3ajk4akqw5ajk6e/S2ei3aejkr4-cny5-e678, which has a slightly shorter rulestring and corresponds to the diagonal equivalent B2c/S2cn3c4c with patterns rotated 45 degrees. They are related to the [[Life-like cellular automaton]] [[2×2]] due to an infinite family of rectangular oscillators that oscillates according to a [[block cellular automaton]] on the [[Margolus neighbourhood]]. For any oscillator with a 2×(4n) box of alive cells in B36/S125 (2×2), the corresponding oscillator is an [[long\|extended]] [[barge]] with 2×(4n) alive cells in B2e3ajk4akqw5ajk6e/S2ei3aejkr4-cny5-e678, or a rectangle of 2×(4n) dots with every coordinate even in B2c/S2cn3c4c.		The [[black/white reversal]] of Banks-I is B2e3ajk4akqw5ajk6e/S2ei3aejkr4-cny5-e678, which has a slightly shorter rulestring and corresponds to the diagonal equivalent B2c/S2cn3c4c with patterns rotated 45 degrees. They are related to the [[Life-like cellular automaton]] [[2×2]] due to an infinite family of rectangular oscillators that oscillates according to a [[block cellular automaton]] on the [[Margolus neighbourhood]]. For any oscillator with a 2×(4n) box of alive cells in B36/S125 (2×2), the corresponding oscillator is an [[long\|extended]] [[barge]] with 2×(4n) alive cells in B2e3ajk4akqw5ajk6e/S2ei3aejkr4-cny5-e678, or a rectangle of 2×(4n) dots with every coordinate even in B2c/S2cn3c4c.

	==References==		== References ==
	<references>		<references>
	<ref name="post35944">{{LinkForumThread		<ref name="post35944">{{LinkForumThread
Line 105:		Line 102:
	</references>		</references>

	==External links==		== External links ==
	*<span id="Banks_1971">Banks, E. R. (1971) [http://www.bottomlayer.com/bottom/banks/banks_thesis_1971.pdf ''Information processing and transmission in cellular automata''].</span>		* <span id="Banks_1971">Banks, E. R. (1971) [http://www.bottomlayer.com/bottom/banks/banks_thesis_1971.pdf ''Information processing and transmission in cellular automata''].</span>
	{{LinkCatagolueRule\|b3e4ejr5cinqy6-ei78s012-e3-ajk4-akqw5-ajk6-e78\|rulename=Banks-I}}		{{LinkCatagolueRule\|b3e4ejr5cinqy6-ei78s012-e3-ajk4-akqw5-ajk6-e78\|rulename=Banks-I}}
	{{LinkMirek\|rullex_gebi.html#Banks\|title=MCell built-in Life rules: Banks}}		{{LinkMirek\|rullex_gebi.html#Banks\|title=MCell built-in Life rules: Banks}}

GUYTU6J: Related rules

2020-12-14T09:19:42Z

Related rules

← Older revision		Revision as of 09:19, 14 December 2020
Line 1:		Line 1:
	{{stub}}		{{stub}}
	{{Rule		{{Rule
	\|name = Banks-I		\|name = Banks-I
	\|b = 3e4ejr5cinqy6-ei78		\|b = 3e4ejr5cinqy6-ei78
	\|s = 012-e3-ajk4-akqw5-ajk6-e78		\|s = 012-e3-ajk4-akqw5-ajk6-e78
	\|char = Stable		\|char = Stable
			\|reversal = B2e3ajk4akqw5ajk6e/S2ei3aejkr4-cny5-e678
	}}		}}
	'''Banks-I''' is an two-state [[cellular automaton]] devised by [[Roger Banks]] in his {{year\|1971}} PhD thesis as a simulated model of a universal computer.		'''Banks-I''' is an two-state [[cellular automaton]] devised by [[Roger Banks]] in his {{year\|1971}} PhD thesis as a simulated model of a universal computer.
Line 15:		Line 16:
	* Any dead cell with three or four orthogonally adjacent live neighbours comes to life; otherwise it remains dead.		* Any dead cell with three or four orthogonally adjacent live neighbours comes to life; otherwise it remains dead.

	In current terminology, what he specified is an [[isotropic non-totalistic Life-like cellular automaton]] on the range-1 [[von Neumann neighbourhood]]. Since the neighbourhood is a subset of the [[Moore neighbourhood]], the rule can also be written in Hensel notation. However, the resulted rulestring (B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78)<ref name="post35944" /> is very bulky due to reflecting all of the possible configurations of a cell's diagonally adjacent neighbour. A way to get around the issue is to consider the diagonal neighbours of a cell only, leading to an equivalent rule B3c4c/S01c2n3c4c where patterns are rotated 45 degrees.<ref name="post91281" />		In current terminology, what he specified is an [[isotropic non-totalistic Life-like cellular automaton]] on the range-1 [[von Neumann neighbourhood]]. Since the neighbourhood is a subset of the [[Moore neighbourhood]], the rule can also be written in Hensel notation. However, the resulted rulestring (B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78)<ref name="post35944" /> is very bulky due to reflecting all of the possible configurations of a cell's diagonally adjacent neighbour.

			A way to get around the issue is to consider the diagonal neighbours of a cell only and leave orthogonal ones dead, leading to an equivalent rule B3c4c/S01c2n3c4c where patterns are rotated 45 degrees.<ref name="post91281" />

	Banks-I is a built-in "general binary" rule in [[Mirek's Cellebration]], and also a rule table in [[Golly]] that can be loaded via [[RuleLoader]] even before supporting non-totalistic rules.		Banks-I is a built-in "general binary" rule in [[Mirek's Cellebration]], and also a rule table in [[Golly]] that can be loaded via [[RuleLoader]] even before supporting non-totalistic rules.
Line 72:		Line 75:

	With some new observations in {{year\|2017}}, [[Peter Naszvadi]] constructed a [[Rule 110]] [[unit cell]] in Banks-I, proving the rule Turing-complete.<ref name="post52584" />		With some new observations in {{year\|2017}}, [[Peter Naszvadi]] constructed a [[Rule 110]] [[unit cell]] in Banks-I, proving the rule Turing-complete.<ref name="post52584" />

			==Related rules==

			The [[black/white reversal]] of Banks-I is B2e3ajk4akqw5ajk6e/S2ei3aejkr4-cny5-e678, which has a slightly shorter rulestring and corresponds to the diagonal equivalent B2c/S2cn3c4c with patterns rotated 45 degrees. They are related to the [[Life-like cellular automaton]] [[2×2]] due to an infinite family of rectangular oscillators that oscillates according to a [[block cellular automaton]] on the [[Margolus neighbourhood]]. For any oscillator with a 2×(4n) box of alive cells in B36/S125 (2×2), the corresponding oscillator is an [[long\|extended]] [[barge]] with 2×(4n) alive cells in B2e3ajk4akqw5ajk6e/S2ei3aejkr4-cny5-e678, or a rectangle of 2×(4n) dots with every coordinate even in B2c/S2cn3c4c.

	==References==		==References==

GUYTU6J: The classical universal rule

2020-12-12T16:54:14Z

The classical universal rule

New page

{{stub}}
{{Rule
|name = Banks-I
|b = 3e4ejr5cinqy6-ei78
|s = 012-e3-ajk4-akqw5-ajk6-e78
|char = Stable
}}
'''Banks-I''' is an two-state [[cellular automaton]] devised by [[Roger Banks]] in his {{year|1971}} PhD thesis as a simulated model of a universal computer.

==Rule definition and simulation==

The original definition of Banks-I by Banks was written in a checkerboard manner and had three rotationally symmetric transition rules, namely:

* Any live cell with two closest orthogonally adjacent live neighbours dies; otherwise it remains alive.
* Any dead cell with three or four orthogonally adjacent live neighbours comes to life; otherwise it remains dead.

In current terminology, what he specified is an [[isotropic non-totalistic Life-like cellular automaton]] on the range-1 [[von Neumann neighbourhood]]. Since the neighbourhood is a subset of the [[Moore neighbourhood]], the rule can also be written in Hensel notation. However, the resulted rulestring (B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78)<ref name="post35944" /> is very bulky due to reflecting all of the possible configurations of a cell's diagonally adjacent neighbour. A way to get around the issue is to consider the diagonal neighbours of a cell only, leading to an equivalent rule B3c4c/S01c2n3c4c where patterns are rotated 45 degrees.<ref name="post91281" />

Banks-I is a built-in "general binary" rule in [[Mirek's Cellebration]], and also a rule table in [[Golly]] that can be loaded via [[RuleLoader]] even before supporting non-totalistic rules.

==Constructions==

In the PhD thesis, Banks demonstrated how [[signal]] [[circuitry]] can be built in Banks-I. A "wire" consists of a three-cell-thick block of live cells, and a "signal" is carried by a [[duoplet]]-shaped perturbation travelling at [[lightspeed]] along the edge of a wire. A five-cell bump extension and an additional cell on the edge can kill a signal.

{{EmbedViewer
|rle = x = 52, y = 56, 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$16ob3o$o5bo12bo!
|position = center
|viewerconfig = #C [[ ZOOM 8 WIDTH 600 HEIGHT 600 ]]
|caption = The wire, signal and "dead-end" in all orientations 
}}

Signals can be emitted at regular intervals with a "clock". These devices are essentially [[period]]-2n signal [[factory|factories]] driven by [[Rule 90]] [[replicator]] loops.

{{EmbedViewer
|rle = x = 30, y = 16, rule = B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78
5bo11bo$5b13o$bo3b13o$b17o$3obo12bo$4bo5$9bo19bo$9b21o$bo7b21o$b29o$7o
bo20bo$8bo!
|position = center
|viewerconfig = #C [[ ZOOM 8 ]]
|caption = Clocks at period 8 and 16 respectively 
}}

A lone signal can be duplicated when passing a [[fanout]] junction, or [[reflect]]ed 90 degrees.

{{EmbedViewer
|rle = x = 75, y = 28, rule = B3e4ejr5cinqy6-ei78/S012-e3-ajk4-akqw5-ajk6-e78
14b5o30b5o$15b3o32b3o$15b3o32bobo$15b3o32b2o$15b3o32b3o$15b3o32b3o$15b
3o32b3o$15b3o32b3o$15b3o32b3o$15b3o32b3o$o14b3o32b3o$3ob14o15bo16b3o$
2ob31o16b3o$15o3b16o15b4o$o12b2o3b16o16b3o$13b2o3b3o12bo16b3o$12b4o2b
3o28b4o4bo$18b3o30b7o16bo$18b3o30b24o$18b3o30bo6b17o$18b3o37b17o$18b3o
37bo15bo$18b3o$18b3o$18b3o$18b3o$18b3o$17b5o!
|position = center
|viewerconfig = #C [[ ZOOM 8 WIDTH 800 HEIGHT 400 ]]
|caption = The signal duplicator (left) and reflector (right) 
}}

Following these, Boolean logic elements including ANDNOT, NOT and NOR gates have been built, which are sufficient to construct a general purpose computer based on the universal [https://en.wikipedia.org/wiki/NOR_logic NOR logic].

With some new observations in {{year|2017}}, [[Peter Naszvadi]] constructed a [[Rule 110]] [[unit cell]] in Banks-I, proving the rule Turing-complete.<ref name="post52584" />

==References==
<references>
<ref name="post35944">{{LinkForumThread
|p = 35944
|format = ref
|title = "Banks" equivalent
|author = PHPBB12345
|date = September 20, 2016
}}</ref>
<ref name="post91281">{{LinkForumThread
|p = 91281
|format = ref
|title = Re: "Banks" equivalent
|author = Hunting
|date = March 16, 2020
}}</ref>
<ref name="post52584">{{LinkForumThread
|p = 52584
|format = ref
|title = Re: List of the Turing-complete totalistic life-like CA
|author = Peter Naszvadi
|date = November 1, 2017
}}</ref>
</references>

==External links==
*Banks, E. R. (1971) [http://www.bottomlayer.com/bottom/banks/banks_thesis_1971.pdf ''Information processing and transmission in cellular automata''].
{{LinkCatagolueRule|b3e4ejr5cinqy6-ei78s012-e3-ajk4-akqw5-ajk6-e78|rulename=Banks-I}}
{{LinkMirek|rullex_gebi.html#Banks|title=MCell built-in Life rules: Banks}}