Bell - Revision history

Polygon: Reorgansied the images

2026-03-28T20:14:50Z

Reorgansied the images

← Older revision		Revision as of 20:14, 28 March 2026
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	where <math>a_0=1</math> and <math>a_k=2a_{k-1}+3\text{ for }k\geq 1.</math>		where <math>a_0=1</math> and <math>a_k=2a_{k-1}+3\text{ for }k\geq 1.</math>

	[[File:1RB0LC 1LA1RB 0RA1LC.png\|thumb\|Spacetime diagram of the cubic bell <span style="white-space: nowrap">{{TM\|1RB0LC_1LA1RB_0RA1LC}}.</span>]] [[File:1RB0LC 1LA1RB 0RA1LC explore.png\|thumb\|300px\|Close-up of the cubic bell <span style="white-space: nowrap">{{TM\|1RB0LC_1LA1RB_0RA1LC}}.</span>]]
	=== Cubic bell ===		=== Cubic bell ===
	{{TM\|1RB0LC_1LA1RB_0RA1LC}} is an example of a cubic bell with 3 states and 2 symbols.		{{TM\|1RB0LC_1LA1RB_0RA1LC}} is an example of a cubic bell with 3 states and 2 symbols.
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	==== Analysis ====		==== Analysis ====
	'''Transcript''': ((A0 B1<sup>k</sup> B0 A1 C1<sup>k</sup> C0 A1 C0)<sup>(k = n, n-1, .. 1)</sup> A0 B0 A1 C0)<sup>(n ≥ 0)</sup>.		'''Transcript''': ((A0 B1<sup>k</sup> B0 A1 C1<sup>k</sup> C0 A1 C0)<sup>(k = n, n-1, .. 1)</sup> A0 B0 A1 C0)<sup>(n ≥ 0)</sup>.

			<table><td>[[File:1RB0LC 1LA1RB 0RA1LC.png\|thumb\|Spacetime diagram of the cubic bell <span style="white-space: nowrap">{{TM\|1RB0LC_1LA1RB_0RA1LC}}.</span>]]</td><td>[[File:1RB0LC 1LA1RB 0RA1LC explore.png\|thumb\|300px\|Close-up of the cubic bell <span style="white-space: nowrap">{{TM\|1RB0LC_1LA1RB_0RA1LC}}.</span>]]</td></table>

	[[Category: Zoology]]		[[Category: Zoology]]

Polygon: Used Template:Stub

2025-08-10T22:28:18Z

Used Template:Stub

← Older revision		Revision as of 22:28, 10 August 2025
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			{{Stub}}
	A '''bell''' is a [[non-halting Turing machine]] whose behavior can be described as a sequence of [[bouncer]]s of increasing size. There are two main variants of bells, depending on whether the bouncers participate in tape growth or not. A bell whose bouncers grow the tape on each bounce is called an '''exponential bell''' or simply '''bell''' for short, while a bell whose bouncers do not grow the tape on each bounce is called a '''cubic bell'''.		A '''bell''' is a [[non-halting Turing machine]] whose behavior can be described as a sequence of [[bouncer]]s of increasing size. There are two main variants of bells, depending on whether the bouncers participate in tape growth or not. A bell whose bouncers grow the tape on each bounce is called an '''exponential bell''' or simply '''bell''' for short, while a bell whose bouncers do not grow the tape on each bounce is called a '''cubic bell'''.

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	[[Category: Zoology]]		[[Category: Zoology]]
	~~[[Category: Stub]]~~

Sligocki: link transcript

2024-11-16T05:08:34Z

link transcript

← Older revision		Revision as of 05:08, 16 November 2024
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	==== Analysis ====		==== Analysis ====
	'''Transcript''': (A0 B0 ((C1 B0)<sup>2k</sup> (C0 A1)<sup>2k+1</sup>)<sup>(k = 0 .. n-1)</sup> (C0 B1)<sup>2n</sup> (C0 A1)<sup>2n</sup> C0 (A0 B1)<sup>2n+1</sup>)<sup>n=''a''<sub>0</sub>, ''a''<sub>1</sub>, ...</sup>,		'''[[Transcript]]''': (A0 B0 ((C1 B0)<sup>2k</sup> (C0 A1)<sup>2k+1</sup>)<sup>(k = 0 .. n-1)</sup> (C0 B1)<sup>2n</sup> (C0 A1)<sup>2n</sup> C0 (A0 B1)<sup>2n+1</sup>)<sup>n=''a''<sub>0</sub>, ''a''<sub>1</sub>, ...</sup>,

	where <math>a_0=1</math> and <math>a_k=2a_{k-1}+3\text{ for }k\geq 1.</math>		where <math>a_0=1</math> and <math>a_k=2a_{k-1}+3\text{ for }k\geq 1.</math>

C7X: Add correct machine and bbch link /* Examples */

2024-11-16T04:35:17Z

Add correct machine and bbch link Examples

← Older revision		Revision as of 04:35, 16 November 2024
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	where <math>a_0=1</math> and <math>a_k=2a_{k-1}+3\text{ for }k\geq 1.</math>		where <math>a_0=1</math> and <math>a_k=2a_{k-1}+3\text{ for }k\geq 1.</math>

	[[File:1RB0LC 1LA1RB 0RA1LC.png\|thumb\|Spacetime diagram of the cubic bell <span style="white-space: nowrap">{{TM\|~~1RB0LC_1RC1RA_1LA0RB~~}}.</span>]] [[File:1RB0LC 1LA1RB 0RA1LC explore.png\|thumb\|300px\|Close-up of the cubic bell <span style="white-space: nowrap">{{TM\|~~1RB0LC_1RC1RA_1LA0RB~~}}.</span>]]		[[File:1RB0LC 1LA1RB 0RA1LC.png\|thumb\|Spacetime diagram of the cubic bell <span style="white-space: nowrap">{{TM\|1RB0LC_1LA1RB_0RA1LC}}.</span>]] [[File:1RB0LC 1LA1RB 0RA1LC explore.png\|thumb\|300px\|Close-up of the cubic bell <span style="white-space: nowrap">{{TM\|1RB0LC_1LA1RB_0RA1LC}}.</span>]]
	=== Cubic bell ===		=== Cubic bell ===
	{{TM\|1RB0LC_1LA1RB_0RA1LC}} is an example of a cubic bell with 3 states and 2 symbols.		{{TM\|1RB0LC_1LA1RB_0RA1LC}} is an example of a cubic bell with 3 states and 2 symbols.

Icy: Mentioned 5-state winner

2024-11-13T15:57:28Z

Mentioned 5-state winner

← Older revision		Revision as of 15:57, 13 November 2024
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	A '''bell''' is a [[non-halting Turing machine]] whose behavior can be described as a sequence of [[bouncer]]s of increasing size. There are two main variants of bells, depending on whether the bouncers participate in tape growth or not. A bell whose bouncers grow the tape on each bounce is called an '''exponential bell''' or simply '''bell''' for short, while a bell whose bouncers do not grow the tape on each bounce is called a '''cubic bell'''.		A '''bell''' is a [[non-halting Turing machine]] whose behavior can be described as a sequence of [[bouncer]]s of increasing size. There are two main variants of bells, depending on whether the bouncers participate in tape growth or not. A bell whose bouncers grow the tape on each bounce is called an '''exponential bell''' or simply '''bell''' for short, while a bell whose bouncers do not grow the tape on each bounce is called a '''cubic bell'''.

			Sometimes a Turing machine displays bell characteristics for some number of steps before phase transitioning to another behavior, such as halting. A famous example is the [[5-state busy beaver winner]]. These may also be called bells, or more precisely, '''transient bells''', to indicate that they only show bell-like features up to a certain point.

	== Examples ==		== Examples ==

Icy: Added page. TODO: Add derivation of transcripts

2024-11-13T15:54:21Z

Added page. TODO: Add derivation of transcripts

New page

A '''bell''' is a [[non-halting Turing machine]] whose behavior can be described as a sequence of [[bouncer]]s of increasing size. There are two main variants of bells, depending on whether the bouncers participate in tape growth or not. A bell whose bouncers grow the tape on each bounce is called an '''exponential bell''' or simply '''bell''' for short, while a bell whose bouncers do not grow the tape on each bounce is called a '''cubic bell'''.

== Examples ==

[[File:1RB0LC 1RC1RA 1LA0RB.png|thumb|300px|Spacetime diagram of the bell {{TM|1RB0LC_1RC1RA_1LA0RB}}.]]
=== Exponential bell ===

{{TM|1RB0LC_1RC1RA_1LA0RB}} is an example of an exponential bell with 3 states and 2 symbols.

==== Analysis ====
'''Transcript''': (A0 B0 ((C1 B0)2k (C0 A1)2k+1)(k = 0 .. n-1) (C0 B1)2n (C0 A1)2n C0 (A0 B1)2n+1)n=''a''0, ''a''1, ...,

where <math>a_0=1</math> and <math>a_k=2a_{k-1}+3\text{ for }k\geq 1.</math>

[[File:1RB0LC 1LA1RB 0RA1LC.png|thumb|Spacetime diagram of the cubic bell {{TM|1RB0LC_1RC1RA_1LA0RB}}.]] [[File:1RB0LC 1LA1RB 0RA1LC explore.png|thumb|300px|Close-up of the cubic bell {{TM|1RB0LC_1RC1RA_1LA0RB}}.]]
=== Cubic bell ===
{{TM|1RB0LC_1LA1RB_0RA1LC}} is an example of a cubic bell with 3 states and 2 symbols.

==== Analysis ====
'''Transcript''': ((A0 B1k B0 A1 C1k C0 A1 C0)(k = n, n-1, .. 1) A0 B0 A1 C0)(n ≥ 0).

[[Category: Zoology]]
[[Category: Stub]]