Iteration - Revision history

Jfromm at 19:54, 1 February 2012

2012-02-01T19:54:53Z

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	== Recursion vs Iteration ==		== Recursion vs Iteration ==

	We know that iteration of functions or L-systems can lead to self-similar fractals. Both ~~Iteration~~ and Recursion run a part of an algorithm repeatedly, a recursive function calls itself with different parameters, while an iterative function includes a loop, which iterates a pre-determined number of times. Therefore iteration is the analog of recursion.		We know that iteration of functions or L-systems can lead to self-similar fractals. Both iteration and [[Recursion\|recursion]] run a part of an algorithm repeatedly, a recursive function calls itself with different parameters, while an iterative function includes a loop, which iterates a pre-determined number of times. Therefore iteration is the analog of [[Recursion\|recursion]].

	== The network analog of a recursive function ==		== The network analog of a recursive function ==

Jfromm at 13:30, 26 February 2011

2011-02-26T13:30:53Z

← Older revision		Revision as of 08:30, 26 February 2011
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	== The network analog of a recursive function ==		== The network analog of a recursive function ==

	What happens if we add interaction to iteration? What is the network analog of a recursive function? (This was one of the [http://forum.wolframscience.com/showthread.php?threadid=952 ambitious questions] in the Wolfram Science Conference 2006) Is iteration in a network of connected nodes the counterpart of a certain recursive function? Iteration in a network of connected nodes leads to nested propagation loops. The patterns in [[Cellular Automata\|CA]] are an example of such nested propagation loops.		What happens if we add interaction to iteration? What is the network analog of a recursive function? (This was one of the [http://forum.wolframscience.com/showthread.php?threadid=952 ambitious questions] in the Wolfram Science Conference 2006) Is iteration in a network of connected nodes the counterpart of a certain recursive function? Iteration in a network of connected nodes leads to nested propagation loops. The patterns in [[Cellular Automata\|CA]] and [[Random_Boolean_Network\|RBN]] are an example of such nested propagation loops.

	== Links ==		== Links ==

Jfromm: /* The network analog of a recursive function */

2011-02-26T13:28:17Z

The network analog of a recursive function

← Older revision		Revision as of 08:28, 26 February 2011
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	== The network analog of a recursive function ==		== The network analog of a recursive function ==

	What happens if we add interaction to iteration? What is the network analog of a recursive function? (This was one of the [~~ambitious questions~~ http://forum.wolframscience.com/showthread.php?threadid=952] in the Wolfram Science Conference 2006) Is iteration in a network of connected nodes the counterpart of a certain recursive function? Iteration in a network of connected nodes leads to nested propagation loops. The patterns in [[Cellular Automata\|CA]] are an example of such nested propagation loops.		What happens if we add interaction to iteration? What is the network analog of a recursive function? (This was one of the [http://forum.wolframscience.com/showthread.php?threadid=952 ambitious questions] in the Wolfram Science Conference 2006) Is iteration in a network of connected nodes the counterpart of a certain recursive function? Iteration in a network of connected nodes leads to nested propagation loops. The patterns in [[Cellular Automata\|CA]] are an example of such nested propagation loops.

	== Links ==		== Links ==

Jfromm at 13:27, 26 February 2011

2011-02-26T13:27:55Z

← Older revision		Revision as of 08:27, 26 February 2011
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	== The network analog of a recursive function ==		== The network analog of a recursive function ==

	What happens if we add interaction to iteration? What is the network analog of a recursive function? Is iteration in a network of connected nodes the counterpart of a certain recursive function?		What happens if we add interaction to iteration? What is the network analog of a recursive function? (This was one of the [ambitious questions http://forum.wolframscience.com/showthread.php?threadid=952] in the Wolfram Science Conference 2006) Is iteration in a network of connected nodes the counterpart of a certain recursive function? Iteration in a network of connected nodes leads to nested propagation loops. The patterns in [[Cellular Automata\|CA]] are an example of such nested propagation loops.

	== Links ==		== Links ==

Jfromm at 13:21, 26 February 2011

2011-02-26T13:21:02Z

← Older revision		Revision as of 08:21, 26 February 2011
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	: "Iteration is the mathematical counterpart of feedback. Feedback in general is any response to something sent out. In mathematics, that translates as "what goes out comes back in again." It is output that returns to serve as input. In temporal processes, feedback is that part of the past that influences the present, or that part of the present that influences the future. Positive feedback amplifies or accelerates the output. It causes an event to become magnified over time. Negative feedback dampens or inhibits output, or causes an event to die away over time. Feedback shows up in climate, biology, electrical engineering, and probably in most other fields in which processes continue over time." (from Chaos Theory Tamed by G. P. Williams)		: "Iteration is the mathematical counterpart of feedback. Feedback in general is any response to something sent out. In mathematics, that translates as "what goes out comes back in again." It is output that returns to serve as input. In temporal processes, feedback is that part of the past that influences the present, or that part of the present that influences the future. Positive feedback amplifies or accelerates the output. It causes an event to become magnified over time. Negative feedback dampens or inhibits output, or causes an event to die away over time. Feedback shows up in climate, biology, electrical engineering, and probably in most other fields in which processes continue over time." (from Chaos Theory Tamed by G. P. Williams)

			== Recursion vs Iteration ==

			We know that iteration of functions or L-systems can lead to self-similar fractals. Both Iteration and Recursion run a part of an algorithm repeatedly, a recursive function calls itself with different parameters, while an iterative function includes a loop, which iterates a pre-determined number of times. Therefore iteration is the analog of recursion.

	== The network analog of a recursive function ==		== The network analog of a recursive function ==

	What is the network analog of a recursive function? Is iteration in a network of connected nodes the counterpart of a recursive function?		What happens if we add interaction to iteration? What is the network analog of a recursive function? Is iteration in a network of connected nodes the counterpart of a certain recursive function?

			== Links ==

			* Wikipedia entry for [http://en.wikipedia.org/wiki/Fractal Fractal]
			* Wikipedia entry for [http://en.wikipedia.org/wiki/L-system L-system]
			* Wikipedia entry for [http://en.wikipedia.org/wiki/Iterated_function_system Iterated function system]

	[[Category:Basic Principles]]		[[Category:Basic Principles]]

Jfromm at 13:10, 26 February 2011

2011-02-26T13:10:57Z

← Older revision		Revision as of 08:10, 26 February 2011
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	: "Iteration is the mathematical counterpart of feedback. Feedback in general is any response to something sent out. In mathematics, that translates as "what goes out comes back in again." It is output that returns to serve as input. In temporal processes, feedback is that part of the past that influences the present, or that part of the present that influences the future. Positive feedback amplifies or accelerates the output. It causes an event to become magnified over time. Negative feedback dampens or inhibits output, or causes an event to die away over time. Feedback shows up in climate, biology, electrical engineering, and probably in most other fields in which processes continue over time." (from Chaos Theory Tamed by G. P. Williams)		: "Iteration is the mathematical counterpart of feedback. Feedback in general is any response to something sent out. In mathematics, that translates as "what goes out comes back in again." It is output that returns to serve as input. In temporal processes, feedback is that part of the past that influences the present, or that part of the present that influences the future. Positive feedback amplifies or accelerates the output. It causes an event to become magnified over time. Negative feedback dampens or inhibits output, or causes an event to die away over time. Feedback shows up in climate, biology, electrical engineering, and probably in most other fields in which processes continue over time." (from Chaos Theory Tamed by G. P. Williams)

			== The network analog of a recursive function ==

			What is the network analog of a recursive function? Is iteration in a network of connected nodes the counterpart of a recursive function?

	[[Category:Basic Principles]]		[[Category:Basic Principles]]

Jfromm at 12:58, 26 February 2011

2011-02-26T12:58:20Z

← Older revision		Revision as of 07:58, 26 February 2011
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	: "Iteration is the mathematical counterpart of feedback. Feedback in general is any response to something sent out. In mathematics, that translates as "what goes out comes back in again." It is output that returns to serve as input. In temporal processes, feedback is that part of the past that influences the present, or that part of the present that influences the future. Positive feedback amplifies or accelerates the output. It causes an event to become magnified over time. Negative feedback dampens or inhibits output, or causes an event to die away over time. Feedback shows up in climate, biology, electrical engineering, and probably in most other fields in which processes continue over time." (from Chaos Theory Tamed by G. P. Williams)		: "Iteration is the mathematical counterpart of feedback. Feedback in general is any response to something sent out. In mathematics, that translates as "what goes out comes back in again." It is output that returns to serve as input. In temporal processes, feedback is that part of the past that influences the present, or that part of the present that influences the future. Positive feedback amplifies or accelerates the output. It causes an event to become magnified over time. Negative feedback dampens or inhibits output, or causes an event to die away over time. Feedback shows up in climate, biology, electrical engineering, and probably in most other fields in which processes continue over time." (from Chaos Theory Tamed by G. P. Williams)

			[[Category:Basic Principles]]

Jfromm: Created page with "Iteration is related to feedback, it is the mathematical counterpart of feedback: : "Iteration is the mathematical counterpart of feedback. Feedback in general is a..."

2011-02-26T12:54:58Z

Created page with "Iteration is related to feedback, it is the mathematical counterpart of feedback: : "Iteration is the mathematical counterpart of feedback. Feedback in general is a..."

New page

Iteration is related to [[Feedback|feedback]], it is the mathematical counterpart of feedback:

: "Iteration is the mathematical counterpart of feedback. Feedback in general is any response to something sent out. In mathematics, that translates as "what goes out comes back in again." It is output that returns to serve as input. In temporal processes, feedback is that part of the past that influences the present, or that part of the present that influences the future. Positive feedback amplifies or accelerates the output. It causes an event to become magnified over time. Negative feedback dampens or inhibits output, or causes an event to die away over time. Feedback shows up in climate, biology, electrical engineering, and probably in most other fields in which processes continue over time." (from Chaos Theory Tamed by G. P. Williams)