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Another update from ingydotnet^djgoku

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Ingy döt Net 2015-11-18 06:14:39 +00:00
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10
Task/Percolation-Mean-run-density/00DESCRIPTION
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{{Percolation Simulation}}
Let <math>v</math> be a vector of <math>n</math> values of either <tt>1</tt> or <tt>0</tt> where the probability of any
value being <tt>1</tt> is <math>p</math>, (and <tt>0</tt> is therefore <math>1-p</math>).
Define a run of <tt>1</tt>'s as being a group of consecutive <tt>1</tt>'s in the vector bounded
either by the limits of the vector or by a <tt>0</tt>. Let the number of runs in a
value being <tt>1</tt> is <math>p</math>; the probability of a value being <tt>0</tt> is therefore <math>1-p</math>.
Define a run of <tt>1</tt>s as being a group of consecutive <tt>1</tt>s in the vector bounded
either by the limits of the vector or by a <tt>0</tt>. Let the number of such runs in a given
vector of length <math>n</math> be <math>R_n</math>.
The following vector has <math>R_{10} = 3</math>
For example, the following vector has <math>R_{10} = 3</math>
<pre>
[1 1 0 0 0 1 0 1 1 1]
^^^ ^ ^^^^^
@ -22,7 +22,7 @@ computed as the average of <math>t</math> runs, where <math>t \ge 100</math>.
For values of <math>p</math> of 0.1, 0.3, 0.5, 0.7, and 0.9, show the effect of varying <math>n</math>
on the accuracy of simulated <math>K(p)</math>.
Show your output here
Show your output here.
;See also
* [http://mathworld.wolfram.com/s-Run.html s-Run] on Wolfram mathworld.