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I was playing with a Manipulateto visually compare calculating the mean of Normal and Cauchy random data. 

Manipulate[ ListLinePlot[ { Table[Mean@Take[#, i], {i, 1000}] &[ RandomVariate[NormalDistribution[10, 1], 1000]], Table[Mean@Take[#, i], {i, 1000}] &[ RandomVariate[CauchyDistribution[10, 1], 1000]] }, PlotRange -> Full, DataRange -> n, Frame -> True, Axes -> False ], {n, 50, 1000} ]

The result looks nice, but there is one problem. It regenerates the random data each time I move the slider for n. Is there some way I could set it up so that is only generates new random data when the Manipulate is first evaluated and when a button is pushed?

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3 Answers 3

Reset to default
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DynamicModule[{randomNormal, randomCauchy, newRandomData}, Manipulate[ ListLinePlot[{Table[Mean@Take[#, i], {i, 1000}] &[randomNormal], Table[Mean@Take[#, i], {i, 1000}] &[randomCauchy]}, PlotRange -> Full, DataRange -> n, Frame -> True, Axes -> False], {n, 50, 1000}, Button["New random data", {randomNormal, randomCauchy} = newRandomData[] ]], Initialization :> ( newRandomData[] := RandomVariate[#[10, 1], 1000] & /@ {NormalDistribution, CauchyDistribution}; {randomNormal, randomCauchy} = newRandomData[];) ]
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Simple and elegant

Manipulate[ ListPlot[list, PlotRange -> {{0, n}, {0, 1}}], {{n, 10}, 1, 20, 1}, {{list, RandomReal[1, 10]}, ControlType -> None}, Button["Generate", {ngen = n; list = RandomReal[1, ngen]}] ]
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Manipulate[ SeedRandom[seed]; (...), {n, 50, 1000}, {seed, 0, 100, 1}]
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