updating a simulation within Manipulate.

• To: mathgroup at smc.vnet.net
• Subject: [mg130075] updating a simulation within Manipulate.
• From: W Craig Carter <ccarter at MIT.EDU>
• Date: Thu, 7 Mar 2013 22:51:42 -0500 (EST)
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```
I *think* I've asked this question before, but I can't find it on mathgroup. In any case, I don't know the answer now.

Here is a simple example of a Manipulate that updates a graphic as long as a boolean is true.  This method seems like a kludge to me---is it? If so, what would be a better way to do this.

This is a constructed example, the real case I am looking at is much more involved; but kudos to anyone who can make a reasonable facsimile of their signature by adjusting the random walker's bias....

randomStep[bias_, stepList_] :=
Module[{angle = RandomVariate[NormalDistribution[bias, 1]]},
Join[stepList, {Last[stepList] + {Cos[angle], Sin[angle]}}]]

walkerGraphic[stepList_, range_] :=
Graphics[GraphicsComplex[stepList, Disk /@ Range[Length[stepList]]],
PlotRange -> range {{-1, 1}, {-1, 1}}]

DynamicModule[
{walkerPath = {{0, 0}}},
Manipulate[
If[keepWalking,  (*  kludge warning---testing for If[True...] seems inefficient   *)
walkerPath = randomStep[bias, walkerPath]
];
If[reset,
reset = False; keepWalking = False;
walkerPath = {{0, 0}}
];
walkerGraphic[walkerPath, range],
{{keepWalking, False}, {True, False}},
{{reset, False}, {True, False}},
Delimiter,
{{range, 20}, 0, 100},
{{a, 0}, -Pi, Pi,
AngularGauge[##, ImageSize -> 160 ,
ScaleOrigin -> {{-4 Pi, 4 Pi}, 1}] &}
]
]

W Craig Carter
Professor of Materials Science, MIT

```

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