Date: Mar 7, 2013 10:48 PM
Author: W. Craig Carter
Subject: updating a simulation within Manipulate.

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}}]

{walkerPath = {{0, 0}}},
If[keepWalking, (* kludge warning---testing for If[True...] seems inefficient *)
walkerPath = randomStep[bias, walkerPath]
reset = False; keepWalking = False;
walkerPath = {{0, 0}}
walkerGraphic[walkerPath, range],
{{keepWalking, False}, {True, False}},
{{reset, False}, {True, False}},
{{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