Re: Manipulate[Plot[Evaluate[expr]]]

*To*: mathgroup at smc.vnet.net*Subject*: [mg125708] Re: Manipulate[Plot[Evaluate[expr]]]*From*: "djmpark" <djmpark at comcast.net>*Date*: Thu, 29 Mar 2012 03:04:08 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <21038857.41440.1332916309211.JavaMail.root@m06>

Other than the extra brackets, there are several other problems with this presentation. One is that the starting values of the sliders should be specified separately from the parameter domains to obtain a smooth action of the sliders. The second problem is that there is, or should be, a maxim: A dynamic presentation always requires a fixed background. This is often violated by allowing Mathematica to automatically adjust the PlotRange. Then one has a varying curve against a varying scale and it is not as easy to see how the parameter affects the shape of the curve. Specifying a fixed PlotRange is one solution to this problem. However, in this case there is a rather large overall vertical range for the function as the parameters are changed. One way to handle this is to provide an additional slider to independently adjust the vertical PlotRange. So then, at least, the background is stable while any of the function parameters are being changed. Manipulate[ Plot[M/\[Tau] \[Phi]^ M E^(-(x/\[Tau])) (1 - E^(-(x/\[Tau])))^(M - 1), {x, 0, 50}, AspectRatio -> 1/2, Frame -> False, PlotRange -> {{0, 50}, {0, 10^ymax}}, PlotRangePadding -> {0.2, 10^ymax/10}, ImagePadding -> {{25, 5}, {15, 5}}, ImageSize -> {430, 220}], {{M, 5.5}, 1, 12, Appearance -> "Labeled"}, {{\[Tau], 9}, 3, 15, Appearance -> "Labeled"}, {{\[Phi], .65}, .5, .8, Appearance -> "Labeled"}, {{ymax, -2.3}, -5, -1}] There are other possibilities. One would be to have a button that finds the maximum value for the function and then snaps the PlotRange to accommodate. Another solution would be to have two curves and a left and right scale with one always showing the full y range and the other showing the adjusted range. Then we would obtain an absolute picture of the function behavior along with an adjustable magnified version. But these get more into custom dynamic presentations. David Park djmpark at comcast.net http://home.comcast.net/~djmpark/index.html From: leigh pascoe [mailto:leigh at evry.inserm.fr] Could someone please help me with the syntax of a dynamic plot? I would like to plot a function with 3 constants, for various values of the constants (M, t and f say) and for the variable x going from zero to 50. I have been unable to find the correct syntax for the Manipulate/Plot command. Here is one attempt that shows the function to be evaluated and the 3 constants Manipulate[ Plot[M/\[Tau] \[Phi]^M E^(-(x/\[Tau])) (1 - E^(-(x/\[Tau])))^( M - 1), {x, 0, 50}], {{M, 1, 12, 1}, {\[Tau], 3, 15, 1}, {\[Phi], .5, .8, .1}}] Any suggestions would be appreciated. LP