Re: PointSize (and shape) frustration

*To*: mathgroup at smc.vnet.net*Subject*: [mg85919] Re: PointSize (and shape) frustration*From*: "David Park" <djmpark at comcast.net>*Date*: Wed, 27 Feb 2008 04:35:31 -0500 (EST)*References*: <fq0uke$kdp$1@smc.vnet.net>

This is a case where you want to show a 'global' view and a 'detailed' view at the same time. Nice if you can do it, but it depends on the details of screen resolution, or print resolution or the acuity of viewer's eyes. I know that this is not totally responsive to your question, but a standard solution to this kind of problem is to use multiple images, a global view and perhaps several local views in higher detail. lm[r_]:=NestList[r # (1-#)&,.5,50000] bif=Join@@Table[{r,#}&/@Union[Take[lm[r],-100],SameTest->(Abs[#1-#2]<1*^-3&)],{r,2.0,3.98,.001}]; ListPlot[bif, PlotRange -> All, PlotStyle -> AbsolutePointSize[.05]] With[{xmin = 3.4, xmax = 3.7, ymin = .3, ymax = .4}, bif2 = Cases[ bif, {x_, y_} /; xmin <= x <= xmax \[And] ymin <= y <= ymax]; Length[bif2]] ListPlot[bif2, PlotRange -> All, PlotStyle -> AbsolutePointSize[2], ImageSize -> 600] Again, I know that you are looking for printed output, but this is just the type of situation where Mathematica notebooks are so much superior with their dynamic capabilities. The following is a Manipulate definition that allows both global and detailed views. Manipulate[ Graphics[{AbsolutePointSize[2], Point[bif]}, AspectRatio -> 1, PlotRange -> {{xcenter - xwidth/2, xcenter + xwidth/2}, {ycenter - ywidth/2, ycenter + ywidth/2}}, Frame -> True, ImageSize -> {400, 400}], Style["Logistics Map Explorer", 20], Delimiter, {xcenter, 3.1, InputField}, {xwidth, 4, InputField}, Delimiter, {ycenter, .6, InputField}, {ywidth, 1.5, InputField} ] -- David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ "Szabolcs Horv=E1t" <szhorvat at gmail.com> wrote in message news:fq0uke$kdp$1 at smc.vnet.net... > While Mathematica 6 can display beautiful graphics on screen compared to > previous versions, graphics export became extremely frustrating and buggy. > > I complained about several issues before, now here's one more: > > I am trying to plot the bifurcation diagram for the logistic map, point > by point. The point size needs to be tuned precisely to get a nice plot > (for print). Mathematica refuses to export *circular* points to PDF/EPS > below a certain size, but in this case I can live with that. However, > Mathematica refuses to draw points below a certain size, no matter what > the value of PointSize or AbsolutePointSize is!! If the points overlap, > the plot is completely ruined. > > Then I tried using Disk[]s instead of points. On screen it looks fine, > but when exported to PDF, Mathematica does something very strange, and > the result doesn't even have the disks any more! Instead there are some > little crosses on a *regular* grid, approximating the shape of the plot. > > I *know* that 30000 points can inflate the file size, and I know that > arbitrarily small points are not printable/displayable, but I can solve > these problems on my own. I don't want Mathematica to try to be smart > and make its own decisions about this, because it will just cause trouble. > > Here's the code to experiment with (I know that it doesn't produce a > precise result): > > lm[r_] := NestList[r # (1 - #) &, .5, 50000] > > bif = Join @@ Table[ > {r, #} & /@ > Union[Take[lm[r], -100], SameTest -> (Abs[#1 - #2] < 1*^-3 &)], > {r, 2.0, 3.98, .001} > ]; > > plot = ListPlot[bif, PlotRange -> All, PlotStyle -> > AbsolutePointSize[.05]] > > plot = Graphics[{PointSize[.0001], Point[bif]}] > > plot = Graphics[Disk[#, 1/1000] & /@ bif] > > Now try exporting each of these plots at reasonable sizes (i.e. not hal= f > a metre). Remember that exporting PDFs at different sizes only works a= s > Export["plot.pdf", Show[plot, ImageSize -> someValue]] because Export i= s > buggy and does not respect the ImageSize options for PDFs! >