Using Map with a function of more than 1 argument

*To*: mathgroup at smc.vnet.net*Subject*: [mg64241] Using Map with a function of more than 1 argument*From*: "Matt" <anonmous69 at netscape.net>*Date*: Tue, 7 Feb 2006 03:36:29 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hello Mathematica group, I'm starting down the path of trying to come up with my own complex mapping function. I'm aware of CartesianMap and PolarMap, but I've been frustrated by those because of the lack of fine control I seem to have (I say 'seem to have' because it might very well be the case that I'm not aware of some of the finer points of these two functions). The fine control that is lacking, is for example, the fact that within CartesianMap, if I want to specify different colors for the lines, I can't really. Let's say I went with the default of $Lines which is I believe 25. In order to have the lines draw in 25 different colours, I believe I'd have to supply 25 color primitives to PlotStyle. If I supply less than 25, then the color primitives are recycled. My first plan of attack was to take the Graphics object that is output by CartesianMap and try to manipulate the coloring primitive for each line drawn based upon starting and ending points (i.e. within a 'Line', if the first point's x value and the last point's x value were 'close', than I knew I was dealing with a vertical line, or if the first point's y value and the last points y value were 'close', then I knew I was dealing with a horizontal line). So, given the Graphics object output by graphicOne = CartesianMap[#1 & , {-1, 1}, {-1, 1}, Lines -> theLines, ImageSize -> {500, Automatic}, PlotStyle -> {RGBColor[1, 0, 0], RGBColor[0, 0, 1]}, PlotPoints -> thePlotPoints]; I was hoping that invoking something like Position[graphicOne, ({RGBColor[__], {Line[_]}})? ((Print[Abs[First[#1[[2,1]]][[1,1]] - Last[#1[[2,1]]][[1,1]]]]; Abs[First[#1[[2,1]]][[1,1]] - Last[#1[[2,1]]][[1,1]]] < 1.*^-9) & )] would give me the positions of all of the horizontal lines, but then, it seems that my lack of familiarity with Mathematica's rules for working with accuracy and precision, led to results that made no sense (i.e. it returned every Line as a match, instead of just the ones where the x-coordinates were 'close'). Even worse than that, I realized that my attempt was doomed to failure because even if I could get that approach to work for a rectangular domain, it would not work once I had applied a function that resulted in a graphic where the lines were curved, twisted and traveling back over themselves. It was at this point that I decided to just work with single lines (i.e. graph a single curve, then operate on each of the points contained within the 'Line' object and then graph the result in another graphic). So, as a first step towards my goal, I thought, "OK, I need to write a function that will be able to be used with Map on a list of points and return the 'transformed' points as well as accept an arbitrary function that will operate on each of the points." Here is what I have thus far: Clear[f, g]; f[z_, func_] := Module[{result}, result = func[Complex[Sequence @@ z]]; {Re[result], Im[result]}]; g[z_] := f[z, #1^2 & ]; Which, using 'g', I can use Map on a list of ordered pairs: g /@ {{x,y}, {x,y}, {x,y}, {x,y}, etc.} If I wanted to use Sin, I would redefine g as follows: g[z_] := f[z, Sin]; then reapply to the list of ordered pairs. So, I'm wondering if there's a way to accomplish my task without the intermediary function definition 'g'? Also, if what I'm attempting is totally wrong, I'd appreciate any pointers as to the correct 'path' as well. Thanks, Matt

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