Re: Color grid with x and y args to visualize effects of 2D

*To*: mathgroup at smc.vnet.net*Subject*: [mg0] Re: Color grid with x and y args to visualize effects of 2D*From*: Fred Bartoli <myname_with_a_dot_inbetween at free.fr>*Date*: Mon, 21 Feb 2011 05:40:16 -0500 (EST)*References*: <ijo588$lk8$1@smc.vnet.net> <ijqqmc$ars$1@smc.vnet.net>*Reply-to*: myname_with_a_dot_inbetween at free.fr

Christopher O. Young a écrit : > On 2/19/11 5:15 AM, in article ijo588$lk8$1 at smc.vnet.net, "Christopher O. > Young" <cy56 at comcast.net> wrote: > >> I'm trying to get a simple kind of color chart function that I can pass x >> and as arguments to. I want to have it running across by hue and up by >> saturation and value. This is to illustrate 2D transformations, so I need to >> have arguments that I can _inversely_ transform in order to illustrate the >> effects of 2D transformations, whether linear or not. >> >> One direct approach would seem to have nested loops, but I can't see how to >> do this if the body of the For loop in Mathematica is part of the function. >> >> Any help getting a "jump start" in this kind of thing would be a huge help >> to me. >> >> For[i = 0, i < 10, i++, >> >> For[j = 0, j < 10, j++, >> >> RegionPlot[(i < x < i + 1) && (j < y < j + 1), {x,0,10}, {y,0,10}] >> >> ] >> >> ] > > > As shown at http://home.comcast.net/~cy56/Grid.nb, I finally got a color > grid with x and y as arguments, but it's hard to believe there isn't a > simpler way to do it. It's quite a struggle to figure out how to specify the > colors. If high school students are going to be comfortable with doing these > visualizations, there needs to be a way to simplify this radically, I think. > > I need to have the arguments x and y since I want to be able to transform > the grid by transforming x and y using the inverse transform. > > RegionPlot[ > {0 < x < 1 && 0 < y < 1, > 0 < x < 1 && 1 < y < 2, > 0 < x < 1 && 2 < y < 3, > 1 < x < 2 && 0 < y < 1, > 1 < x < 2 && 1 < y < 2, > 1 < x < 2 && 2 < y < 3, > 2 < x < 3 && 0 < y < 1, > 2 < x < 3 && 1 < y < 2, > 2 < x < 3 && 2 < y < 3}, > {x, 0, 3}, {y, 0, 3}, > ColorFunction -> Function[{x, y}, > Hue[\[LeftFloor]x\[RightFloor]/3, .5 + .5 \[LeftFloor]y\[RightFloor]/3, > 1]], > ColorFunctionScaling -> False > ] > > > I still can't figure out how to use Table or whatever to get the region > specifications into a general function. > > mappingFunc[{x_, y_, scale_}] = {x/scale, y/scale}; (* or, if you want to vary brightness as well and get your students lost :-) mappingFunc[{x_, y_, scale_}] = {x/scale, y/scale, yourbrightnessfunction[x,y]}; *) data[n_] := Table[mappingFunc@{j, i, n}, {i, 0, n}, {j, 0, n}] data[3] Graphics@Raster[data[10], ColorFunction -> Hue, ColorFunctionScaling -> False] -- Thanks, Fred.