Re: Ploting a transformation of a set
- To: mathgroup at smc.vnet.net
- Subject: [mg123440] Re: Ploting a transformation of a set
- From: Dan <dflatin at rcn.com>
- Date: Wed, 7 Dec 2011 06:15:51 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <4EDCB5F0.813B.006A.0@newcastle.edu.au> <jbkj0l$i30$1@smc.vnet.net>
Another approach would be to look at the transformation of the grid. I
find this sort of visualization more informative for these sorts of
mappings. For example:
With[{n=10,c1=ColorData[1][1],c2=ColorData[1][2]},
refGrid=Show[{
ParametricPlot[Table[{2t,2(k/n)},{k,n}],{t,0,1},PlotStyle->c1],
ParametricPlot[Table[{2(k/n),2t},{k,n}],{t,0,1},PlotStyle->c2]
},ImageSize->200];
Manipulate[
Module[{map},
map=({x,y}\[Function]{(x+a y)^b,(a x+y)^b});
Grid[{{
refGrid,
Show[{
ParametricPlot[Table[map@@{2t,2(k/n)},{k,n}],{t,
0,1},PlotStyle->c1],
ParametricPlot[Table[map@@{2(k/n),2t},{k,n}],{t,
0,1},PlotStyle->c2]
},ImageSize->200]
}}]
],
{{a,0.5},0,1,0.05},
{{b,0.5},0.1,1,0.05}
]
]
-- Dan