kitty2.nb

Transformations, flows, and Arnold's cat

Some linear transformations

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(3 ) horizontal expansion - 2 0 0 1

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(1 ) dilation - 2 0 1 - 0 2

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(3 ) degenerate - 2 1 2 -- -1 3

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( 3) horizontal shear - 1 2 0 1

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(1 Sqrt[3] ) rotation&nbs ... bsp; (by π/3) - ------- 2 2 Sqrt[3] 1 -------- - 2 2

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(1 0 ) reflection 0 -1

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$kittynl[m_, options___] := Show[ParametricPlot[Evaluate[m[#1], Prepend[π/4#2, t]], Displa ... AspectRatio -> 1, Axes -> False, PlotRange -> 2 {{-1, 1}, {-1, 1}}, options]$

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$kittynl[# + .25 {#〚1〛^2, #〚2〛 - #〚1〛} &, DisplayFunction $DisplayFunction]$

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$f1[t_][{x_, y_}] := {x + t x^2, y + t (y - x)}/(1 + t^2)$

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$transf[m_, options___] := Show[GraphicsArray[{Graphics[{{GrayLevel[.5], Arrow[{0, 0}, m . {1, ... 0}, m . {0, 1}]}, AspectRatio->1, PlotRange -> 2 {{-1, 1}, {-1, 1}}], kittym[m, options]}]]$

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Created by Mathematica (November 14, 2003)