{{3,-2},{1,0}}. The matrix has two independent eigenvectors {1,1} and {2,1}, indicated by blue lines. Their significance is that points on those lines will remain on those lines.The following are images of transformations in the plane.
{{3,-2},{1,0}}. The matrix has two independent eigenvectors {1,1} and {2,1}, indicated by blue lines. Their significance is that points on those lines will remain on those lines.
Function[{x,y},({{Cos[#1 n],-Sin[#1 n]},{Sin[#1 n],Cos[#1 n]}}&)[Norm[{x,y}]].{x,y}]
Sin[Norm[v]] * 0.4 * Normalize[v] + v applied to a wallpaper design.
Function[{#1,#2}/(Sqrt[#1^2 +#2^2] + 5)] applied to a wallpaper design of stars. This function is often called fish-eye lens.
Function[{#2, Cos[#1*#2]}] applied to a polar grid.
The notation used on this page is from Mathematica.
{x,y}.Function[#1^2]. The #1 is the first argument and #2 indicate second argument, and so on.Function[#1+#2] is the same as Function[{x,y},x+y], and Function[{#2, Cos[#1*#2]}] is the same as Function[{x,y}, {y, Cos[x*y]}] or f[x_,y_]:={y, Cos[x*y]}.{a,b}*c means {a*c,b*c}. It is automatically distributive. {a,b}/c means {a/c, b/c}.{{a,b},{c,d}}, with {a,b} being the top row.{{a,b},{c,d}} . {x,y} means matrix multiplication with the vector {x,y}, resulting: {a x + b y, c x + d y}.Norm[{x,y}] is the length of a vector {x,y}.Normalize[{x,y}] is the unit vector of {x,y}.These graphics are generated by my Mathematica packages Transform2DPlot.m and PlaneTiling.m. You can get them at Mathematica Package: Geometric Transformation ＆ Complex Function Plot and Geometry: Plane Tiling Mathematica Package.
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