EXPLOOT project
Ivan Cnop 
icnop@vub.ac.be

Matrix acting on a set of points

Make a new logo

Feeding points

Plot[0, {x, -2, 2}, PlotRange -> {{-2, 2}, {-2, 2}}, 
      AspectRatio -> Automatic, Axes -> True]

Highlight this empty graphic and add select by mouse some dots (holding the appropriate keys down)

Perform Copy-Paste before doing anything else, and give the list of points a name. Make shure that a polygon will close by adding the same point at the beginning and at the end (here we chose the origin)

block = {{0. , 0. }, {0.00431628, 0.251795}, {0.00863287, 
            0.467624}, {0.0863287, 0.71223}, {0.0719402, 
            0.928059}, {0.143883, 1.1295}, {0.302158, 1.21583}, {0.446044, 
            1.17267}, {0.474821, 1.02878}, {0.431655, 0.899282}, {0.374101, 
            0.784173}, {0.330935, 0.71223}, {0.287769, 0.61151}, {0.273381, 
            0.482012}, {0.316546, 0.539567}, {0.374101, 0.61151}, {0.446044, 
            0.71223}, {0.561152, 0.741007}, {0.604318, 0.654675}, {0.58993, 
            0.597121}, {0.517987, 0.525178}, {0.460432, 0.482012}, {0.374101, 
            0.424458}, {0.316546, 0.381292}, {0.258992, 0.323738}, {0.17266, 
            0.223017}, {0.115106, 0.179852}, {0.0143857, 0.00935202}, {0. , 
            0. }};

Show[Graphics[Polygon[block]], PlotRange -> {{-2, 2}, {-1, 2}}, 
      AspectRatio -> Automatic, Axes -> True]

Selecting a matrix

A=(({{.82, - .68}, {.88, .42}}))

Eigenvalues[A]

Abs[%]

Apply this matrix a large number of times

k = 30;

matrices = 
        NestList[(A . #) &, IdentityMatrix[2], k];

\(\(Table[
	{Hue[ .05\ j], 
          Polygon[
		Table[
              matrices[\([j]\)] . block[\([l]\)], {l, 
                Length[block]}
		]]}
		, {j, 
          Length[matrices]}];\)\)

Show[Graphics[%], PlotRange -> {{-2, 2}, {-2, 2}}, 
      AspectRatio -> Automatic, Axes -> True]

Try this for many different shapes, (slightly) different matrices and different colourings.
Printing this (without axes) makes a nice  heading for Mother's Day [9/5] greeting card.