Fractal generator: tips   The fractal generator is an application that the developers of Excel probably did not have in mind for their package. It creates graphical images of a certain type of fractals that can be constructed by linear transformations: rotations, line mirrors, multiplications and translations. The probability parameters can be used to make one operation occur more frequent than an other, which may give a more optimal distribution of the points over the graph. The probability parameters will however not affect the shape of the fractal. To play around with the parameters I suggest that you stick to simple operations at first and keep some symmetry between the operations, like with operations 2 and 3 in the above example. Such symmetry is likely to give the most attractive graphs. Using rotations and mirror operations over multiples of 45 degrees is also a good starting point. If you try to create a certain shape, it is best to start by defining a coordinate system around the target shape. Then search for the operations that, within the chosen coordinate system, transform the overall shape into its composing parts. For instance, in the fern shape of the example the coordinate system can be chosen such that the bottom left corner is represented by (-1,0) and the top right corner by (1,1). There are two multiplying rotations, each followed by a translation, that transform the overall triangular shape into the largest right and left leaves. And there is one more multiplication (with its origin at the top of the fern) that transforms the overall shape into its top part. Finally add a small rotation to this last operation to make the fern bend a little. This approach gives different parameters than are shown in the example (which uses additional translations in conjunction with each of the three multiplication operations), but the outcome will be more or less similar.

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