This fractal pattern is created from a series of dilation sequences. Here is an outline of the objects and steps in this construction:[br][color=#ff0000][br]H={A,B,C,D,E}[/color][br][list][*]H is a set of points that will be the centres of dilation.[br][/*][/list][br][color=#ff0000]S0=Polygon[A,B,C,D][/color] [br][list][*]S0 is the first polygon to be dilated.[br][/*][/list][br][color=#ff0000]S1=Sequence[/color][color=#9900ff][[/color][color=#ff0000]Dilate[/color][color=#0000ff][[/color][color=#ff0000]S0,1/3,Element[/color][color=#00ff00][[/color][color=#ff0000]H,k[/color][color=#00ff00]][/color][color=#0000ff]][/color][color=#ff0000],k,1,5[/color][color=#9900ff]][/color] [br][list][*]This sequence command generates a list of objects which are the results of dilating S0 from 5 centres with a factor of 1/3. The centres are the elements of the set H. [br][/*][/list][br][color=#ff0000]S2=Sequence[/color][color=#9900ff][[/color][color=#ff0000]Dilate[/color][color=#0000ff][[/color][color=#ff0000]S1,1/3,Element[/color][color=#00ff00][[/color][color=#ff0000]H,k[/color][color=#00ff00]][/color][color=#0000ff]][/color][color=#ff0000],k,1,5[/color][color=#9900ff]][/color] [br][list][*]The previous sequence command is used again. This time the object to be dilated is S1, that is the set of 5 objects obtained in the previous step. This process is repeated to create S3, S4 and S5.[br][/*][/list][br]In the end, a slider (n) is added and the objects S0 to S5 can be set to be visible based on the value of n.

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