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An Important Class of Fractals

   One of important classes of fractals is represented by parameterized curves. A continuous curve definition was appeared in J.Hutchinson's paper "Fractals and Self Similarity"
   Definition: Iterated Function System F=IFS(X;S1,..,Sn) is called a fractal parameterized curve if the following condition is satisfied:    Hutchinson proved that for any system of contraction, with such condition, there exist a continuous map f from [0,1] segment to F, such that f( [0,1] ) = F.
   The most known fractal curves are: Koch curve, Levy curve, Peano curve and Sierpinsky triangle. Regrettably Dragon set does not satisfy Hutchinson's fractal curve definition. The following Java applet can draw some continuous curves which approximates a curves and sets considered above.
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