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Traditionally simple object is drawn to the screen by drawing functions in pixels, so the slight different form of object should be redrawn by different function. On the other hand, naturally fractal object is drawn by a single algorithm through drawing pixels at the position according to the code of fractal such as IFS code, and interactively to change the form of or to animate the fractal object is accomplished simply by changing the code of fractal at any time. So in this case, animation model of objects in fractal form has an advantage over animation model of objects in traditional form. IFS code is one way of the inverse problem representation of object in fractal form. The IFS fractal objects can be reconstructed by random iteration algorithm and the multi-object of fractal can be reconstructed by partitioned-random iteration algorithm from the IFS code sets. To have the metamorphic animation, the interpolation between the IFS code of source and target objects can be done by a metamorphic animation algorithm. The hybrid animation model is the combination model of a metamorphic animation on one type of object and the multi-object animation independently with or without synchronized mode based on the metamorphic interpolation of IFS code coefficients for the metamorphic animation and the partitioned-random iteration algorithm for the multiobject animation.

A set of artistic characters can be generated by the inverse problem method in the fractal model, which has an advantage over the traditional model in recycling the flexible art composition. The code of iterated function systems of a fractal can be generated by composing the interrelated components in the collage composition design iteratively based on the collage theorem which is ruled by a set of self-affine transformations. The fractal result is displayed by means of the partitioned-random iteration algorithm as the decoding process of multi-object of fractals as the collection of the artistic characters. The number of the partition is set based on the number of characters in a composition of the artistic characters accordingly, so the individual self-affine transformation of a character can be modified independently.

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