UNIFYING ITERATION RULE FOR FRACTAL OBJECTS

We introduce an iteration rule for real numbers capable to generate at tractors with dragon-, snowflake-, sponge-, or Swiss-Bag-like cross se ctions. The idea behind it is the mapping of a torus into two (or more ) shrunken and twisted tori located inside the previous one. Three dis tinct parameters define the symmetry, the dimension, and the connected ness or disconnectedness of the fractal object. For some selected trip les of parameter values, a couple of well known fractal geometries (e. g. the Canter set, the Sierpinski gasket, or the Swiss flag) can be ga ined as special cases.