again.. fractals

From the foundation work of Mandelbrot, fractal geometry provides a way to
describe and to model aesthetic object, especially for those not easily created by Euclidean geometry. Fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly
exceeds the topological dimension. It is used to describe the fragmentation of an object. A
common property of fractal object is self-similar, i.e. a fractal is a shape made of parts similar to
the whole in some way. One deterministic approach to generate or to approximate a
mathematical fractal object is to use Iteration function system (IFS) . An IFS is a family of
specified contraction mappings that map a whole object onto the parts, unionize all the parts and
iteration of these mappings will result in convergence to an invariant set , i.e. a fractal. From
the viewpoint of geometric modeling, unionization in IFS is regularized in order to maintain the
validity of the operands in further iteration.
In particular, the quadric
Fractal curves are self-similar and continuous, but they are nowhere differentiable. The quadric Koch curve consists of a generator and an initiator. The generator is a multi-segment polyline (S) which is also used to derive the IFS. The initiator is a square which is used to derive transformations for replicating other copies.