New Classes of Regular Symmetric Fractals

The paper introduces new fractal families many of which approach optimal information dimension for annular and checkerboard structures and include the Sierpinski carpet and the Menger sponge as special cases. The complementary mapping is defined, and a notation to represent the families is proposed. The new classes represent an enhanced set that goes beyond the recently published results on optimal information dimensionality and they can be expected to have applications in natural and engineered self-similar systems.