The radix representation for number systems shows a fractal structure. The complex number system yields some tiles whose boundaries are fractal curves in the complex plane. The fractal code of their iterated function system of the fractiles can be gen...
The radix representation for number systems shows a fractal structure. The complex number system yields some tiles whose boundaries are fractal curves in the complex plane. The fractal code of their iterated function system of the fractiles can be generalized the inverse of an integral matrix as a contraction. There are three affine types of fractiles homeomorphic to a disk with two pieces, and seven types with three pieces from the expensive matrices. Moreover 29 four piece fractiles are derived from tetrominos. We calculate the fractal dimension of the boundary of 29 fractiles in this paper.