Disk-like tiles derived from complex bases

作者：Luo, J^*; Zhou, ZL

来源：Acta Mathematica Sinica-English Series, 2004, 20(4): 731-738.

DOI：10.1007/s10114-004-0354-y

• representation
• lattice self-affine tile
• disk-like

For each positive integer k, the radix representation of the complex numbers in the base -k i gives rise to a lattice self-affine tile T-k in the plane, which consists of all the complex numbers that can be expressed in the form Sigma(jgreater than or equal to1)d(j)(-k i)(-j), where d(j)is an element of{0, 1, 2, ...,k(2)}. We prove that T-k is homeomorphic to the closed unit disk {zis an element ofC:\z\ less than or equal to 1} if and only if k not equal 2.

• 出版日期2004-7
• 单位中山大学