This paper is devoted to studying the boundary behavior of self-affine sets. We prove that the boundary of an integral self-affine set has Lebesgue measure zero. In addition, we consider the variety of the boundary of a self-affine set when some other contractive maps are added. We show that the complexity of the boundary of the new self-affine set may be the same, more complex, or simpler; any one of the three cases is possible.
Qi-Rong Deng. Xiang-Yang Wang. "On the Boundary of Self-Affine Sets." Abstr. Appl. Anal. 2015 1 - 3, 2015. https://doi.org/10.1155/2015/573604