University of KashanMathematics Interdisciplinary Research2538-36394120190601Independence Fractals of Graphs as Models in Architecture77869338810.22052/mir.2019.169780.1112ENMaryamAdlFaculty of Art and Architecture, Islamic Azad University, Yazd Branch, Yazd, IranSaeidAlikhaniDepartment of Mathematics, Yazd University, Yazd, IranVahidShokriFaculty of Art and Architecture, Islamic Azad University, Yazd Branch, Yazd, IranJournal Article20190127Architectural science requires interdisciplinary science interconnection in order to improve this science. Graph theory and geometrical fractal are two examples of branches of mathematics which have applications in architecture and design. In architecture,<br /> the vertices are the rooms and the edges are the direct connections between each two rooms. <br /> The independence polynomial of a graph $G$ is the polynomial<br /> $I(G,x)=sum i_kx^k$, where $i_k$ denote the number of independent sets<br /> of cardinality $k$ in $G$. The independence fractal of $G$ is the set ${cal I}(G)=lim _{krightarrow infty} Roots<br /> (I({G^{k}},x)-1), $ where $G^{k}=G[G[cdots]]$, and $G[H]$ is the<br /> lexicographic product for two graphs $G$ and $H$. In this paper, we consider graphical presentation of a ground plane as a graph $G$ and use <br /> the sequences of limit roots of independence polynomials of $G^k$ to present some animated structures for building.http://mir.kashanu.ac.ir/article_93388_7892f236158e0d094cd6873f94de7f46.pdf