Independence fractals of graphs as models in architecture

Independence fractals of graphs as models in architecture

Architectural 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, the vertices are the rooms and the edges are the direct connections between each two rooms. The independence polynomial of a graph is the polynomial , where denote the number of independent sets of cardinality in . The independence fractal of is the set where , and is the lexicographic product for two graphs and . In this paper, we consider graphical presentation of a ground plane as a graph and use the sequences of limit roots of independence polynomials of to present some animated structures for building.

Architectural 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, the vertices are the rooms and the edges are the direct connections between each two rooms. The independence polynomial of a graph is the polynomial , where denote the number of independent sets of cardinality in . The independence fractal of is the set where , and is the lexicographic product for two graphs and . In this paper, we consider graphical presentation of a ground plane as a graph and use the sequences of limit roots of independence polynomials of to present some animated structures for building.