Fractal geometry and applicability to biological simulation shapes for sustainable architecture design in Vietnam

Sustainability is the biggest goal that all areas including building architecture aim at. Sustainability is created by the harmony of buildings to the natural environment in many aspects. In terms of form, biological simulations are considered as a way of learning from natural shapes in order to create the similarities of architecture with nature, contributing to creating the sustainability in aesthetics and structure, in which the geometric language is used as a basic tool for composing the complex form of the work. However, Euclidean geometry, which existed for thousands of years, cannot describe nature correctly and is rated “hard dry” and “cold.” In the 1970s, the mathematician Mandelbrot found fractal geometry with a great self-similarity rule, which allowed for precise modeling of many complex structures of nature. After appearing, fractal geometry quickly penetrated into all areas of life, whereas in Vietnam, many people have not known it. This article summarizes the basic knowledge of fractal geometry, its relationship with sustainable historical architectures in Vietnam, and its applicability in drawing biological simulation architectural form that harmonizes the nature, contributing to creating sustainable buildings for the future.