**Nirodha Gunadasa **

Chairman*Archedium (Private) Limited, Colombo*

Architecture and urbanism largely involves thinking of places, volumes, and spaces in basic geometric forms such as rectangles, triangles, and circles. These cubic buildings, linear bridges, or grid road networks, for example, are often not adaptable, inflexible, and have little freedom to merge with each other, which poses a challenge to vertical urbanism and polycentricism. The rigidity and inflexible nature of the elements that make up these compositions greatly limits the possibility of true manifestation of space and form, especially within a practice that is said to incorporate social, economic, cultural, and environment influences. These limitations are rooted in the system of imagining forms and spaces with Cartesian Geometry.

Classical Mathematics has a profound impact on what is ultimately generated as built environment. Recent studies show that mathematics that occur in nature and natural processes create forms and volumes that are not classical, but instead are based on complex numbers and complex vector spaces. Such forms are adaptive and amicable. Our study shows that if we follow the mathematics of nature, we would advance an altogether different kind of architecture, which is adaptive, responsive, sensitive and humane. Understanding mathematicsâ€™ occurrence in nature could generate urban elements that are more adaptive, flexible, and have the capacity to merge together to form sustainable built environments. Specifically, this information could be vital in composing tall buildings, as they are principle elements that form the three-dimensional fabric of an urban environment.