## VORONOI DIAGRAM IN SAFF KAZDAĞLARI

In the design of Saff KAZDAĞLARI, a geometric order, which is observed in the process of existence of many living things and objects and organizes the forms in nature, is used. This order, known as the “Voronoi Diagram”, is the creative mathematics of nature itself.

**What is the Voronoi Diagram, Also Known as the Mathematics of Nature?**

The Voronoi diagram is named after the Russian mathematician Georgy Voronoy.

The Voronoi diagram is the result of Voronoy’s work. Voronoi created a structure that divides regions based on the circumferential distances of a set of points. This structure has become an important tool in the analysis and planning of geometric shapes and objects in space. Today, Voronoi diagrams are widely used in many fields such as computer graphics, geography, physics, biology and engineering. Voronoi is a concept often used in fields such as mathematics, physics, computer science and geography. Voronoi is a technique for measuring distances between objects in a way that separates the regions that divide the space of a set of objects in space. A Voronoi diagram is a structure of polygons drawn based on the circumferential distances of a set of disjoint points. Each polygon has a center and is constructed by connecting the points where this center is closest to all of the drawn polygons. A Voronoi diagram is a network structure formed by joining these polygons and is often used in areas such as the analysis of interactions between groups of objects or points, overlap and coverage problems in space.

Thanks to the layout using this formula, the design offers an aesthetic in harmony with the organic integrity of nature, while at the same time reflecting nature’s power of self-renewal and repair. During cell division in living organisms, cells divide in ways similar to Voronoi diagrams. The two new cells formed by the division of a cell are separated by the intersection of equidistant points. This is the basic principle of the Voronoi diagram, as well as the basic principle of the parcelization in the design. The Voronoi diagram optimizes the resource use of the project. Thus, a more efficient project is achieved with less resource use.

**Voronoi Forming the Structure of Nature **

The Voronoi diagram is a common shape in nature and living things. Some of the Voronoi examples that make up the main shape of nature are as follows:

**Snowflake:** Each snowflake is a unique example of a Voronoi diagram. A snowflake is a Voronoi diagram of polygons formed by the intersection of points equidistant from a center.

**Shellfish:** Shellfish carry patterns similar to Voronoi diagrams on their shells. These patterns make shellfish shells strong and less fragile under stress.

**Plant leaves:** Plant leaves can also have patterns similar to Voronoi diagrams. These patterns allow the plant to photosynthesize most efficiently.

**Cells in the body:** Cells in the body form shapes similar to Voronoi diagrams. These shapes facilitate the interaction of cells with each other and the different functions of cells in different parts of the body.

**Rock formations in the desert:** Rock formations in the desert can form in shapes similar to Voronoi diagrams. Voronoi diagram shapes can result when wind and other natural influences shape these rock formations.

**Honeycomb:** The honeycomb is made up of hexagons, similar to Voronoi diagrams. These hexagons help bees to use the honeycomb as efficiently as possible.

**Stone and shell formations on beaches:** Stone and shell formations on beaches can form in shapes similar to Voronoi diagrams. As waves and other natural influences shape these materials, Voronoi diagram shapes can result.

**Formation of clouds:** In the formation of clouds, water vapor molecules condense in shapes similar to a Voronoi diagram, causing clouds to form.

## VORONOI'S FATHER VORONOY

Voronoy produced many innovative works in the field of mathematics, where he concentrated his studies in the late 19th and early 20th centuries. Voronoy worked in many different branches of mathematics such as mathematical analysis, number theory, geometry and topology. Voronoy made important contributions especially in shortest path problems, ratios of surfaces with respect to each other, integral geometry and multidimensional analysis.

* From the architect of Saff KAZDAĞLARI, Erhan Vural… *