Tag Archive: Voronoi Diagrams

Architecture in future will surely be dependent on various other branches of science and technology.INTER and INTRA dependence of the building architecture, which preciously was considered under civil ,presently electrical and mechanical engineering.Many architects in ages were/are masters in structural designs and applications, for example Frank Llyod Wright, Santiago Calatrava are the best examples where their works reflect the dual skills.

Multidisciplinary in Architecture will be its Future.

“Mathematics” integrated into the building sciences will surely be a great tool to explode various generative forms and iterations as a design part in architecture.It is not that mathematics was not previously integrated to the art field.Concepts of  Proportioning like golden ratio,Le Corbusier’s human scale etc are used way before the decades.

Let us begin with the this mathematical tool as in Nature:

The Voronoi Diagram

It’s easy to make a simple voronoi diagram. Just throw a random scattering of points (“sites”) across a plane, connect these sites with lines (linking each point to those which are closest to it), and then bisect each of these lines with a perpendicular.

First step is to draw a line connecting adjacent points.

Second step is to draw a perpendicular line to the one you just drew in the midpoint of it.

Last step is to connect lines, drawn in the second step, in to an network.

Voronoi and  Nature

Giraffe: Following  Voronoi’s Equation?

The Wings of a Dragonfly

The Tortoise Shell.

Voronoi and Architecture

Voronoi and Architecture

This concept can be implemented in generative forms to save the time for Architects and Designers.

There are many such applications:

1.City Planning

Like Town- planning in Architecture may be simplified by assigning the site as a nodal point and generating the Voronoi diagram as explained above.

For example for comparing areas covered by different hospitals, or shops, etc. With Voronoi diagram one can easily determine where is the nearest  shop or hospital, and urban planners can study if certain area need a new hospital.

2.Other Uses

a. Their structural properties, both in 2d and 3d.

b. As a way to subdivide/organize space, based on proximity/closest neighbor.

c. The fact that they can describe many natural formations, like soap bubbles, sponges or bone cells, which can inform architecture with new ways to organize and structure space.

The above example is in Alibaba Headquarters in Hangzhou architect slightly alliterated the pattern of Voronoi diagram to create stunning shadings for elevations and courtyard.


1.Voronois on encyclopedia

2.Saeed Arida, Masters Thesis Paper.

3.Paper Journals

-Aranda, B., Lasch, C. Tooling New York: Princeton Architectural Press, 2006.
    -Bollobas, B., Riordan, O. Percolation Cambridge: Cambridge University Press, 2006.
    -Kim, M.S., Shimada, K., (eds.) Geometric Modeling and Processing – GMP 2006 Berlin: Springer, 2006.


Generative architecture can be more broadly defined as employing a generative system – such as a set of natural language rules, a computer program, a set of geometrical transformations, a diagram, or other procedural inventions – in the design process through which the final design emerges. The generative system has different degrees of autonomous action, ranging from a fully automated process to a step-by-step user-controlled one. This process involves designing the algorithm (rule), adjusting the starting parameters and shapes, steering the derivation process, and finally selecting the best variant.
Case Study-Nam June Paik Museum.

A Competition Entry by MIT Graduates.

Competition:Nam June Paik was a Korean-born American artist. He worked with a variety of media and is considered to be the first video artist.For Biography click here.The aim of the competition was to design a museum that will enshrine the work of Nam June Paik.

Concept:Approached the design in an experimental manner that would embody the spirit inherent to Nam June Paik’s work, in which notions of improvisation, indeterminism and emergence played a significant role.
A form-generation process that is based on natural form was developed to guide and assist us in this design. The starting point was customized software implementing algorithms for computing the Voronoi diagrams. The challenge that persisted throughout the process was how to concretize the abstraction of mathematically generated forms.

Please check the previous blog article for Voronoi diagrams:Nature and Architecture.

A software was developed by using mathematical parameters by using Voronoi diagrams and increased the complexity of the diagram.

Image shows the seeding done to develop the  software by using 2d Voronoi solutions.

Random amount of seeds and nodes were inserted to get variation in GENERATIVE FORMS.

Parameterizing of the software:

According to the given site situations and restrictions like entrance, services etc where taken care.Hence editing of the Voronoi points where necessary to bring the change in it.

Variation of the building form:

After controlling the given restrictions in the form various free points where assigned at the nodes to further regenerate the model.


Was necessary to be done considering economic point of view.