BESPOKE TALK Series: Discovering the Secret Structure of the King of Fruits

Updated: Nov 15

People either love or despise durian, with very few exceptions. The fruit is infamous for its pungent odor, which some compared to rotting flesh. The durian is also known for its spiky exterior and huge size. Because of its numerous attractive traits, this fruit has been dubbed the "King of Fruits."

The thick, spiky shell protects the delicate flesh of the fruit from the outside. The fruit is also difficult to crack, which makes it a challenge for predators to get to the flesh. The combination of these factors makes the durian fruit a truly unique and special fruit.

While durian may not be everyone's cup of tea, despite its humble appearance, the fruit holds numerous hidden secrets. One of the most intriguing aspects of the durian is its form. The fruit is actually made up of several spheres that have been fused together. The mathematics behind the durian, which is a remarkable fruit in its own right, is rather intriguing.

Fruit so unique applying mathematical patterns.


The durian's shape is not only aesthetically pleasing, but it also has mathematical significance. The repeating patterns in the fruit's shape are known as fractals. Fractals are found throughout nature and are characterized by their self-similarity. That is, no matter how much you zoom in on a fractal, the overall pattern remains the same.

The fractal nature of the durian is also what makes it so fascinating. Every time you cut the fruit in half, each half contains the same proportions of flesh, seeds, and empty space as the whole fruit. This self-similarity can be found in other natural phenomena, such as snowflakes, river basins, and coastlines.

Moreover, when looking at the arrangements of seeds in a durian, one can't help but notice the patterns that emerge. Some of these patterns, like the Delaunay triangle pattern and the Voronoi pattern, have been studied in mathematics and have applications in fields like engineering and architecture.


The durian is a fruit that is distinctively known for its hard outer shell and soft inner flesh. What many people don't realize is that these two characteristics are actually the result of two different patterns—the outer layer is a Delaunay triangle pattern, while the inner layer is a Voronoi pattern.


HISTORY: The Delaunay triangle pattern is named after Russian mathematician Boris Delaunay, who described it in 1934.

DEFINITION: Triangulate tips to form polygonal patterns. Randomization and movement of mapping points.

APPLICATION: The exterior shell of the durian fruit is formed through a process known as triangulation. This is where the shell's tips are turned into polygons, which are subsequently mapped onto a point system. The point system is then randomized, and the polygons are rearranged to form the final pattern.


HISTORY: The Voronoi pattern is named after Ukrainian mathematician Georgy Voronoi, who described it in 1908.

DEFINITION: Isolated patterns are formed by the inner skin. Understanding cell behavior and proliferation.

APPLICATION: The inner soft skin of the durian fruit is patterned with a Voronoi pattern. This pattern is created by dividing a space into polygons or regions based on the distance between two points. The durian seeds are the points that define the Voronoi regions.


In conclusion, the Delaunay triangle and Voronoi patterns are two interesting patterns that arise from the arrangement of durian seeds. These patterns have mathematical significance, and they provide a fascinating glimpse into the hidden structure of the durian fruit.

While the Delaunay triangle and Voronoi patterns are both interesting from a mathematical standpoint, they also have practical applications. The Delaunay triangle pattern can be used to generate a mesh that can be used in finite element analysis, while the Voronoi pattern can be used for cell division and for creating efficient data structures.

Interestingly, the combination of both patterns results in the unique shape and texture of the durian fruit. The hard outer shell protects the soft inner flesh, while the inner flesh is a delicious and unique treat. Without both patterns, the durian would not be the same fruit that we know and love today.


Ar. Neil John Bersabe

Lead Architect

John Michael Jalandra

Content Writer


BERSABARC Design Studio 2022

21 views0 comments