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

Updated: May 30

With rare exceptions, people either adore or loathe durian. The fruit is notorious for its terrible stench, which some have likened to rotting flesh. The durian is also notable for its spiky skin and enormous size. Because of its multiple appealing characteristics, this fruit has been called the "King of Fruits."

The thick, prickly shell shields the delicate flesh of the fruit from the elements. The fruit is extremely tough to shatter, making it harder for predators to reach the meat. The combination of these features makes the durian fruit genuinely distinct and remarkable.

While durian may not be everyone's cup of tea, despite its lowly look, the fruit has countless hidden mysteries. The shape of the durian is one of its most fascinating features. The fruit is really made up of multiple spheres that have been fused together. The mathematics underlying the durian, a wonderful fruit in its own right, is rather interesting.

Fruit so unique applying mathematical patterns.


The form of the durian is not only pleasant to the eye, but it also has mathematical importance. Fractals are repeating patterns in the form of the fruit. Fractals may be found all across nature and are distinguished by their self-similarity. That is, no matter how closely you inspect a fractal, the general pattern stays consistent.

The durian's fractal structure is also what makes it so intriguing. Every time you split the fruit in half, the proportions of meat, seeds, and empty space remain the same. Other natural phenomena with this self-similarity include snowflakes, river basins, and coastlines.

Furthermore, when one examines the seed placements in a durian, one cannot help but observe the patterns that develop. Some of these patterns, such as the Delaunay triangle and Voronoi patterns, have been investigated mathematically and have applications in industries such as engineering and architecture.


The durian is a fruit distinguished by its hard outer shell and delicate inside flesh. Many people are unaware that these two qualities are the consequence of two distinct patterns: the outside 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

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