Voronoi Patterns in Nature (a) Everyday-Life Applications. (b) Switching Thresholds for Gold/Silver Holdings

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The patterns on a Giraffe’s body, Dragonfly’s wing, dried mud, Tortoise shell, Bee Hive honeycomb structure and many other objects in Nature are generated by an algorithm to create Voronoi maps- named after Georgy Voronoy who discovered and write about such patterns.  

Why did Nature create Voronoi patterns?

  • Efficient use of space: The pattern is ideal for maximizing the contents of a limited space, as seen in the construction of bee hives or cellular structures in muscles.
  • Structural strength: It provides a lightweight yet strong design, with properties that can be optimized for specific needs, such as impact absorption in biomimetic components.
  • Optimal resource/function distribution: The pattern helps organize and distribute resources or functions evenly. Voronoi pattern applications in everyday life

Voronoi Algorithm in a nutshell in simple language

A Voronoi diagram splits a plane into regions around a set of seed points so that every location in a region is closest to its seed than to any other. In practice, it shows which seed owns which region of the diagram based on nearest-neighbour distance. 

Some Voronoi applications in everyday life

  • Cell phone towers: Your phone typically connects to the nearest tower; the coverage map looks like a Voronoi diagram (each tower’s region is where it’s the closest tower).
  • Google Searches: Pizza delivery zones, nearest hospital to your location, Shopee goods delivery services zone assignment.
  • Urban planning: Optimal location of facilities
  • Construction: Structural design, strength and space optimization of buildings
  • Drones and autonomous vehicles path planning
  • Materials Sciences: microstructures and lattices of lightweight ultra-strong materials for aerospace and automotive parts.

 An experiment for applying Voronoi in Gold and Silver bullion investing

In the commodities market, a popular strategy is for investors to hold both Gold and Silver in their portfolios and to switch between one and the other based on the 80/50 Gold/Silver ratio- when Gold price exceeds 80 it's overvalued and time to buy Silver. When Silver is above 50, switch to Gold.

A 2-D Voronoi diagram with inputs Gold/Silver Ratio and 20-day Momentum of Gold/Silver Ratio was generated. Thresholds for switching were calculated. See diagram below:

The thresholds for switching looked like this:



Results

Unfortunately, this strategy performed worse than simply holding on to Silver. (Based on walk-forward on unseen data testing by Julius my Agentic AI) . See chart on cumulative performance below. Oh well, back to the drawing board.

Thanks to: Julius my Agentic AI for the coding, modeling construction and testing,  to SciKit-Learn, Seaborn, Pandas, NumPy, Matplotlib for their libraries,  to FRED (Federal Bank of Saint Louis) and EOHD.com for providing me with API Keys to access their data. 



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