Voromoeba
Voromoeba Home Page
Version 1.2
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Voromoeba 1.2.2 for Windows 8.1 or later. Requires 64-bit x86. Tested on Windows 8.1 and Windows 10.
Source
How to Play
The world of Voromoeba is a series of circular ponds. You are a voromoeba, a single-celled creature who lives in a pond. Your dear sweetie is trapped in a frozen pond, and can only be saved by a kiss from you. You must venture forth through the ponds to reach your sweetie! Along the way, you must elude or destroy predators and gather food.
It's an ordinary life for an adventurous fairy-tale protozoan, with a twist: The ponds are Voronoi diagrams. Each thing in the pond is Voronoi cell. The rules behind Voronoi diagrams make the boundaries between cells fluid. Even if you do not follow the math, by playing the game you will get an intuition about how the boundaries behave.
Here is a quick introduction to Voronoi diagrams. Inside each cell, there is a point, called a seed, that defines the cell. The seed's cell is the set of all points closer to that seed than any other seed. In the picture at right, each seed is shown as a black or white dot.
Note two properties:
Voronoi cells are always convex.
The boundary between two adjacent cells is equidistant from their seeds, and perpendicular to a conceptual line segment between those seeds.
In the game, the g key toggles display of the seeds. Displaying the seeds may help you gain intuition for Voronoi diagrams. Seed display is disabled when your score reaches 20, on the assumption that you learned enough.
The Voromoeba manual gives more details.