Voronoi Polygons in an Archimedean Spiral
Voronoi Polygons in an Archimedean Spiral
It is well known that points placed along an Archimedean spiral in angular steps equal to the golden angle yield a pattern that closely matches that of a sunflower’s seeds. This Demonstration shows the patterns that emerge when you vary the angle. It also shows the Voronoi regions corresponding to each seed and computes the average of the set of ratios formed by comparing the area of the largest inscribed circle (centered at the seed) to the area of the Voronoi polygon containing the seed. The colors indicate, for each region, the value of this ratio (green means high ratio; red means low). This experiment illustrates that the greatest efficiency— is greatest—occurs for the golden angle. However, the result is unproved.
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