The post Mona Mosaics showed a number of ways to segment a flat surface and build mosaics by filling regions with the average colour for that region in some underlying image. Here is another example of the same technique but this time using a Phyllotaxy spiral, sometimes called a Fibonacci spiral. It's an arrangement commonly found in plant growth - for example in the Sunflower.
Jim Bumgardner has an excellent tutorial where he develops the idea and gives code for producing the pattern and several variations. I'm using something based on his Example 10 code to produce the mosaic below from a simple radial gradient. I love the swirling spirals in opposite directions found in the pattern.
And of course we must apply it to the Mona Lisa image as well.