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The nautilus shell is often shown as an illustration of the golden ratio in nature, but the spiral of a nautilus shell is NOT a golden spiral, as illustrated below. The golden spiral overlay is provided by PhiMatrix golden ratio software :Nautilus shell spiral compared to a Golden Spiral.he Fibonacci spiral gets closer and closer to a Golden Spiral as it increases in size because of the ratio of each number in the Fibonacci series to the one before it converges on Phi, 1.618, as the series progresses (e.g., 1, 1, 2, 3, 5, 8 and 13 produce ratios of 1, 2, 1.5, 1.67, 1.6 and 1.625, respectively).