A Fibonacci spiral (top) which approximates the golden spiral, using Fibonacci sequence square sizes up to 21. A different approximation to the golden spiral is generated (bottom) from stacking squares whose lengths of sides are numbers belonging to the sequence of Lucas numbers, here up to 76.

The spiral below demonstrates the construction of the logarithmic spiral – a long slow spiral characterized by all radii from its center intersecting the spiral at exactly the same angle. Using the Fibonacci sequence, the spiral grows to accommodate the growing animal inside in a nautilus shell – and additional examples can be seen in the ...

The Fibonacci spiral: an approximation of the golden spiral created by drawing circular arcs connecting the opposite corners of squares in the Fibonacci tiling (see preceding image)

Which spiral is more beautiful, the golden spiral or the Fibonacci spiral? This video provides an answer to this question based on an empirical study.

It is true that they are very similar, but there is a difference between the Fibonacci spiral and the golden spiral. The golden spiral is linear, which means that it can rotate infinitely inward or outward, and because of its unique self-similarity, it is also a key feature for fractals to be realized.