The Logarithmic or Golden Spiral (also known as the equiangular spiral or growth spiral) can be constructed by taking a perfect rectangle or Golden Rectangle and breaking it down into smaller squares based on the Fibonacci sequence. By dividing each rectangle with an arc, a pattern begins to emerge. What we begin to see is the Fibonacci spiral. The Fibonacci spiral represents a good approximation to the so-called logarithmic spiral found in nature. The growth rate of each successive turn of the spiral is approximately equal to the Golden number.

The construction of the Golden Spiral

In flora of the composite family, such as the Sunflower, a set of intertwined logarithmic spirals can be seen. Both spirals run in opposing directions, one being a right-handed spiral and the other being a left-handed spiral with each floret occupying the dual role by belonging to both spirals. There are in total 55 spirals, 21 clockwise spirals and 34 anti-clockwise spirals.

Two Golden Spirals can be seen in the flora of composite flowers, each running in opposing directions.

These numbers are the numbers of the Fibonacci sequence. Such opposing spiral patterns can also be found in the fruit lets of the pineapple (8 and 13 spirals) and in the pine cone (5 and 8 spirals).

As currents move through the ocean and the tide rolls onto the shore, the waves that bring in the tide curl into a spiral that can be mathematically diagrammed onto a plot at the points (1,1), (2, 3), (5, 8), (13, 21) and (34, 55).
Buds on trees, sandolars, starfish, petals on flowers and especially the nautilus shell are formed with the exactly the same blue print of the Golden Rectangle. With each section of growth, the Nautilus adds to itself one more value on Fibonacci’s scale. This blue print can be seen on a small scale every day such as each successive length of our phalanges. But the greatest example, of all lies directly above our heads in the constellation Ursa Major. Located at an estimated distance of 23 million light years, and roughly 3,000 light years across, the Whirlpool Galaxy (M51) is spiral galaxy whose shape is formed with the exact blue print from which the tiny shells are formed.

M51 Whirlpool galaxy located in the constellation Ursa Major.

The short movie ‘Nature by Numbers’ created by Etérea is a beautifully illustrated animation focusing on the enigmatic geometries found throughout nature.