Mathematics meets Nature in an infinitely rotationally symmetric pattern

This is the beautiful head of a Sunflower in the New Forest Observatory garden, and this is a flower that has special meaning to me and my research in optics.  The Sunflower seed head has the seeds arranged according to Fibonacci spiral patterns where the rotation and spacing are directly related to the Golden Ratio.  Since the Golden Ratio is the most irrational, irrational number there is, we might expect some amazing optical properties for devices based on this geometry.  One property became the subject of one of my photonic crystal Patents – namely infinite rotational symmetry.  If you make an optically diffractive device where the optical scattering centres are based on the geometry of the Sunflower seed head pattern, then the diffraction pattern that results is a circle!  This implies that the scattering pattern has infinite rotational symmetry which in turn gives the photonic crystal based on this geometry some very interesting and unique properties.  But leave the Maths & Science for a moment and just gaze at the natural beauty of a Sunflower 🙂

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