Sunflower seed-head – real and simulated versions

I have been going on about intersecting Fibonacci spirals and the like when discussing Sunflower seed-heads, but I haven’t shown a mathematical graph showing just how close the Sunflower seed-head pattern is to a pure maths function.  On the left of this image we have the same (real) Sunflower seed-head image as shown in the article below.  On the right is a mathematically generated graph of points created using the Mathcad 2000 software.  Each X-Y co-ordinate of the points is directly related to the Golden Ratio (phi).  Phi also happens to be the most irrational, irrational number there is.  So it might not be too suprising to find out that the Sunflower seed-head pattern has an infinite rotational symmetry.  An infinite rotational symmetry has applications in optical devices called photonic quasicrystals and so the Sunflower seed-head pattern became the basis of my Patent for an entirely new class of photonic crystal with extremely interesting optical properties.  Lots of mathematics and heavy science – all from a Sunflower seed-head 🙂


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