Algorithmic beauty of plants
The surprising mathematical beauty of plants serves a purpose, the economy. To maximize access to water and to light and to increase the chances of survival and reproduction. The plant must place optimally the maximum seeds, shoots, leaves and branches in the minimum space. It follows for that complex algorithms dominated by the golden angle.
This angle is the circumference divided by the golden number: 360/1.618 which gives an angle of divergence of 222,496...°in a majority of cases, the plant will therefore place the next seed, leaf, grows branch according to this angle. The shortest angle 360-222.5 = 137.5 is called the golden angle.
But why plant must be fan of the golden angle? Simply because any other angle would not allow it to put the maximum of stuff in the minimum of space. This allows it to get everything it needs and it offers us the beauty premium.
This angle is the circumference divided by the golden number: 360/1.618 which gives an angle of divergence of 222,496...°in a majority of cases, the plant will therefore place the next seed, leaf, grows branch according to this angle. The shortest angle 360-222.5 = 137.5 is called the golden angle.
But why plant must be fan of the golden angle? Simply because any other angle would not allow it to put the maximum of stuff in the minimum of space. This allows it to get everything it needs and it offers us the beauty premium.
Mathematical occupation of the space by a flower.
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 Need of support of a 3D printed object
Today, 3D printing has not yet solved the problem of gravity, in every process, the object always need a support (see picture right). Plants do not have this problem and "print" in the air.
We also take for granted the surprising mathematical abilities of the plant. How this humble little flower of the fields can know with anticipation, with which orientation and to which distance it must send its branches, to optimize the occupation of the space. |
Golden angle phyllotaxy
These beautiful patterns are based on the golden angle, 137,5; the perfect angle for an optimized occupation of space
Plants are mathematically constructed,you can explore these algorithms: http://algorithmicbotany.org/papers/abop/abop.pdf
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phi fractal in plant
Everlasting vegetal fractal
Golden angle fractal in plant
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