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Vogel Spiral


VogelSpiral

A Vogel spiral is a discrete arrangement of points whose polar coordinates are

r_n=csqrt(n)
(1)
theta_n=nalpha,
(2)

where n=0,1,..., c>0, and alpha is a fixed divergence angle (Vogel 1979). The customary choice alpha=pi(3-sqrt(5)) is the golden angle and produces the interlacing spiral patterns used to model phyllotaxis in sunflower heads.

The radii satisfy the equation of Fermat's spiral, but a Vogel spiral is a discrete point set rather than a continuous plane curve.

A daisy similarly produces a flower-like family of visible spirals by placing repeated shapes along a spiral, but it generally uses different radial scaling.


See also

Daisy, Fermat's Spiral, Golden Angle, Phyllotaxis

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References

Vogel, H. "A Better Way to Construct the Sunflower Head." Math. Biosci. 44, 179-189, 1979. https://doi.org/10.1016/0025-5564(79)90080-4.

Cite this as:

Weisstein, Eric W. "Vogel Spiral." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/VogelSpiral.html

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