Types of Spirals.
Logarithmic Spiral - self-similar spiral curve which often appears in Nature. Spira Mirabilis, Latin for “miraculous spiral”, is another name for the Logarithmic Spiral. The size of the spiral increases but its shape is unaltered with each successive curve, a property known as Self-Similarity. Possibly as a result of this unique property, the Spira Mirabilis has evolved in Nature, appearing in certain growing forms such as nautilus shells and sunflower heads.
Fermat’s Spiral - in the sunflower and daisy, the mesh of spirals occurs in Fibonacci Numbers because Divergence (angle of succession in a single spiral arrangement) approaches the Golden Ratio. The shape of the spirals depends on the growth of the elements generated sequentially. In mature-disc phyllotaxis, when all the elements are the same size, the shape of the spirals is that of Fermat Spirals - ideally. That is because Fermat’s Spiral traverses equal annuli in equal turns.
Archimedean Spiral - it is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line which rotates with constant angular velocity. The Archimedean Spiral has the property that any ray from the origin intersects successive turnings of the spiral in points with a constant separation distance, hence the name “Arithmetic Spiral”.
Hyperbolic Spiral - transcendental plane curve also known as a Reciprocal Spiral. A Hyperbolic Spiral is the opposite of an Archimedean Spiral. It begins at an infinite distance from the pole in the center (for θ starting from zero r = a/θ starts from infinity), and it winds faster and faster around as it approaches the pole; the distance from any point to the pole, following the curve, is Infinite.
janainaart
titsay
gummygunk
snowghoul
