Fermat's Spiral

Fermat's spiral (also known as a parabolic spiral) was first studied by Pierre de Fermat in 1636. Unlike an Archimedean spiral, whose radius grows linearly with the angle, a Fermat spiral's radius grows with the square root of the angle — and because a square root has both a positive and a negative branch, the full curve is symmetric about the origin, forming two opposing arms that together resemble a pair of interlocking spirals. This growth pattern also appears in nature, in the spiral arrangement of seeds in a sunflower head and other phyllotactic patterns. It follows the equation:

$r = \pm\theta^{1/2}$