Logarithmic spiralA logarithmic spiral, equiangular spiral, or growth spiral is a self-similar spiral curve that often appears in nature. The first to describe a logarithmic spiral was Albrecht Dürer (1525) who called it an "eternal line" ("ewige Linie"). More than a century later, the curve was discussed by Descartes (1638), and later extensively investigated by Jacob Bernoulli, who called it Spira mirabilis, "the marvelous spiral".
PhyllotaxisIn botany, phyllotaxis () or phyllotaxy is the arrangement of leaves on a plant stem. Phyllotactic spirals form a distinctive class of patterns in nature. The basic arrangements of leaves on a stem are opposite and alternate (also known as spiral). Leaves may also be whorled if several leaves arise, or appear to arise, from the same level (at the same node) on a stem. With an opposite leaf arrangement, two leaves arise from the stem at the same level (at the same node), on opposite sides of the stem.
SpiralIn mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point. It is a subtype of whorled patterns, a broad group that also includes concentric objects. Two major definitions of "spiral" in the American Heritage Dictionary are: a curve on a plane that winds around a fixed center point at a continuously increasing or decreasing distance from the point. a three-dimensional curve that turns around an axis at a constant or continuously varying distance while moving parallel to the axis; a helix.
Patterns in naturePatterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. Early Greek philosophers studied pattern, with Plato, Pythagoras and Empedocles attempting to explain order in nature. The modern understanding of visible patterns developed gradually over time.
Common sunflowerThe common sunflower (Helianthus annuus) is a species of large annual forb of the genus Helianthus. It is commonly grown as a crop for its edible oily seeds. Apart from cooking oil production, it is also used as livestock forage (as a meal or a silage plant), as bird food, in some industrial applications, and as an ornamental in domestic gardens. Wild H. annuus is a widely branched annual plant with many flower heads. The domestic sunflower, however, often possesses only a single large inflorescence (flower head) atop an unbranched stem.
