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A 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").
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. The full model proposed by H. Vogel in 1979 [5] is
For <, spiral-ring pattern; =, regular spiral; >, loose spiral. R is the distance of spiral starting point (0, R) to the center. The calculated x and y have to be rotated backward by for plotting. [13] [predatory publisher]
The Archimedean spiral (also known as Archimedes' spiral, the arithmetic spiral) is a spiral named after the 3rd-century BC Greek mathematician Archimedes. The term Archimedean spiral is sometimes used to refer to the more general class of spirals of this type (see below), in contrast to Archimedes' spiral (the specific arithmetic spiral of ...
The Ulam spiral or prime spiral is a graphical depiction of the set of prime numbers, devised by mathematician Stanisław Ulam in 1963 and popularized in Martin Gardner's Mathematical Games column in Scientific American a short time later. [1] It is constructed by writing the positive integers in a square spiral and specially marking the prime ...
Two well-known spiral space curves are conical spirals and spherical spirals, defined below. Another instance of space spirals is the toroidal spiral. [8] A spiral wound around a helix, [9] also known as double-twisted helix, [10] represents objects such as coiled coil filaments.
Heighway dragon curve. A dragon curve is any member of a family of self-similar fractal curves, which can be approximated by recursive methods such as Lindenmayer systems.The dragon curve is probably most commonly thought of as the shape that is generated from repeatedly folding a strip of paper in half, although there are other curves that are called dragon curves that are generated differently.
An animation that shows how the turtle is used to create graphics by combining forward and turn commands while a pen is touching the paper A spiral drawn with an iterative turtle graphics algorithm A turtle graphic pattern drawn with a Python program. The turtle has three attributes: a location, an orientation (or direction), and a pen.