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Logarithmic spiral (pitch 10°) A section of the Mandelbrot set following a logarithmic spiral. 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").
For <, spiral-ring pattern; =, regular spiral; >, loose spiral. R is the distance of spiral starting point (0, R) to the center. R is the distance of spiral starting point (0, R) to the center. The calculated x and y have to be rotated backward by ( − θ {\displaystyle -\theta } ) for plotting.
An Archimedean spiral is, for example, generated while coiling a carpet. [5] A hyperbolic spiral appears as image of a helix with a special central projection (see diagram). A hyperbolic spiral is some times called reciproke spiral, because it is the image of an Archimedean spiral with a circle-inversion (see below). [6]
The polar equation for a golden spiral is the same as for other logarithmic spirals, but with a special value of the growth factor b: [10] = or = (/), with e being the base of natural logarithms, a being the initial radius of the spiral, and b such that when θ is a right angle (a quarter turn in either direction): =.
Hyperbolic spiral; Lituus; Logarithmic spiral; Nielsen's spiral; Golden spiral; Syntractrix; Tractrix; Trochoid; ... but a diagram showing how the elements meet ...
A supersilver spiral is a logarithmic spiral that gets wider by a factor of for every quarter turn. It is described by the polar equation r ( θ ) = a exp ( k θ ) , {\displaystyle r(\theta )=a\exp(k\theta ),} with initial radius a {\displaystyle a} and parameter k = 2 ln ( ς ) π . {\displaystyle k={\frac {2\ln ...
Conical spiral with an archimedean spiral as floor projection Floor projection: Fermat's spiral Floor projection: logarithmic spiral Floor projection: hyperbolic spiral. In mathematics, a conical spiral, also known as a conical helix, [1] is a space curve on a right circular cone, whose floor projection is a plane spiral.
# Output to svg file: set terminal svg size 1024 768 set output "logarithmic_spiral.svg" # Same scale for both axes, half-size output: set size ratio -1 0.5, 0.5 # More sample points to produce smoother picture: set samples 480 # Axes in the center, no tick marks: set zeroaxis unset xtics unset ytics unset border set polar plot [-4*pi:4*pi] [-8 ...