Logarithmic spiral

A logarithmic spiral, equiangular spiral or growth spiral is a self-similar spiral curve which often appears in nature. The logarithmic spiral was first described by Descartes and later extensively investigated by Jacob Bernoulli, who called it Spira mirabilis, 'the marvelous spiral'.A section of the Mandelbrot set following a logarithmic spiralAn extratropical cyclone over Iceland shows an approximately logarithmic spiral patternThe arms of spiral galaxies often have the shape of a logarithmic spiral, here the Whirlpool Galaxy]] A logarithmic spiral, equiangular spiral or growth spiral is a self-similar spiral curve which often appears in nature. The logarithmic spiral was first described by Descartes and later extensively investigated by Jacob Bernoulli, who called it Spira mirabilis, 'the marvelous spiral'. In polar coordinates ( r , θ ) {displaystyle (r, heta )} the logarithmic curve can be written as