Can One Equation Grow a Seashell?

BEHIND THE WORK

Can one equation grow a seashell?

The polar radius r(t) = 0.18 exp(0.085t)[1 + 0.085 cos(37t/2)] combines two motions. The exponential term makes every new turn larger than the last, while cos(37t/2) adds eighteen and a half fine ridges during each revolution. That extra half-ridge shifts every new coil out of alignment. Converting the radius with x(t) = r(t) cos(t) and y(t) = r(t) sin(t) grows one continuous shell-like spiral through six complete turns.

Artismathic turns equations into visual art—one function at a time.

Music: 'Eternal Garden' by Dan Henig

#MathArt #LogarithmicSpiral #Geometry