Fractals/trigonometric

=How to compute it =

One can use Maxima CAS to find it :

(%i1) z: x+y*%i; (%o1) %i*y+x (%o2) %i*y+x (%i3) realpart(sinh(z)); (%o3) sinh(x)*cos(y) (%i8) trigrat(sinh(x)); (%o8) (%e^−x*(%e^(2*x)−1))/2 (%i11) expand(%); (%o11) %e^x/2−%e^−x/2

sin(Z) =

$$ Real = \sin(x)   ((\exp(y) + \exp(-y))/2) $$

$$ Imag = \cos(x)  ((\exp(y) - \exp(-y))/2) $$

cos(Z)

$$ Real = \cos(x)   ((\exp(y) + \exp(-y))/2) $$

$$ Imag = -\sin(x)  ((\exp(y) - \exp(-y))/2) $$

sinh(Z)

$$ Real = \cos(y)   ((\exp(x) - \exp(-x))/2) $$ $$ Imag = \sin(y)  ((\exp(x) + \exp(-x))/2) $$

cosh(Z)

$$ Real = \cos(y)   ((\exp(x) + \exp(-x))/2) $$ $$ Imag = \sin(y)  ((\exp(x) - \exp(-x))/2) $$

=Images= See : commons:Category:Trigonometric maps =Videos=
 * youtube : Spirals and Slarips by Gary Welz

=See also=
 * Thorn Fractal, alternatively named the "Secant Sea"
 * Paul Bourke : sinjulia fractal