I tried few more spirals of the same type. When signs are varied at t in any place, they display interesting behaviour -some disapper, become point at coordinate beginning, few become scattered points in certain regions of argument t. For example this:

(t^(1/t))^(((((((1/t)^t)^((((((1/t)^t))^(((((-t^(1/t))^(((((1/t)^t)^(((t)^(1/t))^((1/t)^(t))))))))))))))))))

Is having Integral = 0 until 0,322Pi, then points are appearing which oscillating between close to 0 and close to 1 , and it stops at 4,4*pi. So software tries to sum these oscillating values , givin raise for the integral in the region up to 4,4*pi . Then it stops growing.

In polar coordinates(spiral) it has a point at origin and scatered points along segment of spiral.

May be my software can not calculate properly such long nested operations.

(t^(1/t))^(((((((1/t)^t)^((((((1/t)^t))^(((((-t^(1/t))^(((((1/t)^t)^(((t)^(1/t))^((1/t)^(t))))))))))))))))))

Is having Integral = 0 until 0,322Pi, then points are appearing which oscillating between close to 0 and close to 1 , and it stops at 4,4*pi. So software tries to sum these oscillating values , givin raise for the integral in the region up to 4,4*pi . Then it stops growing.

In polar coordinates(spiral) it has a point at origin and scatered points along segment of spiral.

May be my software can not calculate properly such long nested operations.