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I incorporated the suggestions and worked the bounds into two different loops. Seems to have fixed it.

u,v = var('u,v')

def is_even(n):
    return n%2 == 0

def c(n):
    return 2/3*(4^(n+1)-4)

def torus(n,u,v):
    if is_even(n):
        return [(2*4**n + 4**n*cos(u))*cos(v), (2*4**n + 4**n*cos(u))*sin(v)+c(n), 4**n*sin(u)]
    else:
        return [4**n*sin(u), (2*4**n + 4**n*cos(u))*sin(v)+c(n),  (2*4**n + 4**n*cos(u))*cos(v)]
T0 = []
for i in srange(0,2*pi+0.1, 0.1):
    T0.append(parametric_plot3d(torus(0,u,v), (u,0,2*pi),(v,i, i+0.1), aspect_ratio=1, frame=False, axes=False))

T = []    
for i in range(len(T0)):
    T.append(sum(T0[j] for j in range(i)))

a = animate(T)
a.show()