def summer_branch2():
    cloud = ps.PointCloud()
    shape6 = ps.Shape(cloud)
    t = 0
    while t < 2 * math.pi:
        x = 2*math.sin(t)*math.cos(t)
        y = math.sin(3*t)*math.sin(t)
        z = math.sin(t)+t
        cloud.add(ps.Point(x,y,z))
        t += 0.1

    return shape6
def spring_branch1():
    cloud = ps.PointCloud()
    shape4 = ps.Shape(cloud)
    t = 0
    while t < 2 * math.pi:
        x = 4*math.sin(t)*math.cos(t)
        y = math.sin(3*t)*math.sin(t)
        z = math.sin(t)+t
        cloud.add(ps.Point(x,y,z))
        t += 0.1

    return shape4
def spring_branch2():
    cloud = ps.PointCloud()
    shape5 = ps.Shape(cloud)
    t = 0
    while t < 2 * math.pi:
        x = (t**t)*math.sin(t)
        y = t*math.cos(2*t)
        z = 2*t
        cloud.add(ps.Point(x,y,z))
        t += 0.1

    return shape5
def winter_branch3f():
    cloud = ps.PointCloud()
    shape3 = ps.Shape(cloud)
    t = 0
    while t < 2 * math.pi:
        x = 5*math.cos(t)-math.cos(2*t) + math.sin(5*t)
        y = 5*math.sin(t)-math.sin(2*t)+math.cos(3*t)
        z = t
        cloud.add(ps.Point(x,y,z))
        t += 0.1

    return shape3
def leanne_branch():
    cloud = ps.PointCloud()
    shapel = ps.Shape(cloud)
    t = 0
    while t < 3.1 * math.pi:
        x = 5*math.cos(t)-math.cos(4*t)+5*math.sin(5*t)
        y = 5*math.sin(t)-math.sin(5*t)-math.cos(3*t)
        z = t
        cloud.add(ps.Point(x,y,z))
        t += 0.1

    return shapel
def olivia_branch():
    cloud = ps.PointCloud()
    shape0 = ps.Shape(cloud)
    t = 0
    while t < 5 * math.pi:
        x = 5*math.cos(t)-5*math.cos(2*t)+math.sin(9*t)
        y = 5*math.sin(t)-5*math.sin(2*t)-math.cos(3*t)
        z = t
        cloud.add(ps.Point(x,y,z))
        t += 0.1

    return shape0
def summer_branch4():
    cloud = ps.PointCloud()
    shape8 = ps.Shape(cloud)
    t = 0
    while t < 2 * math.pi:
        x = 4*(t**5) * 3*(t**4) + 9*(t*t) - 6*t
        y = t
        z = (t*t)
        cloud.add(ps.Point(x,y,z))
        t += 0.1

    return shape8
def summer_branch3():
    cloud = ps.PointCloud()
    shape7 = ps.Shape(cloud)
    t = 0
    while t < 2 * math.pi:
        x = t*math.sin(t)
        y = math.sin(3*t)+math.sin(t)+math.cos(t)
        z = (t*t)+math.sin(t)
        cloud.add(ps.Point(x,y,z))
        t += 0.1

    return shape7