##########

# Task 1 #

##########

def connect_ends(curve1, curve2):
    x1,y1,x2,y2 = x_of(curve1(1)),y_of(curve1(1)),x_of(curve2(0)),y_of(curve2(0))
    x,y = x1 - x2, y1 - y2
    return connect_rigidly(curve1,translate(x,y)(curve2))

##########
# Task 2 #
##########

def show_points_gosper(level, num_points,initial_curve):

    return draw_points(num_points, squeeze_curve_to_rect (-0.5, -0.5, 1.5, 1.5)(repeated(gosperize,level)(initial_curve) ))

##########

# Task 3 #

##########

def your_gosper_curve_with_angle(level, angle_at_level):
    if level == 0:
        return unit_line
    else:
        return your_gosperize_with_angle(angle_at_level(level))(your_gosper_curve_with_angle(level-1, angle_at_level))

def your_gosperize_with_angle(theta):
    def inner_gosperize(curve_fn):
        return put_in_standard_position(connect_ends( rotate(theta)(curve_fn), rotate(-theta)(curve_fn)))
    return inner_gosperize