diff --git a/manimlib/animation/movement.py b/manimlib/animation/movement.py
index 0edf38b1..e5671df2 100644
--- a/manimlib/animation/movement.py
+++ b/manimlib/animation/movement.py
@@ -14,15 +14,13 @@ if TYPE_CHECKING:
 
 
 class Homotopy(Animation):
-    CONFIG = {
-        "run_time": 3,
-        "apply_function_kwargs": {},
-    }
+    apply_function_config: dict = dict()
 
     def __init__(
         self,
         homotopy: Callable[[float, float, float, float], Sequence[float]],
         mobject: Mobject,
+        run_time: float = 3.0,
         **kwargs
     ):
         """
@@ -30,13 +28,12 @@ class Homotopy(Animation):
         (x, y, z, t) to (x', y', z')
         """
         self.homotopy = homotopy
-        super().__init__(mobject, **kwargs)
+        super().__init__(mobject, run_time=run_time, **kwargs)
 
-    def function_at_time_t(
-        self,
-        t: float
-    ) -> Callable[[np.ndarray], Sequence[float]]:
-        return lambda p: self.homotopy(*p, t)
+    def function_at_time_t(self, t: float) -> Callable[[np.ndarray], Sequence[float]]:
+        def result(p):
+            return self.homotopy(*p, t)
+        return result
 
     def interpolate_submobject(
         self,
@@ -47,20 +44,18 @@ class Homotopy(Animation):
         submob.match_points(start)
         submob.apply_function(
             self.function_at_time_t(alpha),
-            **self.apply_function_kwargs
+            **self.apply_function_config
         )
 
 
 class SmoothedVectorizedHomotopy(Homotopy):
-    CONFIG = {
-        "apply_function_kwargs": {"make_smooth": True},
-    }
+    apply_function_config: dict = dict(make_smooth=True)
 
 
 class ComplexHomotopy(Homotopy):
     def __init__(
         self,
-        complex_homotopy: Callable[[complex, float], Sequence[float]],
+        complex_homotopy: Callable[[complex, float], complex],
         mobject: Mobject,
         **kwargs
     ):
@@ -72,24 +67,30 @@ class ComplexHomotopy(Homotopy):
         def homotopy(x, y, z, t):
             c = complex_homotopy(complex(x, y), t)
             return (c.real, c.imag, z)
+
         super().__init__(homotopy, mobject, **kwargs)
 
 
 class PhaseFlow(Animation):
-    CONFIG = {
-        "virtual_time": 1,
-        "rate_func": linear,
-        "suspend_mobject_updating": False,
-    }
-
     def __init__(
         self,
         function: Callable[[np.ndarray], np.ndarray],
         mobject: Mobject,
+        virtual_time: float | None = None,
+        suspend_mobject_updating: bool = False,
+        rate_func: Callable[[float], float] = linear,
+        run_time: float =3.0,
         **kwargs
     ):
         self.function = function
-        super().__init__(mobject, **kwargs)
+        self.virtual_time = virtual_time or run_time
+        super().__init__(
+            mobject,
+            rate_func=rate_func,
+            run_time=run_time,
+            suspend_mobject_updating=suspend_mobject_updating,
+            **kwargs
+        )
 
     def interpolate_mobject(self, alpha: float) -> None:
         if hasattr(self, "last_alpha"):
@@ -101,13 +102,15 @@ class PhaseFlow(Animation):
 
 
 class MoveAlongPath(Animation):
-    CONFIG = {
-        "suspend_mobject_updating": False,
-    }
-
-    def __init__(self, mobject: Mobject, path: Mobject, **kwargs):
+    def __init__(
+        self,
+        mobject: Mobject,
+        path: Mobject,
+        suspend_mobject_updating: bool = False,
+        **kwargs
+    ):
         self.path = path
-        super().__init__(mobject, **kwargs)
+        super().__init__(mobject, suspend_mobject_updating=suspend_mobject_updating, **kwargs)
 
     def interpolate_mobject(self, alpha: float) -> None:
         point = self.path.point_from_proportion(alpha)