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Preditor prey scenes
This commit is contained in:
Grant Sanderson
parent
3550ec3234
commit
719f24c0dc
1 changed files with 298 additions and 28 deletions
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@ -13,6 +13,7 @@ DEFAULT_SCALAR_FIELD_COLORS = [BLUE_E, GREEN, YELLOW, RED]
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# the stream lines. Certainly while developing, things were not
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# run at production quality.
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FOX_COLOR = "#DF7F20"
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# Helper functions
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def get_flow_start_points(x_min=-8, x_max=8,
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@ -221,8 +222,17 @@ def get_electron(radius=0.05):
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def preditor_prey_vector_field(point):
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alpha = 30.0
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beta = 1.0
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gamma = 30.0
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delta = 1.0
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x, y = point[:2]
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return -(y - 30) * RIGHT + (x - 30) * UP
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result = 0.05 * np.array([
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alpha * x - beta * x * y,
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delta * x * y - gamma * y,
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0,
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])
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return rotate(result, 1 * DEGREES)
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# Mobjects
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@ -2386,6 +2396,9 @@ class IllustrateGaussMagnetic(IllustrateGaussLaw):
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"colors": [BLUE_E, BLUE_D, BLUE_C],
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"stroke_width": 3,
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},
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"stream_line_animation_config": {
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"start_up_time": 0,
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},
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"flow_time": 10,
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}
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@ -2426,12 +2439,14 @@ class IllustrateGaussMagnetic(IllustrateGaussLaw):
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def func(self, point):
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x, y = point[:2]
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top_part = np.array([(y - 0.25), -x, 0])
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bottom_part = np.array([-(y + 0.25), x, 0])
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top_part = np.array([(y - 1.0), -x, 0])
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bottom_part = np.array([-(y + 1.0), x, 0])
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norm = np.linalg.norm
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return 3 * op.add(
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top_part / (norm(top_part)**2 + 1),
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bottom_part / (norm(bottom_part)**2 + 1),
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return 1 * op.add(
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top_part / (norm(top_part) * norm(point - UP) + 0.1),
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bottom_part / (norm(bottom_part) * norm(point - DOWN) + 0.1),
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# top_part / (norm(top_part)**2 + 1),
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# bottom_part / (norm(bottom_part)**2 + 1),
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)
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@ -2457,9 +2472,9 @@ class RelevantInNonSpatialCircumstances(TeacherStudentsScene):
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class ShowTwoPopulations(Scene):
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CONFIG = {
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"total_num_animals": 50,
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"start_num_foxes": 20,
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"start_num_rabbits": 30,
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"total_num_animals": 80,
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"start_num_foxes": 40,
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"start_num_rabbits": 20,
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"animal_height": 0.5,
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"final_wait_time": 30,
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}
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@ -2484,7 +2499,7 @@ class ShowTwoPopulations(Scene):
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for mob in examples:
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mob.save_state()
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mob.scale_to_fit_height(3)
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examples.arrange_submobjects(RIGHT, buff=2)
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examples.arrange_submobjects(LEFT, buff=2)
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preditor, prey = words = VGroup(
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TextMobject("Preditor"),
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@ -2529,10 +2544,10 @@ class ShowTwoPopulations(Scene):
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preditor_prey_vector_field,
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))
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def get_num_foxes():
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def get_num_rabbits():
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return phase_point.get_center()[0]
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def get_num_rabbits():
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def get_num_foxes():
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return phase_point.get_center()[1]
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def get_updater(pop_size_getter):
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@ -2592,9 +2607,14 @@ class ShowTwoPopulations(Scene):
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file_name=name,
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height=self.animal_height,
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fill_color=color,
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# stroke_color=BLACK,
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# stroke_width=0.5
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)
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for submob in result.family_members_with_points():
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if submob.is_subpath:
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submob.is_subpath = False
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submob.set_fill(
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interpolate_color(color, BLACK, 0.8),
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opacity=1
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)
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x_shift, y_shift = [
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(2 * random.random() - 1) * max_val
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for max_val in [
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@ -2606,7 +2626,7 @@ class ShowTwoPopulations(Scene):
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return result
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def get_fox(self):
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return self.get_animal("fox", "#DF7F20")
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return self.get_animal("fox", FOX_COLOR)
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def get_rabbit(self):
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return self.get_animal("rabbit", WHITE)
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@ -2627,30 +2647,280 @@ class ShowTwoPopulations(Scene):
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return count
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class PhaseSpaceOfPopulationModel(ShowTwoPopulations):
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class PhaseSpaceOfPopulationModel(ShowTwoPopulations, PiCreatureScene):
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CONFIG = {
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"origin": 5 * LEFT + 2.5 * DOWN,
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"vector_field_config": {
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"max_magnitude": 50,
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},
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"pi_creatures_start_on_screen": False,
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"default_pi_creature_kwargs": {
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"height": 1.8
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},
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"flow_time": 10,
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}
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def construct(self):
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self.add_population_size_labels()
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self.add_axes()
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self.add_example_point()
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self.write_differential_equations()
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self.add_vectors()
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self.show_evolution_of_one_point()
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self.show_phase_flow()
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def add_population_size_labels(self):
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pass
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def add_axes(self):
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pass
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axes = self.axes = Axes(
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x_min=0,
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x_max=55,
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x_axis_config={"unit_size": 0.15},
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y_min=0,
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y_max=55,
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y_axis_config={"unit_size": 0.09},
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number_line_config={
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"tick_frequency": 10,
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},
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)
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axes.shift(self.origin)
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for axis in axes.x_axis, axes.y_axis:
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axis.add_numbers(*range(10, 60, 10))
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axes_labels = self.axes_labels = VGroup(*[
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VGroup(
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method().scale_to_fit_height(0.75),
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TextMobject("Population"),
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).arrange_submobjects(RIGHT, buff=MED_SMALL_BUFF)
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for method in self.get_rabbit, self.get_fox
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])
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for axis, label, vect in zip(axes, axes_labels, [RIGHT, UP]):
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label.next_to(
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axis.main_line, vect,
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submobject_to_align=label[0]
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)
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self.add(axes, axes_labels)
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def add_example_point(self):
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pass
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axes = self.axes
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origin = self.origin
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x = self.start_num_rabbits
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y = self.start_num_foxes
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point = axes.coords_to_point(x, y)
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x_point = axes.coords_to_point(x, 0)
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y_point = axes.coords_to_point(0, y)
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v_line = DashedLine(x_point, point)
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h_line = DashedLine(y_point, point)
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v_line.set_color(FOX_COLOR)
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h_line.set_color(LIGHT_GREY)
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dot = Dot(point)
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coord_pair = TexMobject(
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"(10, 10)", substrings_to_isolate=["10"]
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)
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pop_sizes = VGroup(Integer(10), Integer(10))
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pop_sizes[0].set_color(LIGHT_GREY)
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pop_sizes[1].set_color(FOX_COLOR)
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tens = coord_pair.get_parts_by_tex("10")
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tens.fade(1)
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def get_pop_size_update(i):
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return ContinualChangingDecimal(
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pop_sizes[i],
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lambda a: int(np.round(
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axes.point_to_coords(dot.get_center())[i]
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)),
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position_update_func=lambda m: m.move_to(tens[i])
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)
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coord_pair.add_background_rectangle()
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coord_pair_update = ContinualUpdateFromFunc(
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coord_pair, lambda m: m.next_to(dot, UR, SMALL_BUFF)
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)
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pop_sizes_updates = [get_pop_size_update(i) for i in 0, 1]
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phase_space = TextMobject("``Phase space''")
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phase_space.set_color(YELLOW)
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phase_space.scale(1.5)
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phase_space.to_edge(UP)
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phase_space.shift(2 * RIGHT)
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self.play(ShowCreation(v_line))
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self.play(ShowCreation(h_line))
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dot.save_state()
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dot.move_to(origin)
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self.add(coord_pair_update)
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self.add(*pop_sizes_updates)
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self.play(
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dot.restore,
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UpdateFromAlphaFunc(pop_sizes, lambda m, a: m.set_fill(opacity=a)),
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VFadeIn(coord_pair)
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)
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self.wait()
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self.play(Write(phase_space))
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self.wait(2)
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self.play(FadeOut(VGroup(h_line, v_line, phase_space)))
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self.play(Rotating(
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dot,
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about_point=axes.coords_to_point(30, 30),
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rate_func=smooth,
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))
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self.dot = dot
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self.coord_pair = coord_pair
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self.coord_pair_update = coord_pair_update
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self.pop_sizes = pop_sizes
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self.pop_sizes_updates = pop_sizes_updates
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def write_differential_equations(self):
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variables = ["XX", "YY"]
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equations = TexMobject(
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"""
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{dXX \\over dt} =
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30 \\cdot XX - XX \\cdot YY \\\\
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\\quad \\\\
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{dYY \\over dt} =
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XX \\cdot YY - 30 \\cdot YY
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""",
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substrings_to_isolate=variables
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)
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animals = [self.get_fox().flip(), self.get_rabbit()]
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for char, animal in zip(variables, animals):
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for part in equations.get_parts_by_tex(char):
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animal_copy = animal.copy()
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animal_copy.scale_to_fit_height(0.5)
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animal_copy.move_to(part, DL)
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Transform(part, animal_copy).update(1)
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equations.shift(2 * DOWN)
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rect = SurroundingRectangle(equations, color=YELLOW)
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rect.set_fill(BLACK, 0.8)
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title = TextMobject("Differential equations")
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title.next_to(rect, UP)
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title.set_color(rect.get_stroke_color())
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self.differential_equation_group = VGroup(
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rect, equations, title
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)
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self.differential_equation_group.to_corner(UR)
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randy = self.pi_creature
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randy.next_to(rect, DL)
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self.play(
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Write(title, run_time=1),
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ShowCreation(rect)
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)
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self.play(
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LaggedStart(FadeIn, equations),
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randy.change, "confused", equations,
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VFadeIn(randy),
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)
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self.wait(3)
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def add_vectors(self):
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pass
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origin = self.axes.coords_to_point(0, 0)
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dot = self.dot
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randy = self.pi_creature
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def show_evolution_of_one_point(self):
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pass
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def rescaled_field(point):
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x, y = self.axes.point_to_coords(point)
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result = preditor_prey_vector_field(np.array([x, y, 0]))
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return self.axes.coords_to_point(*result[:2]) - origin
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self.vector_field_config.update({
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"x_min": origin[0] + 0.5,
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"x_max": self.axes.get_right()[0] + 1,
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"y_min": origin[1] + 0.5,
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"y_max": self.axes.get_top()[1],
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})
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vector_field = VectorField(
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rescaled_field, **self.vector_field_config
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)
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def get_dot_vector():
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vector = vector_field.get_vector(dot.get_center())
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vector.scale(1, about_point=vector.get_start())
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return vector
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dot_vector = get_dot_vector()
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self.play(
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LaggedStart(GrowArrow, vector_field),
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randy.change, "thinking", dot,
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Animation(self.differential_equation_group)
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)
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self.wait(3)
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self.play(
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Animation(dot),
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vector_field.set_fill, {"opacity": 0.2},
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GrowArrow(dot_vector),
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randy.change, "pondering",
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)
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self.wait()
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self.play(
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dot.move_to, dot_vector.get_end(),
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dot.align_to, dot, RIGHT,
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run_time=3,
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)
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self.wait(2)
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self.play(
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dot.move_to, dot_vector.get_end(),
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run_time=3,
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)
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self.wait(2)
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for x in range(6):
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new_dot_vector = get_dot_vector()
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fade_anims = [
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FadeOut(dot_vector),
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FadeIn(new_dot_vector),
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Animation(dot),
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]
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if x == 4:
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fade_anims += [
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vector_field.set_fill, {"opacity": 0.5},
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FadeOut(randy),
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FadeOut(self.differential_equation_group),
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]
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self.play(*fade_anims)
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dot_vector = new_dot_vector
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self.play(dot.move_to, dot_vector.get_end())
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dot_movement = VectorFieldFlow(
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dot, lambda p: 0.3 * vector_field.func(p)
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)
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self.add(dot_movement)
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self.play(FadeOut(dot_vector))
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self.wait(10)
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self.play(
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vector_field.set_fill, {"opacity": 1.0},
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VFadeOut(dot),
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VFadeOut(self.coord_pair),
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UpdateFromAlphaFunc(self.pop_sizes, lambda m, a: m.set_fill(opacity=1 - a)),
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)
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self.remove(
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dot_movement,
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self.coord_pair_update,
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*self.pop_sizes_updates
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)
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self.wait()
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self.vector_field = vector_field
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def show_phase_flow(self):
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pass
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vector_field = self.vector_field
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stream_lines = StreamLines(
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vector_field.func,
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start_points_generator_config={
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"x_min": vector_field.x_min,
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"x_max": vector_field.x_max,
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"y_min": vector_field.y_min,
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"y_max": vector_field.y_max,
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"delta_x": 0.25,
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"delta_y": 0.25,
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},
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min_magnitude=vector_field.min_magnitude,
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max_magnitude=vector_field.max_magnitude,
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virtual_time=4,
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)
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stream_line_animation = StreamLineAnimation(
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stream_lines,
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)
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self.add(stream_line_animation)
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self.add_foreground_mobjects(vector_field)
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self.wait(self.flow_time)
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