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Final(?) animations for chessbaord puzzle part 1
This commit is contained in:
Grant Sanderson
parent
5b1ce542d7
commit
6451371a75
1 changed files with 299 additions and 111 deletions
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@ -1323,6 +1323,22 @@ class TwoSquareCase(ThreeDScene):
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self.wait()
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class IGotThis(TeacherStudentsScene):
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def construct(self):
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self.student_says(
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"Pssh, I got this",
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target_mode="tease",
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look_at_arg=self.screen,
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added_anims=[self.teacher.change, "happy", self.screen],
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run_time=2,
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)
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self.change_student_modes(
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"thinking", "pondering",
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look_at_arg=self.screen
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)
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self.wait(6)
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class WalkingTheSquare(ThreeDScene):
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def construct(self):
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# Setup objects
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@ -1967,6 +1983,82 @@ class SeventyFivePercentChance(Scene):
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self.wait()
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class DoesFlippingAddOrSubtract(Scene):
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def construct(self):
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# Setup sum
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full_sum = Group()
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coins = Group()
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n_shown = 5
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for n in it.chain(range(n_shown), range(64 - n_shown, 64)):
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coin = Coin(numeric_labels=True)
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coin.set_height(0.7)
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coins.add(coin)
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if (random.random() < 0.5 or (n == 2)) and (n != 62):
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coin.flip()
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num = Integer(n)
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summand = Group(
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coin,
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TexMobject("\\cdot"),
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num,
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TexMobject("+"),
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)
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VGroup(*summand[1:]).set_stroke(BLACK, 3, background=True)
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summand.arrange(RIGHT, buff=MED_SMALL_BUFF)
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full_sum.add(summand)
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dots = TexMobject("\\dots")
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full_sum = Group(*full_sum[:n_shown], dots, *full_sum[n_shown:])
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full_sum.arrange(RIGHT, buff=MED_SMALL_BUFF)
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full_sum.set_width(FRAME_WIDTH - 1)
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full_sum[-1][-1].scale(0, about_edge=LEFT)
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full_sum.move_to(UP)
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brace = Brace(full_sum, DOWN)
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s_label = VGroup(
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TextMobject("Sum mod 64 = "),
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Integer(53),
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)
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s_label[1].set_color(BLUE)
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s_label[1].match_height(s_label[0])
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s_label.arrange(RIGHT)
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s_label.next_to(brace, DOWN)
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words = TextMobject("Can't know if a flip will add or subtract")
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words.to_edge(UP)
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self.add(full_sum)
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self.add(brace)
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self.add(s_label)
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self.add(words)
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self.wait()
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# Do some flips
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s_label[1].add_updater(lambda m: m.set_value(m.get_value() % 64))
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for x in range(10):
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n = random.randint(-n_shown, n_shown - 1)
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coin = coins[n]
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n = n % 64
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diff_label = Integer(n, include_sign=True)
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if not coin.is_heads():
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diff_label.set_color(GREEN)
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else:
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diff_label.set_color(RED)
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diff_label.set_value(-diff_label.get_value())
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diff_label.next_to(coin, UP, aligned_edge=LEFT)
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self.play(
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ChangeDecimalToValue(
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s_label[1],
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s_label[1].get_value() + n,
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rate_func=squish_rate_func(smooth, 0.5, 1)
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),
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FlipCoin(coin),
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FadeIn(diff_label, 0.5 * DOWN)
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)
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self.play(FadeOut(diff_label))
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self.wait()
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class ShowCube(ThreeDScene):
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def construct(self):
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# Camera stuffs
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@ -2154,34 +2246,99 @@ class ShowCube(ThreeDScene):
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)
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colors = [RED, GREEN, BLUE_D]
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color_chars = ["R", "G", "B"]
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color_labels = VGroup()
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anims = []
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for sphere, cl, coords in zip(spheres, coord_labels, vert_coords):
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index = np.dot(coords, [0, 1, 2]) % 3
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color = colors[index]
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color_label = TexMobject(color_chars[index])
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color_label.rotate(PI / 2, RIGHT)
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color_label.set_color(color)
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color_label.next_to(cl, RIGHT, SMALL_BUFF)
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color_label.match_depth(cl)
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anims.append(AnimationGroup(
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ApplyMethod(sphere.set_color, color),
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ApplyMethod(cl.set_color, color),
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FadeIn(color_label, LEFT)
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))
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color_labels.add(color_label)
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self.play(LaggedStart(*anims, run_time=6, lag_ratio=0.3))
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self.wait(7)
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self.play(FadeOut(color_labels))
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title = TextMobject("Strategy", "\\, $\\Leftrightarrow$ \\,", "Coloring")
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title[2].set_submobject_colors_by_gradient(*colors)
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title.set_stroke(BLACK, 5, background=True)
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title.set_height(0.7)
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title.to_edge(UP)
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title.shift(LEFT)
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title.fix_in_frame()
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color_label_templates = [
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TexMobject(char, color=color).rotate(PI / 2, RIGHT).match_depth(coord_labels[0])
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for char, color in zip("RGB", colors)
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]
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coord_labels.color_labels = VGroup(*[VMobject() for cl in coord_labels])
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def get_coloring_animation(ns,
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spheres=spheres,
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coord_labels=coord_labels,
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colors=colors,
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color_label_templates=color_label_templates,
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):
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anims = []
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new_color_labels = VGroup()
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for n, sphere, coord_label, old_color_label in zip(ns, spheres, coord_labels, coord_labels.color_labels):
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color = colors[int(n)]
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sphere.generate_target()
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coord_label.generate_target()
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sphere.target.set_color(color)
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coord_label.target.set_fill(color)
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color_label = color_label_templates[n].copy()
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color_label.next_to(coord_label, RIGHT, SMALL_BUFF)
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anims += [
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MoveToTarget(sphere),
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MoveToTarget(coord_label),
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FadeIn(color_label, 0.25 * IN),
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FadeOut(old_color_label, 0.25 * OUT),
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]
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new_color_labels.add(color_label)
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coord_labels.color_labels = new_color_labels
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return LaggedStart(*anims, run_time=2)
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self.play(
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FadeIn(title, DOWN),
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get_coloring_animation(np.random.randint(0, 3, 8)),
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)
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self.wait()
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for x in range(4):
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self.play(get_coloring_animation(np.random.randint(0, 3, 8)))
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self.wait()
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# Some specific color examples
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S0 = TexMobject("S = 0")
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S0.to_edge(LEFT)
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S0.shift(UP)
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S0.fix_in_frame()
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self.play(
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FadeIn(S0, DOWN),
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get_coloring_animation([0] * 8)
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)
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self.wait(5)
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bit_sum = TexMobject("S = \\,&(c_0 + c_1 + c_2) \\\\ &\\quad \\mod 3")
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bit_sum.scale(0.8)
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bit_sum.to_edge(LEFT)
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bit_sum.shift(UP)
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bit_sum.fix_in_frame()
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self.play(
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FadeIn(bit_sum, DOWN),
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FadeOut(S0, UP),
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get_coloring_animation([sum(coords) % 3 for coords in vert_coords])
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)
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self.wait(6)
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bit_sum_with_coefs = TexMobject(
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"S = \\,&(0\\cdot c_0 + 1\\cdot c_1 + 2\\cdot c_2) \\\\ &\\quad \\mod 3"
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)
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bit_sum_with_coefs.scale(0.8)
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bit_sum_with_coefs.move_to(bit_sum, LEFT)
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bit_sum_with_coefs.fix_in_frame()
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self.play(
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FadeIn(bit_sum_with_coefs, DOWN),
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FadeOut(bit_sum, UP),
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get_coloring_animation([np.dot(coords, [0, 1, 2]) % 3 for coords in vert_coords])
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)
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self.wait(4)
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# Focus on (0, 0, 0)
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self.play(
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LaggedStartMap(FlipCoin, coins),
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FlipCoin(coins),
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coord_labels[1:].set_opacity, 0.2,
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coord_labels.color_labels[1:].set_opacity, 0.2,
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spheres[1:].set_opacity, 0.2,
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)
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self.wait(6)
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self.wait(2)
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lines = VGroup()
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for n in [1, 2, 4]:
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@ -2192,11 +2349,9 @@ class ShowCube(ThreeDScene):
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ShowCreationThenDestruction(line),
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spheres[n].set_opacity, 1,
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coord_labels[n].set_opacity, 1,
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spheres[0].set_opacity, 0.2,
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coord_labels[0].set_opacity, 0.2,
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coord_labels.color_labels[n].set_opacity, 1,
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FlipCoin(coin)
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)
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self.wait()
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line.reverse_points()
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self.add(line, coord_labels)
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self.play(
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@ -2204,7 +2359,7 @@ class ShowCube(ThreeDScene):
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ShowCreation(line)
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)
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lines.add(line)
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self.wait(15)
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self.wait(10)
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# Focus on (0, 1, 0)
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self.play(
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@ -2212,11 +2367,12 @@ class ShowCube(ThreeDScene):
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Uncreate(lines[1]),
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FadeOut(lines[::2]),
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Group(
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spheres[1], coord_labels[1],
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spheres[4], coord_labels[4],
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spheres[0], coord_labels[0], coord_labels.color_labels[0],
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spheres[1], coord_labels[1], coord_labels.color_labels[1],
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spheres[4], coord_labels[4], coord_labels.color_labels[4],
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).set_opacity, 0.2,
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)
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self.wait(6)
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self.wait(3)
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lines = VGroup()
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curr_n = 2
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@ -2229,11 +2385,9 @@ class ShowCube(ThreeDScene):
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ShowCreationThenDestruction(line),
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spheres[new_n].set_opacity, 1,
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coord_labels[new_n].set_opacity, 1,
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# spheres[curr_n].set_opacity, 0.2,
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# coord_labels[curr_n].set_opacity, 0.2,
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coord_labels.color_labels[new_n].set_opacity, 1,
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FlipCoin(coin)
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)
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self.wait()
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line.reverse_points()
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self.add(line, coord_labels)
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self.play(
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@ -2242,66 +2396,17 @@ class ShowCube(ThreeDScene):
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)
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lines.add(line)
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self.wait(10)
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# Show a few more colorings
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self.play(
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LaggedStartMap(Uncreate, lines),
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spheres.set_opacity, 1,
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coord_labels.set_opacity, 1,
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coord_labels.color_labels.set_opacity, 1,
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FadeOut(bit_sum_with_coefs),
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)
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self.wait()
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title = TextMobject("Strategy", "\\, $\\Leftrightarrow$ \\,", "Coloring")
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title[2].set_submobject_colors_by_gradient(*colors)
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title.set_stroke(BLACK, 5, background=True)
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title.set_height(0.7)
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title.to_edge(UP)
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title.shift(LEFT)
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title.fix_in_frame()
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def get_coloring_animation(ns, spheres=spheres, coord_labels=coord_labels, colors=colors):
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anims = []
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for n, sphere, cl in zip(ns, spheres, coord_labels):
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color = colors[int(n)]
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sphere.generate_target()
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cl.generate_target()
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sphere.target.set_color(color)
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cl.target.set_fill(color)
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anims += [MoveToTarget(sphere), MoveToTarget(cl)]
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return LaggedStart(*anims, run_time=1)
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self.play(FadeIn(title, DOWN))
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for x in range(8):
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self.play(get_coloring_animation(np.random.randint(0, 3, 8)))
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self.wait()
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S0 = TexMobject("S = 0")
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S0.to_edge(LEFT)
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S0.shift(UP)
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S0.fix_in_frame()
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self.play(
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FadeIn(S0, DOWN),
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get_coloring_animation([0] * 8)
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)
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self.wait(5)
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bit_sum = TexMobject("S = &(c_0 + c_1 + c_2) \\\\ &\\quad \\mod 3")
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bit_sum.to_edge(LEFT)
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bit_sum.shift(UP)
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bit_sum.fix_in_frame()
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self.play(
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FadeIn(bit_sum, DOWN),
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FadeOut(S0, UP),
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get_coloring_animation([sum(coords) % 3 for coords in vert_coords])
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)
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self.wait(6)
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self.play(
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FadeOut(bit_sum, UP),
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get_coloring_animation([
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sum([n * c for n, c in enumerate(coords)]) % 3
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for coords in vert_coords
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])
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)
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self.wait()
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# Count all strategies
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count = TextMobject("$3^8$ total strategies")
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@ -2320,7 +2425,7 @@ class ShowCube(ThreeDScene):
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full_coins.flip_by_message("64^ 2^64")
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self.play(FadeIn(count, DOWN))
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self.wait(15)
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self.wait(4)
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self.remove(board, coins)
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frame.clear_updaters()
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frame.generate_target()
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@ -2356,7 +2461,7 @@ class ShowCube(ThreeDScene):
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frame.generate_target()
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frame.target.shift(2 * DOWN)
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frame.target.set_rotation(-15 * DEGREES, 70 * DEGREES)
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self.add(full_coins)
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full_coins.unlock_shader_data()
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self.play(
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MoveToTarget(frame, run_time=3),
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LaggedStartMap(FadeOut, full_board),
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@ -2364,12 +2469,15 @@ class ShowCube(ThreeDScene):
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FadeOut(count),
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FadeOut(count64),
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)
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self.play(FadeIn(color_labels))
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frame.add_updater(lambda m, dt: m.increment_theta(0.01 * dt))
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self.wait(30)
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class CubeSupplement(ThreeDScene):
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CONFIG = {
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"try_different_strategies": False,
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}
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def construct(self):
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# Map 8 states to square choices
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boards = Group(*[Chessboard(shape=(1, 3)) for x in range(8)])
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@ -2385,49 +2493,72 @@ class CubeSupplement(ThreeDScene):
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for coords, coins in zip(vert_coords, coin_sets):
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coins.flip_by_bools(coords)
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def get_choice_boards(values, boards):
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choices = VGroup()
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for value, board in zip(values, boards):
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choice = VGroup(*[Square() for x in range(3)])
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choice.arrange(RIGHT, buff=0)
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choice.match_height(board)
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choice.next_to(board, RIGHT, buff=1.25)
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choice.set_fill(GREY_D, 1)
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choice.set_stroke(WHITE, 1)
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choice[value].set_fill(TEAL)
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choices.add(choice)
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return choices
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colors = [RED, GREEN, BLUE_D]
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color_words = ["Red", "Green", "Blue"]
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s_values = [sum([n * v for n, v in enumerate(cs)]) % 3 for cs in vert_coords]
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s_labels = VGroup()
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choice_boards = get_choice_boards(s_values, boards)
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c_labels = VGroup()
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s_arrows = VGroup()
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for value, board in zip(s_values, boards):
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for value, board, choice_board in zip(s_values, boards, choice_boards):
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arrow = Vector(RIGHT)
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arrow.next_to(board, RIGHT, SMALL_BUFF)
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label = VGroup(*[Square() for x in range(3)])
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label.arrange(RIGHT, buff=0)
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label.match_height(board)
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label.next_to(arrow, RIGHT, MED_SMALL_BUFF)
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label.set_fill(GREY_D, 1)
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label.set_stroke(WHITE, 1)
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label[value].set_fill(TEAL)
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label.generate_target()
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label.target[value].set_fill(colors[value])
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c_label = TextMobject(color_words[value], color=colors[value])
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c_label.next_to(label, RIGHT)
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s_labels.add(label)
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c_label.next_to(choice_board, RIGHT)
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c_labels.add(c_label)
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s_arrows.add(arrow)
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choice_board.generate_target()
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choice_board.target[value].set_fill(colors[value])
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self.play(
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LaggedStartMap(FadeIn, boards, lag_ratio=0.25),
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LaggedStartMap(FadeIn, coin_sets, lag_ratio=0.25),
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)
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self.play(
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LaggedStartMap(GrowArrow, s_arrows, lag_ratio=0.25),
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LaggedStartMap(FadeIn, s_labels, lambda m: (m, LEFT), lag_ratio=0.25),
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LaggedStartMap(FadeIn, choice_boards, lambda m: (m, LEFT), lag_ratio=0.25),
|
||||
)
|
||||
self.wait()
|
||||
|
||||
# Associate choices with colors
|
||||
self.play(
|
||||
LaggedStartMap(MoveToTarget, s_labels),
|
||||
LaggedStartMap(FadeIn, c_labels),
|
||||
)
|
||||
self.wait()
|
||||
# Fork
|
||||
if self.try_different_strategies:
|
||||
for x in range(5):
|
||||
values = list(np.arange(8) % 3)
|
||||
random.shuffle(values)
|
||||
new_cboards = get_choice_boards(values, boards)
|
||||
self.play(
|
||||
LaggedStartMap(FadeOut, choice_boards, lambda m: (m, 0.25 * UP)),
|
||||
LaggedStartMap(FadeIn, new_cboards, lambda m: (m, 0.25 * DOWN)),
|
||||
)
|
||||
choice_boards = new_cboards
|
||||
self.wait(2)
|
||||
|
||||
else:
|
||||
# Associate choices with colors
|
||||
self.play(
|
||||
LaggedStartMap(MoveToTarget, choice_boards),
|
||||
LaggedStartMap(FadeIn, c_labels),
|
||||
)
|
||||
self.wait()
|
||||
|
||||
|
||||
class TryDifferentCaseThreeStrategies(CubeSupplement):
|
||||
CONFIG = {
|
||||
"try_different_strategies": True,
|
||||
}
|
||||
|
||||
|
||||
class CubeEdgeDescription(Scene):
|
||||
|
|
@ -3429,6 +3560,61 @@ class SimpleRect(Scene):
|
|||
self.play(FadeOut(rect))
|
||||
|
||||
|
||||
class WhenIsItHopeless(Scene):
|
||||
def construct(self):
|
||||
boards = Group(
|
||||
Chessboard(shape=(1, 3)),
|
||||
Chessboard(shape=(2, 2)),
|
||||
Chessboard(shape=(2, 3)),
|
||||
Chessboard(shape=(2, 3)),
|
||||
Chessboard(shape=(2, 4)),
|
||||
Chessboard(shape=(2, 4)),
|
||||
Chessboard(shape=(3, 3)),
|
||||
Chessboard(shape=(3, 4)),
|
||||
Chessboard(shape=(3, 4)),
|
||||
Chessboard(shape=(3, 4)),
|
||||
)
|
||||
last_board = None
|
||||
last_coins = None
|
||||
last_words = None
|
||||
for n, board in zip(it.count(3), boards):
|
||||
board.scale(1 / board[0].get_height())
|
||||
coins = CoinsOnBoard(board)
|
||||
coins.flip_at_random()
|
||||
diff = len(board) - n
|
||||
if diff > 0:
|
||||
board[-diff:].set_opacity(0)
|
||||
coins[-diff:].set_opacity(0)
|
||||
|
||||
if sum(int_to_bit_coords(n)) == 1:
|
||||
words = TextMobject("Maybe possible")
|
||||
words.set_color(GREEN)
|
||||
else:
|
||||
words = TextMobject("Futile!")
|
||||
words.set_color(RED)
|
||||
words.scale(1.5)
|
||||
words.next_to(board, UP, MED_LARGE_BUFF)
|
||||
|
||||
if n == 3:
|
||||
self.play(
|
||||
FadeIn(board),
|
||||
FadeIn(coins),
|
||||
FadeIn(words, DOWN),
|
||||
)
|
||||
else:
|
||||
self.play(
|
||||
ReplacementTransform(last_board, board),
|
||||
ReplacementTransform(last_coins, coins),
|
||||
FadeOut(last_words),
|
||||
FadeIn(words, DOWN),
|
||||
)
|
||||
self.wait()
|
||||
|
||||
last_board = board
|
||||
last_coins = coins
|
||||
last_words = words
|
||||
|
||||
|
||||
class FourDCubeColoringFromTrees(ThreeDScene):
|
||||
def construct(self):
|
||||
# Camera stuffs
|
||||
|
|
@ -3677,7 +3863,9 @@ class IntroduceHypercube(FourDCubeColoringFromTrees):
|
|||
self.wait(15)
|
||||
|
||||
|
||||
# TODO, have this read names in from a file
|
||||
# Animations for Matt
|
||||
|
||||
|
||||
class ChessEndScreen(PatreonEndScreen):
|
||||
CONFIG = {
|
||||
"scroll_time": 20,
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue