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https://github.com/3b1b/manim.git
synced 2025-07-31 14:03:59 +08:00
New scene for chessboard video
This commit is contained in:
Grant Sanderson
@ -1,12 +1,24 @@
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from manimlib.imports import *
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def boolian_linear_combo(bools):
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return reduce(op.xor, [b * n for n, b in enumerate(bools)], 0)
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def string_to_bools(message):
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# For easter eggs on the board
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bits = bin(int.from_bytes(message.encode(), 'big'))[2:]
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bits = (len(message) * 8 - len(bits)) * '0' + bits
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return [bool(int(b)) for b in bits]
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class Chessboard(SGroup):
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CONFIG = {
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"shape": (8, 8),
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"height": 7,
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"depth": 0.25,
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"colors": [LIGHT_GREY, DARKER_GREY]
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"colors": [LIGHT_GREY, DARKER_GREY],
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"gloss": 0.2,
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}
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def __init__(self, **kwargs):
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@ -25,11 +37,12 @@ class Chessboard(SGroup):
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color = self.colors[(i + j) % 2]
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self[i * nc + j].set_color(color)
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self.center()
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self.set_gloss(self.gloss)
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class Coin(Group):
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CONFIG = {
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"n_sides": 24,
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"disk_resolution": (4, 51),
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"height": 1,
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"depth": 0.1,
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"color": GOLD_D,
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@ -39,11 +52,14 @@ class Coin(Group):
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def __init__(self, **kwargs):
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super().__init__(**kwargs)
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n = self.n_sides + 1
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self.top = Disk3D(resolution=(4, n)).shift(OUT)
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self.bottom = Disk3D(resolution=(4, n)).shift(IN)
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self.edge = Cylinder(height=2, resolution=(n, 2))
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res = self.disk_resolution
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self.top = Disk3D(resolution=res, gloss=0.2)
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self.bottom = self.top.copy()
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self.top.shift(OUT)
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self.bottom.shift(IN)
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self.edge = Cylinder(height=2, resolution=(res[1], 2))
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self.add(self.top, self.bottom, self.edge)
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self.rotate(90 * DEGREES, OUT)
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self.set_color(self.color)
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self.bottom.set_color(RED)
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@ -62,6 +78,9 @@ class Coin(Group):
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self.set_height(self.height)
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self.set_depth(self.depth, stretch=True)
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def is_heads(self):
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return self.top.get_center()[2] > self.bottom.get_center()[2]
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class CoinsOnBoard(Group):
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CONFIG = {
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@ -104,40 +123,269 @@ class FlipCoin(Animation):
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coin.shift(4 * alpha * (1 - alpha) * self.shift_vect)
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return coin
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# Scenes
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# Scenes
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class IntroducePuzzle(Scene):
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CONFIG = {
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"camera_config": {
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"apply_depth_test": True,
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"samples": 8,
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}
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"camera_class": ThreeDCamera,
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}
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def construct(self):
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# Setup
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frame = self.camera.frame
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chessboard = Chessboard()
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chessboard.move_to(ORIGIN, OUT)
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plane = NumberPlane(
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grid = NumberPlane(
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x_range=(0, 8), y_range=(0, 8),
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faded_line_ratio=1,
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faded_line_ratio=0
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)
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grid.match_height(chessboard)
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grid.next_to(chessboard, OUT, 1e-8)
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low_grid = grid.copy()
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low_grid.next_to(chessboard, IN, 1e-8)
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grid.add(low_grid)
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grid.set_stroke(GREY, width=2)
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grid.set_gloss(0.5)
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grid.prepare_for_nonlinear_transform(0)
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coins = CoinsOnBoard(chessboard, include_labels=False)
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coins_random_order = Group(*coins)
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coins_random_order.shuffle()
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coins.set_gloss(0.2)
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coins_to_flip = Group()
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head_bools = string_to_bools('3b1b :)')
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for coin, heads in zip(coins, head_bools):
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if not heads:
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coins_to_flip.add(coin)
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coins_to_flip.shuffle()
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frame.set_phi(45 * DEGREES)
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count_label = VGroup(
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Integer(0, edge_to_fix=RIGHT),
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TextMobject("Coins")
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)
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count_label.arrange(RIGHT, aligned_edge=DOWN)
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count_label.to_corner(UL)
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count_label.fix_in_frame()
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self.add(chessboard)
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self.play(LaggedStartMap(FadeIn, coins_random_order, lambda m: (m, UP), run_time=1))
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# Draw board and coins
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frame.set_rotation(-25 * DEGREES, 70 * DEGREES, 0)
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self.play(
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FadeIn(chessboard),
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ShowCreationThenDestruction(grid, lag_ratio=0.01),
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frame.set_theta, 0,
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frame.set_phi, 45 * DEGREES,
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run_time=3,
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)
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self.wait()
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self.add(count_label)
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self.play(
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ShowIncreasingSubsets(coins),
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UpdateFromFunc(count_label[0], lambda m, c=coins: m.set_value(len(c))),
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rate_func=bezier([0, 0, 1, 1]),
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run_time=2,
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)
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self.wait()
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self.play(LaggedStartMap(FlipCoin, coins_to_flip, run_time=6, lag_ratio=0.1))
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self.add(coins)
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coins.unlock_shader_data()
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self.wait()
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coins_to_flip = Group(*[c for c in coins_random_order if random.random() < 0.5])
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self.play(LaggedStartMap(FlipCoin, coins_to_flip, run_time=1, lag_ratio=0.05))
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# Show key
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key = SVGMobject("key")
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key.set_stroke(GOLD, 0)
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key.set_fill(GOLD, 1)
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key.set_gloss(0.5)
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key.rotate(PI / 2, OUT)
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key.rotate(PI / 4, RIGHT)
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key.move_to(3 * OUT)
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key.scale(0.8)
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key.to_edge(LEFT, buff=1)
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k = boolian_linear_combo(head_bools) ^ 63 # To make the flip below the actual solution
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key_cube = Cube(resolution=(6, 6))
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key_cube.match_color(chessboard[k])
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key_cube.replace(chessboard[k], stretch=True)
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chessboard.replace_submobject(k, key_cube)
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key_square = key_cube[0]
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chessboard.generate_target()
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chessboard.save_state()
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for i, cube in enumerate(chessboard.target):
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if i == k:
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cube[0].set_color(MAROON_E)
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else:
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cube.set_color(interpolate_color(cube.get_color(), BLACK, 0.8))
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key.generate_target()
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key.target.rotate(PI / 4, LEFT)
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key.target.set_width(0.7 * key_square.get_width())
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key.target.next_to(key_square, IN, buff=SMALL_BUFF)
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self.play(FadeIn(key, LEFT))
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self.wait()
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self.play(
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FadeOut(coins, lag_ratio=0.01),
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MoveToTarget(chessboard),
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)
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ks_top = key_square.get_top()
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self.play(
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Rotate(key_square, PI / 2, axis=LEFT, about_point=ks_top),
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MoveToTarget(key),
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frame.set_phi, 60 * DEGREES,
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run_time=2,
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)
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self.play(
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Rotate(key_square, PI / 2, axis=RIGHT, about_point=ks_top),
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run_time=2,
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)
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chessboard.unlock_shader_data()
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chessboard.saved_state[k][0].match_color(key_square)
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self.play(
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chessboard.restore,
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FadeIn(coins),
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frame.set_phi, 20 * DEGREES,
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frame.move_to, 2 * LEFT,
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run_time=3
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)
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# State goal
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goal = TextMobject(
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"Communicate where\\\\the key is",
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" by turning\\\\over one coin.",
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alignment=""
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)
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goal.next_to(count_label, DOWN, LARGE_BUFF, LEFT)
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goal.fix_in_frame()
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goal[1].set_color(YELLOW)
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self.play(FadeIn(goal[0]))
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self.wait()
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self.play(FadeIn(goal[1]))
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self.wait()
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coin = coins[63]
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rect = SurroundingRectangle(coin, color=TEAL)
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self.play(FadeInFromLarge(rect))
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self.play(FlipCoin(coin), FadeOut(rect))
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class FromCoinToSquareMaps(Scene):
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CONFIG = {
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"camera_class": ThreeDCamera,
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"messages": [
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"Please, ",
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"go watch",
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"Stand-up",
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"Maths on",
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"YouTube."
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],
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"flip_lag_ratio": 0.05,
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}
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def construct(self):
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messages = self.messages
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board1 = Chessboard()
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board1.set_width(5.5)
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board1.to_corner(DL)
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board2 = board1.copy()
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board2.to_corner(DR)
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coins = CoinsOnBoard(board1)
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bools = string_to_bools(messages[0])
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for coin, head in zip(coins, bools):
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if not head:
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coin.flip(RIGHT)
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for cube in board2:
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cube.original_color = cube.get_color()
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arrow = Arrow(board1.get_right(), board2.get_left())
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arrow.tip.set_stroke(width=0)
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title1 = TextMobject("Pattern of coins")
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title2 = TextMobject("Individual square")
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for title, board in [(title1, board1), (title2, board2)]:
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title.scale(0.5 / title[0][0].get_height())
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title.next_to(board, UP, MED_LARGE_BUFF)
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title2.align_to(title1, UP)
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def get_special_square(coins=coins, board=board2):
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bools = [coin.is_heads() for coin in coins]
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return board[boolian_linear_combo(bools)]
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self.add(board1)
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self.add(title1)
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self.add(coins)
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self.play(
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GrowArrow(arrow),
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FadeIn(board2, 2 * LEFT)
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)
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square = get_special_square()
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rect = SurroundingRectangle(square, buff=0)
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rect.set_color(PINK)
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rect.next_to(square, OUT, buff=0.01)
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self.play(
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square.set_color, MAROON_C,
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ShowCreation(rect),
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FadeIn(title2)
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)
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for message in messages[1:]:
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new_bools = string_to_bools(message)
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coins_to_flip = Group()
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for coin, to_heads in zip(coins, new_bools):
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if coin.is_heads() ^ to_heads:
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coins_to_flip.add(coin)
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coins_to_flip.shuffle()
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self.play(LaggedStartMap(
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FlipCoin, coins_to_flip,
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lag_ratio=self.flip_lag_ratio,
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run_time=1,
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))
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new_square = get_special_square()
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self.play(
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square.set_color, square.original_color,
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new_square.set_color, MAROON_C,
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rect.move_to, new_square, OUT,
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rect.shift, 0.01 * OUT,
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)
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square = new_square
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self.wait()
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class FromCoinToSquareMapsSingleFlips(FromCoinToSquareMaps):
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CONFIG = {
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"messages": [
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"FlipBits",
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"BlipBits",
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"ClipBits",
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"ChipBits",
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"ChipBats",
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"ChipRats",
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]
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}
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class DiagramOfProgression(Scene):
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def construct(self):
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stages = VGroup(*[Rectangle(4, 2) for x in range(4)])
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stages.arrange_in_grid(buff=1)
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stages.set_height(6)
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stages.to_edge(DOWN)
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titles = VGroup(
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TextMobject("Prisoners conspire"),
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TextMobject("Prisoner 1 sees key"),
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TextMobject("Prisoner 1 flips coin"),
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)
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self.add(stages)
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self.embed()
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