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Move prime race animations
This commit is contained in:
Grant Sanderson
parent
92224c69c0
commit
8cc62eaf16
2 changed files with 236 additions and 92 deletions
236
_2023/numberphile/prime_race.py
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236
_2023/numberphile/prime_race.py
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@ -0,0 +1,236 @@
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from manim_imports_ext import *
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import sympy
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class PrimeRace(InteractiveScene):
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race_length = 26863
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def construct(self):
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ONE_COLOR = BLUE
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THREE_COLOR = RED
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colors = [ONE_COLOR, THREE_COLOR]
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# Labels
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labels = VGroup(
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Tex(R"p \equiv 1 \mod 4", t2c={"1": ONE_COLOR}),
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Tex(R"p \equiv 3 \mod 4", t2c={"3": THREE_COLOR}),
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)
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labels.arrange(DOWN, buff=0.75)
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labels.to_edge(LEFT)
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h_line = Line(LEFT, RIGHT)
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h_line.set_width(100)
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h_line.to_edge(LEFT)
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v_line = Line(UP, DOWN)
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v_line.set_height(1.5 * labels.get_height())
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v_line.next_to(labels, RIGHT)
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v_line.set_y(0)
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VGroup(h_line, v_line).set_stroke(width=2)
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self.add(h_line, v_line)
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self.add(labels)
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# Start the race
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primes: list[int] = list(sympy.primerange(3, self.race_length))
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team1 = VGroup()
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team3 = VGroup()
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teams = [team1, team3]
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blocks = []
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for prime in primes:
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index = int((prime % 4) == 3)
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square = Square(side_length=1)
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square.set_fill(colors[index], 0.5)
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square.set_stroke(colors[index], 1.0)
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p_mob = Integer(prime)
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p_mob.set_max_width(0.8 * square.get_width())
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block = VGroup(square, p_mob)
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teams[index].add(block)
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blocks.append(block)
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for team, label in zip(teams, labels):
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team.arrange(RIGHT, buff=0)
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team.next_to(v_line, RIGHT, buff=SMALL_BUFF)
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team.match_y(label)
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h_line.set_width(teams[1].get_width() + 10, about_edge=LEFT)
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for block in blocks[:10]:
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self.play(FadeIn(block[0]), Write(block[1]))
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# Next sets
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frame = self.frame
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frame.target = frame.generate_target()
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frame.target.scale(1.75, about_edge=LEFT)
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self.play(
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LaggedStartMap(
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FadeIn, VGroup(*blocks[10:30]),
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lag_ratio=0.9,
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),
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MoveToTarget(frame, rate_func=rush_into),
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run_time=12,
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)
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# Last set
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curr = 30
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tups = [
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(200, 10, linear, 1.25),
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(len(blocks) - 100, 60, linear, 1.25),
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(len(blocks) - 1, 5, smooth, 0.8)
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]
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for index, rt, func, sf in tups:
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frame.target = frame.generate_target()
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frame.target.scale(sf)
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frame.target.set_x(blocks[index].get_right()[0] + 1)
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self.play(
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ShowIncreasingSubsets(VGroup(*blocks[curr:index])),
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MoveToTarget(frame),
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run_time=rt,
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rate_func=func,
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)
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curr = index
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blocks = VGroup(*blocks)
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self.add(blocks)
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self.play(frame.animate.set_height(8, about_point=blocks.get_right() + 2 * LEFT), run_time=3)
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self.wait()
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class RaceGraph(InteractiveScene):
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race_length = 26863
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y_range = (-4, 30, 2)
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def construct(self):
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# Compute differences
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primes: list[int] = list(sympy.primerange(3, self.race_length))
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diffs = [0]
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colors = [WHITE]
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y_max = self.y_range[1]
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for p in primes:
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diff = diffs[-1] + (p % 4 - 2)
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diffs.append(diff)
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if diff < 0:
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colors.append(BLUE)
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elif diff < y_max / 2:
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colors.append(interpolate_color(WHITE, RED, clip(2 * diff / y_max, 0, 1)))
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else:
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colors.append(interpolate_color(RED, RED_E, clip(2 * (diff - y_max / 2) / y_max, 0, 1)))
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# Axes and graph
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x_unit = 10
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axes = Axes(
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x_range=(0, len(primes) + 10, x_unit),
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y_range=self.y_range,
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width=len(primes) / x_unit / 1.6,
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height=7,
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axis_config=dict(tick_size=0.05),
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)
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axes.to_edge(LEFT, buff=0.8)
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y_label = TexText(R"\#Team3 $-$ \#Team1")
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y_label["Team3"].set_color(RED)
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y_label["Team1"].set_color(BLUE)
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y_label.next_to(axes.y_axis.get_top(), RIGHT)
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y_label.fix_in_frame()
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axes.y_axis.add_numbers(font_size=14, buff=0.15)
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graph = VMobject()
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graph.set_points_as_corners([
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axes.c2p(i, diff)
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for i, diff in enumerate(diffs)
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])
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graph.set_stroke(colors, width=3)
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self.add(axes)
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self.add(y_label)
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self.add(graph)
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# Set blocking rectangle
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rect = FullScreenRectangle()
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rect.set_fill(BLACK, 1)
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rect.set_stroke(BLACK, 0)
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rect.match_x(axes.c2p(0, 0), LEFT)
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def set_x_shift(x, anims=[], **kwargs):
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self.play(
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rect.animate.match_x(axes.c2p(x, 0), LEFT),
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*anims,
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**kwargs
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)
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self.clear()
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self.add(graph, rect, axes.x_axis, axes.y_axis, y_label)
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# First blocks, total runtime should be 12
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frame = self.frame
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frame.save_state()
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zoom_point = axes.c2p(0, 0)
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frame.set_height(3, about_point=zoom_point)
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for x in range(10):
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set_x_shift(x + 1)
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for x in range(10, 30):
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set_x_shift(x + 1, run_time = 6 / 20)
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self.wait(6 / 20)
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# Next block
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set_x_shift(
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200,
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anims=[Restore(frame)],
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run_time=10, rate_func=linear
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)
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# Squish the graph
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full_width = get_norm(axes.c2p(200, 0) - axes.c2p(0, 0))
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origin = axes.c2p(0, 0)
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prime_label = Integer(primes[200])
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prime_label.next_to(rect, LEFT, buff=0.7)
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prime_label.to_edge(DOWN, buff=0.3)
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prime_label.fix_in_frame()
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self.add(prime_label)
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def set_x_squish(x1, x2, **kwargs):
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group = VGroup(axes.x_axis, graph)
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self.add(group, rect)
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self.play(
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UpdateFromAlphaFunc(
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group,
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lambda m, a: m.stretch(
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full_width / get_norm(axes.c2p(interpolate(x1, x2, a), 0) - origin),
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0,
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about_point=origin,
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),
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),
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UpdateFromAlphaFunc(
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prime_label,
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lambda m, a: m.set_value(
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primes[min(int(interpolate(x1, x2, a)), len(primes) - 1)]
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)
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),
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**kwargs
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)
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set_x_squish(200, len(primes) - 100, rate_func=linear, run_time=60)
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set_x_squish(len(primes) - 100, len(primes), rate_func=smooth, run_time=5)
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# Reset frame
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self.play(
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VGroup(axes, graph).animate.set_width(
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len(primes) / 10, about_point=axes.c2p(len(primes), 0), stretch=True
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),
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FadeOut(rect),
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run_time=6,
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)
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self.wait()
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class LongRaceGraph(RaceGraph):
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race_length = 650000
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y_range = (-10, 100, 5)
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@ -1,92 +0,0 @@
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from manim_imports_ext import *
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import sympy
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class PrimeRace(InteractiveScene):
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race_length = 2000
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def construct(self):
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ONE_COLOR = BLUE
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THREE_COLOR = RED
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colors = [ONE_COLOR, THREE_COLOR]
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# Labels
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labels = VGroup(
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Tex(R"p \equiv 1 \mod 4", t2c={"1": ONE_COLOR}),
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Tex(R"p \equiv 3 \mod 4", t2c={"3": THREE_COLOR}),
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)
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labels.arrange(DOWN, buff=0.75)
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labels.to_edge(LEFT)
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h_line = Line(LEFT, RIGHT)
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h_line.set_width(100)
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h_line.to_edge(LEFT)
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v_line = Line(UP, DOWN)
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v_line.set_height(1.5 * labels.get_height())
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v_line.next_to(labels, RIGHT)
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v_line.set_y(0)
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VGroup(h_line, v_line).set_stroke(width=2)
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self.add(h_line, v_line)
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self.add(labels)
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# Start the race
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primes: list[int] = list(sympy.primerange(3, self.race_length))
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team1 = VGroup()
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team3 = VGroup()
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teams = [team1, team3]
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blocks = []
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for prime in primes:
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index = int((prime % 4) == 3)
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square = Square(side_length=1)
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square.set_fill(colors[index], 0.5)
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square.set_stroke(colors[index], 1.0)
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p_mob = Integer(prime)
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p_mob.set_max_width(0.8 * square.get_width())
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block = VGroup(square, p_mob)
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teams[index].add(block)
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blocks.append(block)
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for team, label in zip(teams, labels):
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team.arrange(RIGHT, buff=0)
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team.next_to(v_line, RIGHT, buff=SMALL_BUFF)
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team.match_y(label)
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h_line.match_width(teams[1], about_edge=LEFT)
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for block in blocks[:10]:
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self.play(FadeIn(block[0]), Write(block[1]))
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# Next sets
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frame = self.frame
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frame.target = frame.generate_target()
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frame.target.scale(1.5, about_edge=LEFT)
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frame.target.shift(RIGHT)
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self.play(
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LaggedStartMap(
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FadeIn, VGroup(*blocks[10:30]),
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lag_ratio=0.9,
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),
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MoveToTarget(frame, rate_func=rush_into),
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run_time=12,
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)
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# Last set
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curr = 30
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for index, rt in [(200, 10), (len(blocks) - 1, 60)]:
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frame.target = frame.generate_target()
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frame.target.scale(1.25)
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frame.target.set_x(blocks[index].get_right()[0] + 2)
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self.play(
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ShowIncreasingSubsets(VGroup(*blocks[curr:index])),
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MoveToTarget(frame, rate_func=linear),
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run_time=rt,
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)
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curr = index
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class RaceGraph(InteractiveScene):
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def construct(self):
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pass
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