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2^t example for exp_footnote in eoc
This commit is contained in:
Grant Sanderson
parent
dc24f0eaf4
commit
01630a4958
3 changed files with 439 additions and 6 deletions
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@ -25,7 +25,6 @@ from camera import Camera
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from mobject.svg_mobject import *
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from mobject.tex_mobject import *
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from eoc.chapter1 import OpeningQuote, PatreonThanks
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from eoc.graph_scene import *
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class LastVideo(TeacherStudentsScene):
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@ -48,7 +47,7 @@ class LastVideo(TeacherStudentsScene):
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DOWN, buff = MED_LARGE_BUFF,
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)
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known_formulas.scale_to_fit_height(2.5)
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exp_question = TexMobject("2^x, 7^x, e^x ???")
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exp_question = TexMobject("2^x", ", 7^x", ", e^x", " ???")
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last_video_brace = Brace(last_video)
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known_formulas.next_to(last_video_brace, DOWN)
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@ -96,8 +95,396 @@ class LastVideo(TeacherStudentsScene):
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for pi in self.get_students()
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]
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)
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class PopulationSizeGraphVsPopulationMassGraph(Scene):
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def construct(self):
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pass
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class DoublingPopulation(PiCreatureScene):
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CONFIG = {
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"time_color" : YELLOW,
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"pi_creature_grid_dimensions" : (8, 8),
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"pi_creature_grid_height" : 6,
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}
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def construct(self):
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self.remove(self.get_pi_creatures())
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self.introduce_expression()
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self.introduce_pi_creatures()
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self.count_through_days()
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self.ask_about_dM_dt()
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self.growth_per_day()
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self.relate_growth_rate_to_pop_size()
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def introduce_expression(self):
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f_x = TexMobject("f(x)", "=", "2^x")
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f_t = TexMobject("f(t)", "=", "2^t")
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P_t = TexMobject("P(t)", "=", "2^t")
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M_t = TexMobject("M(t)", "=", "2^t")
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functions = VGroup(f_x, f_t, P_t, M_t)
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for function in functions:
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function.scale(1.2)
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function.to_corner(UP+LEFT)
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for function in functions[1:]:
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for i, j in (0, 2), (2, 1):
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function[i][j].highlight(self.time_color)
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t_expression = TexMobject("t", "=", "\\text{Time (in days)}")
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t_expression.to_corner(UP+RIGHT)
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t_expression[0].highlight(self.time_color)
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pop_brace, mass_brace = [
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Brace(function[0], DOWN)
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for function in P_t, M_t
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]
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for brace, word in (pop_brace, "size"), (mass_brace, "mass"):
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text = brace.get_text("Population %s"%word)
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text.to_edge(LEFT)
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brace.text = text
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self.play(Write(f_x))
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self.dither()
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self.play(
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Transform(f_x, f_t),
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FadeIn(
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t_expression,
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run_time = 2,
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submobject_mode = "lagged_start"
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)
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)
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self.play(Transform(f_x, P_t))
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self.play(
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GrowFromCenter(pop_brace),
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Write(pop_brace.text, run_time = 2)
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)
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self.dither(2)
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self.function = f_x
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self.pop_brace = pop_brace
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self.t_expression = t_expression
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self.mass_function = M_t
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self.mass_brace = mass_brace
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def introduce_pi_creatures(self):
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creatures = self.get_pi_creatures()
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total_num_days = self.get_num_days()
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num_start_days = 4
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self.reset()
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for x in range(num_start_days):
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self.let_one_day_pass()
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self.dither()
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self.play(
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Transform(self.function, self.mass_function),
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Transform(self.pop_brace, self.mass_brace),
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Transform(self.pop_brace.text, self.mass_brace.text),
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)
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self.dither()
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for x in range(total_num_days-num_start_days):
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self.let_one_day_pass()
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self.dither()
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self.joint_blink(shuffle = False)
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self.dither()
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def count_through_days(self):
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self.reset()
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brace = self.get_population_size_descriptor()
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days_to_let_pass = 3
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self.play(GrowFromCenter(brace))
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self.dither()
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for x in range(days_to_let_pass):
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self.let_one_day_pass()
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new_brace = self.get_population_size_descriptor()
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self.play(Transform(brace, new_brace))
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self.dither()
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self.population_size_descriptor = brace
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def ask_about_dM_dt(self):
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dM_dt_question = TexMobject("{dM", "\\over dt}", "=", "???")
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dM, dt, equals, q_marks = dM_dt_question
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dM_dt_question.next_to(self.function, DOWN, buff = LARGE_BUFF)
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dM_dt_question.to_edge(LEFT)
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self.play(
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FadeOut(self.pop_brace),
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FadeOut(self.pop_brace.text),
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Write(dM_dt_question)
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)
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self.dither(3)
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for mob in dM, dt:
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self.play(Indicate(mob))
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self.dither()
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self.dM_dt_question = dM_dt_question
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def growth_per_day(self):
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day_to_day, frac = self.get_from_day_to_day_label()
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self.play(
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FadeOut(self.dM_dt_question),
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FadeIn(day_to_day)
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)
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rect = self.let_day_pass_and_highlight_new_creatures(frac)
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for x in range(2):
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new_day_to_day, new_frac = self.get_from_day_to_day_label()
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self.play(*map(FadeOut, [rect, frac]))
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frac = new_frac
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self.play(Transform(day_to_day, new_day_to_day))
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rect = self.let_day_pass_and_highlight_new_creatures(frac)
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self.play(*map(FadeOut, [rect, frac, day_to_day]))
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def let_day_pass_and_highlight_new_creatures(self, frac):
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num_new_creatures = 2**self.get_curr_day()
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brace = self.population_size_descriptor
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self.let_one_day_pass()
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new_brace = self.get_population_size_descriptor()
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self.play(Transform(brace, new_brace))
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new_creatures = VGroup(
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*self.get_on_screen_pi_creatures()[-num_new_creatures:]
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)
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rect = Rectangle(
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color = GREEN,
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fill_color = BLUE,
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fill_opacity = 0.3,
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)
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rect.replace(new_creatures, stretch = True)
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rect.stretch_to_fit_height(rect.get_height()+MED_SMALL_BUFF)
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rect.stretch_to_fit_width(rect.get_width()+MED_SMALL_BUFF)
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self.play(DrawBorderThenFill(rect))
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self.play(Write(frac))
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self.dither()
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return rect
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def relate_growth_rate_to_pop_size(self):
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false_deriv = TexMobject(
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"{d(2^t) ", "\\over dt}", "= 2^t"
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)
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difference_eq = TexMobject(
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"{ {2^{t+1} - 2^t} \\over", "1}", "= 2^t"
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)
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real_deriv = TexMobject(
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"{ {2^{t+dt} - 2^t} \\over", "dt}", "= \\, ???"
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)
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VGroup(
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false_deriv[0][3],
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false_deriv[2][-1],
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difference_eq[0][1],
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difference_eq[0][-2],
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difference_eq[2][-1],
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difference_eq[2][-1],
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real_deriv[0][1],
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real_deriv[0][-2],
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).highlight(YELLOW)
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VGroup(
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difference_eq[0][3],
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difference_eq[1][-1],
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real_deriv[0][3],
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real_deriv[0][4],
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real_deriv[1][-2],
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real_deriv[1][-1],
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).highlight(GREEN)
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expressions = [false_deriv, difference_eq, real_deriv]
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text_arg_list = [
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("Tempting", "...",),
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("Rate of change", "\\\\ per day"),
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("Rate of change", "\\\\ in a small time"),
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]
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for expression, text_args in zip(expressions, text_arg_list):
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expression.next_to(
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self.function, DOWN,
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buff = LARGE_BUFF,
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aligned_edge = LEFT,
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)
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expression.brace = Brace(expression, DOWN)
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expression.brace_text = expression.brace.get_text(*text_args)
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time = self.t_expression[-1]
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new_time = TexMobject("3")
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new_time.move_to(time, LEFT)
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fading_creatures = VGroup(*self.get_on_screen_pi_creatures()[8:])
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brace = self.population_size_descriptor
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self.play(*map(FadeIn, [
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false_deriv, false_deriv.brace, false_deriv.brace_text
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]))
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self.dither()
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self.play(
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Transform(time, new_time),
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FadeOut(fading_creatures)
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)
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new_brace = self.get_population_size_descriptor()
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self.play(Transform(brace, new_brace))
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self.dither()
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for x in range(3):
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self.let_one_day_pass(run_time = 2)
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new_brace = self.get_population_size_descriptor()
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self.play(Transform(brace, new_brace))
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self.dither(2)
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for expression in difference_eq, real_deriv:
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expression.brace_text[1].highlight(GREEN)
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self.play(
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Transform(false_deriv, expression),
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Transform(false_deriv.brace, expression.brace),
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Transform(false_deriv.brace_text, expression.brace_text),
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)
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self.dither(3)
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self.play(FadeOut(brace))
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self.reset()
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for x in range(self.get_num_days()):
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self.let_one_day_pass()
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self.dither()
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rect = Rectangle(color = YELLOW)
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rect.replace(real_deriv)
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rect.stretch_to_fit_width(rect.get_width()+MED_SMALL_BUFF)
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rect.stretch_to_fit_height(rect.get_height()+MED_SMALL_BUFF)
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self.play(*map(FadeOut, [
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false_deriv.brace, false_deriv.brace_text
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]))
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self.play(ShowCreation(rect))
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self.play(*[
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ApplyFunction(
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lambda pi : pi.change_mode("pondering").look_at(real_deriv),
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pi,
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run_time = 2,
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rate_func = squish_rate_func(smooth, a, a+0.5)
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)
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for pi in self.get_pi_creatures()
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for a in [0.5*random.random()]
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])
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self.dither(3)
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###########
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def create_pi_creatures(self):
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width, height = self.pi_creature_grid_dimensions
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creature_array = VGroup(*[
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VGroup(*[
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PiCreature(mode = "plain")
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for y in range(height)
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]).arrange_submobjects(UP, buff = MED_LARGE_BUFF)
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for x in range(width)
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]).arrange_submobjects(RIGHT, buff = MED_LARGE_BUFF)
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creatures = VGroup(*it.chain(*creature_array))
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creatures.scale_to_fit_height(self.pi_creature_grid_height)
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creatures.to_corner(DOWN+RIGHT)
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colors = color_gradient([BLUE, GREEN, GREY_BROWN], len(creatures))
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random.shuffle(colors)
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for creature, color in zip(creatures, colors):
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creature.set_color(color)
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return creatures
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def reset(self):
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time = self.t_expression[-1]
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faders = [time] + list(self.get_on_screen_pi_creatures())
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new_time = TexMobject("0")
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new_time.next_to(self.t_expression[-2], RIGHT)
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first_creature = self.get_pi_creatures()[0]
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self.play(*map(FadeOut, faders))
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self.play(*map(FadeIn, [first_creature, new_time]))
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self.t_expression.submobjects[-1] = new_time
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def let_one_day_pass(self, run_time = 2):
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all_creatures = self.get_pi_creatures()
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on_screen_creatures = self.get_on_screen_pi_creatures()
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low_i = len(on_screen_creatures)
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high_i = min(2*low_i, len(all_creatures))
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new_creatures = VGroup(*all_creatures[low_i:high_i])
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to_children_anims = []
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growing_anims = []
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for old_pi, pi in zip(on_screen_creatures, new_creatures):
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pi.save_state()
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child = pi.copy()
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child.scale(0.25, about_point = child.get_bottom())
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child.eyes.scale(1.5, about_point = child.eyes.get_bottom())
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pi.move_to(old_pi)
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pi.set_fill(opacity = 0)
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index = list(new_creatures).index(pi)
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prop = float(index)/len(new_creatures)
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alpha = np.clip(len(new_creatures)/8.0, 0, 0.5)
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rate_func = squish_rate_func(
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smooth, alpha*prop, alpha*prop+(1-alpha)
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)
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to_child_anim = Transform(pi, child, rate_func = rate_func)
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to_child_anim.update(1)
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growing_anim = ApplyMethod(pi.restore, rate_func = rate_func)
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to_child_anim.update(0)
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to_children_anims.append(to_child_anim)
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growing_anims.append(growing_anim)
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time = self.t_expression[-1]
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total_new_creatures = len(on_screen_creatures) + len(new_creatures)
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new_time = TexMobject(str(int(np.log2(total_new_creatures))))
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new_time.move_to(time, LEFT)
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growing_anims.append(Transform(time, new_time))
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self.play(*to_children_anims, run_time = run_time/2.0)
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self.play(*growing_anims, run_time = run_time/2.0)
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def get_num_pi_creatures_on_screen(self):
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mobjects = self.get_mobjects()
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return sum([
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pi in mobjects for pi in self.get_pi_creatures()
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])
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def get_population_size_descriptor(self):
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on_screen_creatures = self.get_on_screen_pi_creatures()
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brace = Brace(on_screen_creatures, LEFT)
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n = len(on_screen_creatures)
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label = brace.get_text(
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"$2^%d$"%int(np.log2(n)),
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"$=%d$"%n,
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)
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brace.add(label)
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return brace
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def get_num_days(self):
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x, y = self.pi_creature_grid_dimensions
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return int(np.log2(x*y))
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def get_curr_day(self):
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return int(np.log2(len(self.get_on_screen_pi_creatures())))
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def get_from_day_to_day_label(self):
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curr_day = self.get_curr_day()
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top_words = TextMobject(
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"From day", str(curr_day),
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"to", str(curr_day+1), ":"
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)
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top_words.scale_to_fit_width(4)
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top_words.next_to(
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self.function, DOWN,
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buff = MED_LARGE_BUFF,
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aligned_edge = LEFT,
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)
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top_words[1].highlight(GREEN)
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bottom_words = TexMobject(
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str(2**curr_day),
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"\\text{ creatures}", "\\over {1 \\text{ day}}"
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)
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bottom_words[0].highlight(GREEN)
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bottom_words.next_to(top_words, DOWN, buff = MED_LARGE_BUFF)
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return top_words, bottom_words
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@ -325,6 +325,16 @@ class Scene(object):
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self.add_frames(*[self.get_frame()]*int(duration / self.frame_duration))
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return self
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def force_skipping(self):
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self.original_skipping_status = self.skip_animations
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self.skip_animations = True
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return self
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def revert_to_original_skipping_status(self):
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if hasattr(self, "original_skipping_status"):
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self.skip_animations = self.original_skipping_status
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return self
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def add_frames(self, *frames):
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self.frames += list(frames)
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|
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@ -346,9 +346,11 @@ class PiCreatureScene(Scene):
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CONFIG = {
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"total_dither_time" : 0,
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"seconds_to_blink" : 3,
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"pi_creatures_start_on_screen" : True,
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}
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def setup(self):
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self.pi_creatures = VGroup(*self.create_pi_creatures())
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if self.pi_creatures_start_on_screen:
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self.add(*self.pi_creatures)
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def create_pi_creatures(self):
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@ -367,6 +369,17 @@ class PiCreatureScene(Scene):
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def get_primary_pi_creature(self):
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return self.pi_creatures[0]
|
||||
|
||||
def any_pi_creatures_on_screen(self):
|
||||
mobjects = self.get_mobjects()
|
||||
return any([pi in mobjects for pi in self.get_pi_creatures()])
|
||||
|
||||
def get_on_screen_pi_creatures(self):
|
||||
mobjects = self.get_mobjects()
|
||||
return VGroup(*filter(
|
||||
lambda pi : pi in mobjects,
|
||||
self.get_pi_creatures()
|
||||
))
|
||||
|
||||
def introduce_bubble(
|
||||
self,
|
||||
pi_creature,
|
||||
|
|
@ -434,7 +447,7 @@ class PiCreatureScene(Scene):
|
|||
first mobject being animated with each .play call
|
||||
"""
|
||||
animations = Scene.compile_play_args_to_animation_list(self, *args)
|
||||
if not any([pi in self.get_mobjects() for pi in self.get_pi_creatures()]):
|
||||
if not self.any_pi_creatures_on_screen():
|
||||
return animations
|
||||
|
||||
non_pi_creature_anims = filter(
|
||||
|
|
@ -473,11 +486,34 @@ class PiCreatureScene(Scene):
|
|||
return animations
|
||||
|
||||
def blink(self):
|
||||
self.play(Blink(random.choice(self.get_pi_creatures())))
|
||||
self.play(Blink(random.choice(self.get_on_screen_pi_creatures())))
|
||||
|
||||
def joint_blink(self, pi_creatures = None, shuffle = True, **kwargs):
|
||||
if pi_creatures is None:
|
||||
pi_creatures = self.get_on_screen_pi_creatures()
|
||||
creatures_list = list(pi_creatures)
|
||||
if shuffle:
|
||||
random.shuffle(creatures_list)
|
||||
|
||||
def get_rate_func(pi):
|
||||
index = creatures_list.index(pi)
|
||||
proportion = float(index)/len(creatures_list)
|
||||
start_time = 0.8*proportion
|
||||
return squish_rate_func(
|
||||
there_and_back,
|
||||
start_time, start_time + 0.2
|
||||
)
|
||||
|
||||
self.play(*[
|
||||
Blink(pi, rate_func = get_rate_func(pi), **kwargs)
|
||||
for pi in creatures_list
|
||||
])
|
||||
return self
|
||||
|
||||
def dither(self, time = 1, blink = True):
|
||||
while time > 0:
|
||||
if blink and self.total_dither_time%self.seconds_to_blink == 0:
|
||||
time_to_blink = self.total_dither_time%self.seconds_to_blink == 0
|
||||
if blink and self.any_pi_creatures_on_screen() and time_to_blink:
|
||||
self.blink()
|
||||
else:
|
||||
Scene.dither(self)
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue