mirror of
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More fractal additions
This commit is contained in:
Grant Sanderson
parent
0835d52bb4
commit
b0e53b8f2a
3 changed files with 296 additions and 15 deletions
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@ -25,6 +25,21 @@ from mobject.svg_mobject import *
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from mobject.tex_mobject import *
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class Britain(SVGMobject):
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CONFIG = {
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"file_name" : "Britain.svg",
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"stroke_width" : 1,
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"stroke_color" : WHITE,
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"fill_opacity" : 0,
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"height" : 5,
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"mark_paths_closed" : True,
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}
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def __init__(self, **kwargs):
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SVGMobject.__init__(self, **kwargs)
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self.scale_to_fit_height(self.height)
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self.center()
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class KochTest(Scene):
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def construct(self):
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koch = KochCurve(order = 5, stroke_width = 2)
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@ -51,6 +66,27 @@ class SierpinskiTest(Scene):
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# self.play(sierp.scale, 2, sierp.get_top())
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# self.dither(3)
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class FractalCreation(Scene):
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CONFIG = {
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"fractal_class" : PentagonalFractal,
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"max_order" : 6,
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"path_arc" : np.pi/6,
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"submobject_mode" : "lagged_start"
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}
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def construct(self):
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fractal = self.fractal_class(order = 0)
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self.play(FadeIn(fractal))
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for order in range(1, self.max_order+1):
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new_fractal = self.fractal_class(order = order)
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self.play(Transform(
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fractal, new_fractal,
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path_arc = self.path_arc,
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submobject_mode = self.submobject_mode,
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run_time = 2
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))
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self.dither()
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self.dither()
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###################################
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@ -122,7 +158,7 @@ class ZoomInOnFractal(PiCreatureScene):
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class WhatAreFractals(TeacherStudentsScene):
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def construct(self):
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self.student_says(
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"But what \\emph{is} a fractal",
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"But what \\emph{is} a fractal?",
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student_index = 2,
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width = 6
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)
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@ -150,13 +186,186 @@ class WhatAreFractals(TeacherStudentsScene):
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self.play(self.get_teacher().change_mode, "happy")
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self.dither(2)
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class IntroduceVonKochCurve(Scene):
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CONFIG = {
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"order" : 5,
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"stroke_width" : 3,
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}
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def construct(self):
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snowflake = self.get_snowflake()
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name = TextMobject("Von Koch Snowflake")
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name.to_edge(UP)
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self.play(ShowCreation(snowflake, run_time = 3))
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self.play(Write(name, run_time = 2))
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curve = self.isolate_one_curve(snowflake)
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self.dither()
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self.zoom_in_on(curve)
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def get_snowflake(self):
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triangle = RegularPolygon(n = 3, start_angle = np.pi/2)
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triangle.scale_to_fit_height(4)
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curves = VGroup(*[
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KochCurve(
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order = self.order,
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stroke_width = self.stroke_width
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)
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for x in range(3)
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])
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for index, curve in enumerate(curves):
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width = curve.get_width()
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curve.move_to(
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(np.sqrt(3)/6)*width*UP, DOWN
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)
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curve.rotate(-index*2*np.pi/3)
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curves.gradient_highlight(BLUE, WHITE, BLUE)
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return curves
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def isolate_one_curve(self, snowflake):
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self.play(*[
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ApplyMethod(curve.shift, curve.get_center()/2)
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for curve in snowflake
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])
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self.dither()
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self.play(
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snowflake.scale, 2.1,
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snowflake.next_to, UP, DOWN
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)
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self.remove(*snowflake[1:])
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return snowflake[0]
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def zoom_in_on(self, curve):
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larger_curve = KochCurve(order = self.order+1)
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larger_curve.replace(curve)
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larger_curve.scale(3, about_point = curve.get_corner(DOWN+LEFT))
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larger_curve.gradient_highlight(
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curve[0].get_color(),
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curve[-1].get_color(),
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)
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self.play(Transform(curve, larger_curve, run_time = 2))
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n_parts = len(curve.split())
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sub_portion = VGroup(*curve[:n_parts/4])
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self.play(
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sub_portion.highlight, YELLOW,
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rate_func = there_and_back
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)
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self.dither()
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class IntroduceSierpinskiTriangle(PiCreatureScene):
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CONFIG = {
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"order" : 7,
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}
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def construct(self):
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sierp = Sierpinski(order = self.order)
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sierp.save_state()
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self.play(FadeIn(
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sierp,
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run_time = 2,
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submobject_mode = "lagged_start"
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))
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self.dither()
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self.play(
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self.pi_creature.change_mode, "pondering",
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*[
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ApplyMethod(submob.shift, submob.get_center())
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for submob in sierp
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]
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)
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self.dither()
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for submob in sierp:
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self.play(sierp.shift, -submob.get_center())
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self.dither()
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self.play(sierp.restore)
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self.change_mode("happy")
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self.dither()
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class SelfSimilarFractalsAsSubset(Scene):
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CONFIG = {
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"fractal_width" : 1.5
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}
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def construct(self):
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self.add_self_similar_fractals()
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self.add_general_fractals()
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def add_self_similar_fractals(self):
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fractals = VGroup(
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DiamondFractal(order = 5),
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KochSnowFlake(order = 3),
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Sierpinski(order = 5),
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)
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for submob in fractals:
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submob.scale_to_fit_width(self.fractal_width)
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fractals.arrange_submobjects(RIGHT)
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fractals[-1].next_to(VGroup(*fractals[:-1]), DOWN)
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title = TextMobject("Self-similar fractals")
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title.next_to(fractals, UP)
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small_rect = Rectangle()
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small_rect.replace(VGroup(fractals, title), stretch = True)
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small_rect.scale_in_place(1.2)
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self.small_rect = small_rect
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group = VGroup(fractals, title, small_rect)
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group.to_corner(UP+LEFT, buff = 2*MED_BUFF)
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self.play(
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Write(title),
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ShowCreation(fractals),
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run_time = 3
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)
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self.play(ShowCreation(small_rect))
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self.dither()
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def add_general_fractals(self):
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big_rectangle = Rectangle(
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width = 2*SPACE_WIDTH - 2*MED_BUFF,
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height = 2*SPACE_HEIGHT - 2*MED_BUFF,
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)
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title = TextMobject("Fractals")
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title.scale(1.5)
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title.next_to(ORIGIN, RIGHT, buff = LARGE_BUFF)
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title.to_edge(UP, buff = 2*MED_BUFF)
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britain = Britain()
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britain.next_to(self.small_rect, RIGHT)
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britain.shift(2*DOWN)
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randy = Randolph().flip().scale(1.4)
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randy.next_to(britain, buff = SMALL_BUFF)
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randy.generate_target()
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randy.target.change_mode("pleading")
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fractalify(randy.target, order = 2)
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self.play(
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ShowCreation(big_rectangle),
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Write(title),
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)
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self.play(ShowCreation(britain), run_time = 5)
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self.play(
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britain.set_stroke, BLACK, 0,
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britain.set_fill, BLUE, 1,
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)
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self.play(FadeIn(randy))
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self.play(MoveToTarget(randy, run_time = 2))
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self.dither(2)
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class ConstrastSmoothAndFractal(Scene):
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def construct(self):
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v_line = Line(UP, DOWN).scale(SPACE_HEIGHT)
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smooth = TextMobject("Smooth")
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smooth.shift(SPACE_WIDTH*LEFT/2)
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fractal = TextMobject("Fractal")
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fractal.shift(SPACE_WIDTH*RIGHT/2)
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VGroup(smooth, fractal).to_edge(UP)
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self.add(v_line, smooth, fractal)
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britain = Britain()
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anchors = britain.get_anchors()
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smooth_britain =
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@ -62,6 +62,8 @@ class SVGMobject(VMobject):
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result.append(self.rect_to_mobject(element))
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elif element.tagName == 'circle':
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result.append(self.circle_to_mobject(element))
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elif element.tagName == 'polygon':
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result.append(self.polygon_to_mobject(element))
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else:
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warnings.warn("Unknown element type: " + element.tagName)
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result = filter(lambda m : m is not None, result)
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@ -86,6 +88,14 @@ class SVGMobject(VMobject):
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self.ref_to_element[ref]
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)
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def polygon_to_mobject(self, polygon_element):
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#TODO, This seems hacky...
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path_string = polygon_element.getAttribute("points")
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for digit in string.digits:
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path_string = path_string.replace(" " + digit, " L" + digit)
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path_string = "M" + path_string
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return self.path_string_to_mobject(path_string)
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# <circle class="st1" cx="143.8" cy="268" r="22.6"/>
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def circle_to_mobject(self, circle_element):
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@ -14,6 +14,50 @@ def rotate(points, angle = np.pi, axis = OUT):
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points = np.dot(points, np.transpose(matrix))
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return points
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def fractalify(vmobject, order = 3, *args, **kwargs):
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for x in range(order):
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fractalification_iteration(vmobject)
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return vmobject
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def fractalification_iteration(vmobject,
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dimension = 1.05,
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num_inserted_anchors_range = range(1, 4)
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):
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num_points = vmobject.get_num_points()
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if num_points > 0:
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# original_anchors = vmobject.get_anchors()
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original_anchors = [
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vmobject.point_from_proportion(x)
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for x in np.linspace(0, 0.99, num_points)
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]
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new_anchors = []
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for p1, p2, in zip(original_anchors, original_anchors[1:]):
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num_inserts = random.choice(num_inserted_anchors_range)
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inserted_points = [
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interpolate(p1, p2, alpha)
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for alpha in np.linspace(0, 1, num_inserts+2)[1:-1]
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]
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mass_scaling_factor = 1./(num_inserts+1)
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length_scaling_factor = mass_scaling_factor**(1./dimension)
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target_length = np.linalg.norm(p1-p2)*length_scaling_factor
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curr_length = np.linalg.norm(p1-p2)*mass_scaling_factor
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#offset^2 + curr_length^2 = target_length^2
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offset_len = np.sqrt(target_length**2 - curr_length**2)
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unit_vect = (p1-p2)/np.linalg.norm(p1-p2)
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offset_unit_vect = rotate_vector(unit_vect, np.pi/2)
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inserted_points = [
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point + u*offset_len*offset_unit_vect
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for u, point in zip(it.cycle([-1, 1]), inserted_points)
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]
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new_anchors += [p1] + inserted_points
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new_anchors.append(original_anchors[-1])
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vmobject.set_points_as_corners(new_anchors)
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vmobject.submobjects = [
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fractalification_iteration(submob, dimension, num_inserted_anchors_range)
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for submob in vmobject.submobjects
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]
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return vmobject
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class SelfSimilarFractal(VMobject):
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CONFIG = {
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@ -87,15 +131,31 @@ class DiamondFractal(SelfSimilarFractal):
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VGroup(*subparts).rotate(np.pi/4)
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class PentagonalFractal(SelfSimilarFractal):
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CONFIG = {
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"num_subparts" : 5,
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"colors" : [MAROON_B, YELLOW, RED]
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}
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def get_seed_shape(self):
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return RegularPolygon(n = 5, start_angle = np.pi/2)
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def arrange_subparts(self, *subparts):
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phi = (1 + np.sqrt(5))/2
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for x, part in enumerate(subparts):
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part.shift(0.95*part.get_height()*UP)
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part.rotate(2*np.pi*x/5)
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######## Space filling curves ############
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class SpaceFillingCurve(VMobject):
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class FractalCurve(VMobject):
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CONFIG = {
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"radius" : 3,
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"order" : 5,
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"colors" : [RED, GREEN],
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"monochromatic" : False,
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"stroke_width" : 2,
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"stroke_width" : 3,
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"propogate_style_to_family" : True,
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}
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def generate_points(self):
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@ -107,13 +167,15 @@ class SpaceFillingCurve(VMobject):
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corner = VMobject()
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corner.set_points_as_corners(triplet)
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self.add(corner)
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def init_colors(self):
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self.gradient_highlight(*self.colors)
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def get_anchor_points(self):
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raise Exception("Not implemented")
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class LindenmayerCurve(SpaceFillingCurve):
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class LindenmayerCurve(FractalCurve):
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CONFIG = {
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"axiom" : "A",
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"rule" : {},
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@ -154,7 +216,7 @@ class LindenmayerCurve(SpaceFillingCurve):
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return np.array(result) - center_of_mass(result)
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class SelfSimilarSpaceFillingCurve(SpaceFillingCurve):
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class SelfSimilarSpaceFillingCurve(FractalCurve):
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CONFIG = {
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"offsets" : [],
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#keys must awkwardly be in string form...
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@ -339,7 +401,7 @@ class SierpinskiCurve(LindenmayerCurve):
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class KochSnowFlake(LindenmayerCurve):
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CONFIG = {
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"colors" : [BLUE_D, WHITE],
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"colors" : [BLUE_D, WHITE, BLUE_D],
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"axiom" : "A--A--A--",
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"rule" : {
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"A" : "A+A--A+A"
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@ -374,7 +436,7 @@ class StellarCurve(LindenmayerCurve):
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"angle" : 2*np.pi/5,
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}
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class SnakeCurve(SpaceFillingCurve):
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class SnakeCurve(FractalCurve):
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CONFIG = {
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"start_color" : BLUE,
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"end_color" : YELLOW,
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@ -409,7 +471,7 @@ class SpaceFillingCurveScene(Scene):
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curve_class_name, order_str = arg_str.split()
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space_filling_curves = dict([
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(Class.__name__, Class)
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for Class in get_all_descendent_classes(SpaceFillingCurve)
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for Class in get_all_descendent_classes(FractalCurve)
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])
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if curve_class_name not in space_filling_curves:
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raise Exception(
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