def construct(self): val = 0.3 text = TextMobject([ "PHC", "$_n", "(", "%3.1f"%val, ")$", " has a ", "limit point ", "as $n \\to \\infty$" ]) func_parts = text.copy().split()[:5] Mobject(*func_parts).center().to_edge(UP) num_str, val_str = func_parts[1], func_parts[3] curve = UnitInterval() curve.sort_points(lambda p : p[0]) dot = Dot().shift(curve.number_to_point(val)) arrow = Arrow(val_str, dot, buff = 0.1) curve.add_numbers(0, 1) self.play(ShowCreation(curve)) self.play( ShimmerIn(val_str), ShowCreation(arrow), ShowCreation(dot) ) self.wait() self.play( FadeOut(arrow), *[ FadeIn(func_parts[i]) for i in 0, 1, 2, 4 ] ) for num in range(2,9): new_curve = HilbertCurve(order = num) new_curve.scale(0.8) new_dot = Dot(new_curve.points[int(val*new_curve.get_num_points())]) new_num_str = TexMobject(str(num)).replace(num_str) self.play( Transform(curve, new_curve), Transform(dot, new_dot), Transform(num_str, new_num_str) ) self.wait() text.to_edge(UP) text_parts = text.split() for index in 1, -1: text_parts[index].set_color() starters = Mobject(*func_parts + [ Point(mob.get_center(), stroke_width=1) for mob in text_parts[5:] ]) self.play(Transform(starters, text)) arrow = Arrow(text_parts[-2].get_bottom(), dot, buff = 0.1) self.play(ShowCreation(arrow)) self.wait()
def construct(self, order): start_color, end_color = RED, GREEN curve = HilbertCurve(order = order) line = Line(5*LEFT, 5*RIGHT) for mob in curve, line: mob.gradient_highlight(start_color, end_color) freq_line = get_freq_line() freq_line.replace(line, stretch = True) unit = 6./(2**order) #sidelength of pixel up = unit*UP right = unit*RIGHT lower_left = 3*(LEFT+DOWN) squares = Mobject(*[ Square( side_length = unit, color = WHITE ).shift(x*right+y*up) for x, y in it.product(range(2**order), range(2**order)) ]) squares.center() targets = Mobject() for square in squares.submobjects: center = square.get_center() distances = np.apply_along_axis( lambda p : np.linalg.norm(p-center), 1, curve.points ) index_along_curve = np.argmin(distances) fraction_along_curve = index_along_curve/float(curve.get_num_points()) target = square.copy().center().scale(0.8/(2**order)) line_index = int(fraction_along_curve*line.get_num_points()) target.shift(line.points[line_index]) targets.add(target) self.add(squares) self.play(ShowCreation( curve, run_time = 5, rate_func = None )) self.dither() self.play( Transform(curve, line), Transform(squares, targets), run_time = 3 ) self.dither() self.play(ShowCreation(freq_line)) self.dither()
def construct(self): start_words = TextMobject([ "``", "Space Filling", "Curve ''", ]).to_edge(TOP, buff = 0.25) quote, space_filling, curve_quote = start_words.copy().split() curve_quote.shift( space_filling.get_left()-\ curve_quote.get_left() ) space_filling = Point(space_filling.get_center()) end_words = Mobject(*[ quote, space_filling, curve_quote ]).center().to_edge(TOP, buff = 0.25) space_filling_fractal = TextMobject(""" ``Space Filling Fractal'' """).to_edge(UP) curve = HilbertCurve(order = 2).shift(DOWN) fine_curve = HilbertCurve(order = 8) fine_curve.replace(curve) dots = Mobject(*[ Dot( curve.points[n*curve.get_num_points()/15], color = YELLOW_C ) for n in range(1, 15) if n not in [4, 11] ]) start_words.shift(2*(UP+LEFT)) self.play( ApplyMethod(start_words.shift, 2*(DOWN+RIGHT)) ) self.wait() self.play(Transform(start_words, end_words)) self.wait() self.play(ShowCreation(curve)) self.wait() self.play(ShowCreation( dots, run_time = 3, )) self.wait() self.clear() self.play(ShowCreation(fine_curve, run_time = 5)) self.wait() self.play(ShimmerIn(space_filling_fractal)) self.wait()
def construct(self): val = 0.7 text = TexMobject([ "\\text{HC}(", "x", ")", "=\\lim_{n \\to \\infty}\\text{PHC}_n(", "x", ")" ]) text.to_edge(UP) x1 = text.split()[1] x2 = text.split()[-2] x2.set_color(BLUE) explanation = TextMobject("Actual Hilbert curve function") exp_arrow = Arrow(explanation, text.split()[0]) curve = UnitInterval() dot = Dot(curve.number_to_point(val)) x_arrow = Arrow(x1.get_bottom(), dot, buff = 0) curve.sort_points(lambda p : p[0]) curve.add_numbers(0, 1) self.add(*text.split()[:3]) self.play( ShimmerIn(explanation), ShowCreation(exp_arrow) ) self.wait() self.remove(explanation, exp_arrow) self.play(ShowCreation(curve)) self.play( ApplyMethod(x1.set_color, BLUE), ShowCreation(x_arrow), ShowCreation(dot) ) self.wait() self.remove(x_arrow) limit = Mobject(*text.split()[3:]).ingest_submobjects() limit.stroke_width = 1 self.play(ShimmerIn(limit)) for num in range(1, 9): new_curve = HilbertCurve(order = num) new_curve.scale(0.8) new_dot = Dot(new_curve.points[int(val*new_curve.get_num_points())]) self.play( Transform(curve, new_curve), Transform(dot, new_dot), )
def construct(self): val = 0.7 text = TexMobject([ "\\text{HC}(", "x", ")", "=\\lim_{n \\to \\infty}\\text{PHC}_n(", "x", ")" ]) text.to_edge(UP) x1 = text.split()[1] x2 = text.split()[-2] x2.highlight(BLUE) explanation = TextMobject("Actual Hilbert curve function") exp_arrow = Arrow(explanation, text.split()[0]) curve = UnitInterval() dot = Dot(curve.number_to_point(val)) x_arrow = Arrow(x1.get_bottom(), dot, buff = 0) curve.sort_points(lambda p : p[0]) curve.add_numbers(0, 1) self.add(*text.split()[:3]) self.play( ShimmerIn(explanation), ShowCreation(exp_arrow) ) self.wait() self.remove(explanation, exp_arrow) self.play(ShowCreation(curve)) self.play( ApplyMethod(x1.highlight, BLUE), ShowCreation(x_arrow), ShowCreation(dot) ) self.wait() self.remove(x_arrow) limit = Mobject(*text.split()[3:]).ingest_submobjects() limit.stroke_width = 1 self.play(ShimmerIn(limit)) for num in range(1, 9): new_curve = HilbertCurve(order = num) new_curve.scale(0.8) new_dot = Dot(new_curve.points[int(val*new_curve.get_num_points())]) self.play( Transform(curve, new_curve), Transform(dot, new_dot), )
def construct(self): curve = HilbertCurve(order = 1) grid = Grid(2, 2, stroke_width=1) self.add(grid, curve) for order in range(2, 6): self.wait() new_grid = Grid(2**order, 2**order, stroke_width=1) self.play( ShowCreation(new_grid), Animation(curve) ) self.remove(grid) grid = new_grid self.play(Transform( curve, HilbertCurve(order = order) )) square = Square(side_length = 6, color = WHITE) square.corner = Mobject1D() square.corner.add_line(3*DOWN, ORIGIN) square.corner.add_line(ORIGIN, 3*RIGHT) square.digest_mobject_attrs() square.scale(2**(-5)) square.corner.set_color( Color(rgb = curve.rgbas[curve.get_num_points()/3]) ) square.shift( grid.get_corner(UP+LEFT)-\ square.get_corner(UP+LEFT) ) self.wait() self.play( FadeOut(grid), FadeOut(curve), FadeIn(square) ) self.play( ApplyMethod(square.replace, grid) ) self.wait()
def construct(self): start_words = TextMobject([ "``", "Space Filling", "Curve ''", ]).to_edge(TOP, buff=0.25) quote, space_filling, curve_quote = start_words.copy().split() curve_quote.shift( space_filling.get_left()-\ curve_quote.get_left() ) space_filling = Point(space_filling.get_center()) end_words = Mobject( *[quote, space_filling, curve_quote]).center().to_edge(TOP, buff=0.25) space_filling_fractal = TextMobject(""" ``Space Filling Fractal'' """).to_edge(UP) curve = HilbertCurve(order=2).shift(DOWN) fine_curve = HilbertCurve(order=8) fine_curve.replace(curve) dots = Mobject(*[ Dot(curve.points[n * curve.get_num_points() / 15], color=YELLOW_C) for n in range(1, 15) if n not in [4, 11] ]) start_words.shift(2 * (UP + LEFT)) self.play(ApplyMethod(start_words.shift, 2 * (DOWN + RIGHT))) self.wait() self.play(Transform(start_words, end_words)) self.wait() self.play(ShowCreation(curve)) self.wait() self.play(ShowCreation( dots, run_time=3, )) self.wait() self.clear() self.play(ShowCreation(fine_curve, run_time=5)) self.wait() self.play(ShimmerIn(space_filling_fractal)) self.wait()
def construct(self): curve = HilbertCurve(order = 1) grid = Grid(2, 2, stroke_width=1) self.add(grid, curve) for order in range(2, 6): self.wait() new_grid = Grid(2**order, 2**order, stroke_width=1) self.play( ShowCreation(new_grid), Animation(curve) ) self.remove(grid) grid = new_grid self.play(Transform( curve, HilbertCurve(order = order) )) square = Square(side_length = 6, color = WHITE) square.corner = Mobject1D() square.corner.add_line(3*DOWN, ORIGIN) square.corner.add_line(ORIGIN, 3*RIGHT) square.digest_mobject_attrs() square.scale(2**(-5)) square.corner.highlight( Color(rgb = curve.rgbas[curve.get_num_points()/3]) ) square.shift( grid.get_corner(UP+LEFT)-\ square.get_corner(UP+LEFT) ) self.wait() self.play( FadeOut(grid), FadeOut(curve), FadeIn(square) ) self.play( ApplyMethod(square.replace, grid) ) self.wait()
def construct(self): val = 0.3 text = TextMobject([ "PHC", "$_n", "(", "%3.1f" % val, ")$", " has a ", "limit point ", "as $n \\to \\infty$" ]) func_parts = text.copy().split()[:5] Mobject(*func_parts).center().to_edge(UP) num_str, val_str = func_parts[1], func_parts[3] curve = UnitInterval() curve.sort_points(lambda p: p[0]) dot = Dot().shift(curve.number_to_point(val)) arrow = Arrow(val_str, dot, buff=0.1) curve.add_numbers(0, 1) self.play(ShowCreation(curve)) self.play(ShimmerIn(val_str), ShowCreation(arrow), ShowCreation(dot)) self.wait() self.play(FadeOut(arrow), *[FadeIn(func_parts[i]) for i in (0, 1, 2, 4)]) for num in range(2, 9): new_curve = HilbertCurve(order=num) new_curve.scale(0.8) new_dot = Dot(new_curve.points[int(val * new_curve.get_num_points())]) new_num_str = TexMobject(str(num)).replace(num_str) self.play(Transform(curve, new_curve), Transform(dot, new_dot), Transform(num_str, new_num_str)) self.wait() text.to_edge(UP) text_parts = text.split() for index in 1, -1: text_parts[index].set_color() starters = Mobject(*func_parts + [ Point(mob.get_center(), stroke_width=1) for mob in text_parts[5:] ]) self.play(Transform(starters, text)) arrow = Arrow(text_parts[-2].get_bottom(), dot, buff=0.1) self.play(ShowCreation(arrow)) self.wait()
def construct(self): text = TextMobject([ "PHC", "_n", "(", "x", ")$", " has a limit point ", "as $n \\to \\infty$", "\\\\ for all $x$" ]) parts = text.split() parts[-1].next_to(Mobject(*parts[:-1]), DOWN) parts[-1].set_color(BLUE) parts[3].set_color(BLUE) parts[1].set_color() parts[-2].set_color() text.to_edge(UP) curve = UnitInterval() curve.sort_points(lambda p : p[0]) vals = np.arange(0.1, 1, 0.1) dots = Mobject(*[ Dot(curve.number_to_point(val)) for val in vals ]) curve.add_numbers(0, 1) starter_dots = dots.copy().ingest_submobjects() starter_dots.shift(2*UP) self.add(curve, text) self.wait() self.play(DelayByOrder(ApplyMethod(starter_dots.shift, 2*DOWN))) self.wait() self.remove(starter_dots) self.add(dots) for num in range(1, 10): new_curve = HilbertCurve(order = num) new_curve.scale(0.8) new_dots = Mobject(*[ Dot(new_curve.points[int(val*new_curve.get_num_points())]) for val in vals ]) self.play( Transform(curve, new_curve), Transform(dots, new_dots), )
def construct(self): text = TextMobject([ "PHC", "_n", "(", "x", ")$", " has a limit point ", "as $n \\to \\infty$", "\\\\ for all $x$" ]) parts = text.split() parts[-1].next_to(Mobject(*parts[:-1]), DOWN) parts[-1].highlight(BLUE) parts[3].highlight(BLUE) parts[1].highlight() parts[-2].highlight() text.to_edge(UP) curve = UnitInterval() curve.sort_points(lambda p : p[0]) vals = np.arange(0.1, 1, 0.1) dots = Mobject(*[ Dot(curve.number_to_point(val)) for val in vals ]) curve.add_numbers(0, 1) starter_dots = dots.copy().ingest_submobjects() starter_dots.shift(2*UP) self.add(curve, text) self.wait() self.play(DelayByOrder(ApplyMethod(starter_dots.shift, 2*DOWN))) self.wait() self.remove(starter_dots) self.add(dots) for num in range(1, 10): new_curve = HilbertCurve(order = num) new_curve.scale(0.8) new_dots = Mobject(*[ Dot(new_curve.points[int(val*new_curve.get_num_points())]) for val in vals ]) self.play( Transform(curve, new_curve), Transform(dots, new_dots), )
def construct(self, order): start_color, end_color = RED, GREEN curve = HilbertCurve(order=order) line = Line(5 * LEFT, 5 * RIGHT) for mob in curve, line: mob.set_color_by_gradient(start_color, end_color) freq_line = get_freq_line() freq_line.replace(line, stretch=True) unit = 6. / (2**order) #sidelength of pixel up = unit * UP right = unit * RIGHT lower_left = 3 * (LEFT + DOWN) squares = Mobject(*[ Square(side_length=unit, color=WHITE).shift(x * right + y * up) for x, y in it.product(range(2**order), range(2**order)) ]) squares.center() targets = Mobject() for square in squares.submobjects: center = square.get_center() distances = np.apply_along_axis( lambda p: np.linalg.norm(p - center), 1, curve.points) index_along_curve = np.argmin(distances) fraction_along_curve = index_along_curve / float( curve.get_num_points()) target = square.copy().center().scale(0.8 / (2**order)) line_index = int(fraction_along_curve * line.get_num_points()) target.shift(line.points[line_index]) targets.add(target) self.add(squares) self.play(ShowCreation(curve, run_time=5, rate_func=None)) self.wait() self.play(Transform(curve, line), Transform(squares, targets), run_time=3) self.wait() self.play(ShowCreation(freq_line)) self.wait()