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A few more fractal animations
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Grant Sanderson
parent
7dbbcf82ff
commit
2930c094f1
2 changed files with 81 additions and 89 deletions
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@ -32,7 +32,6 @@ class FractalCreation(Scene):
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"run_time" : 2,
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},
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"fractal_kwargs" : {},
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"modify_stroke_width" : True,
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}
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def construct(self):
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fractal = self.fractal_class(order = 0, **self.fractal_kwargs)
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@ -42,12 +41,7 @@ class FractalCreation(Scene):
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order = order,
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**self.fractal_kwargs
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)
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if self.modify_stroke_width:
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smallest = new_fractal.family_members_with_points()[0]
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if smallest.get_width() < 0.25:
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new_fractal.set_stroke(width = 2)
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if smallest.get_width() < 0.1:
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new_fractal.set_stroke(width = 1)
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fractal.align_data(new_fractal)
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self.play(Transform(
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fractal, new_fractal,
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**self.transform_kwargs
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@ -70,7 +64,7 @@ class DiamondFractalCreation(FractalCreation):
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class PiCreatureFractalCreation(FractalCreation):
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CONFIG = {
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"fractal_class" : PiCreatureFractal,
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"max_order" : 5,
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"max_order" : 6,
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"fractal_kwargs" : {"height" : 6},
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"transform_kwargs" : {
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"submobject_mode" : "all_at_once",
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@ -102,8 +96,11 @@ class QuadraticKochFractalCreation(FractalCreation):
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class KochSnowFlakeFractalCreation(FractalCreation):
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CONFIG = {
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"fractal_class" : KochSnowFlake,
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"max_order" : 5,
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"fractal_kwargs" : {"radius" : 6},
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"max_order" : 6,
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"fractal_kwargs" : {
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"radius" : 6,
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"num_submobjects" : 100,
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},
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"transform_kwargs" : {
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"submobject_mode" : "lagged_start",
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"path_arc" : np.pi/6,
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@ -117,11 +114,15 @@ class WonkyHexagonFractalCreation(FractalCreation):
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"fractal_class" : WonkyHexagonFractal,
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"max_order" : 5,
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"fractal_kwargs" : {"height" : 6},
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"transform_kwargs" : {
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"submobject_mode" : "lagged_start",
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"path_arc" : np.pi/6,
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"run_time" : 2,
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},
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}
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class CircularFractalCreation(FractalCreation):
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CONFIG = {
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"fractal_class" : CircularFractal,
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"max_order" : 5,
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"fractal_kwargs" : {"height" : 6},
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}
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@ -3,7 +3,7 @@ from mobject.vectorized_mobject import VMobject, VGroup, VectorizedPoint
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from scene import Scene
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from animation.transform import Transform
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from animation.simple_animations import ShowCreation
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from topics.geometry import Line, Polygon, RegularPolygon, Square
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from topics.geometry import Line, Polygon, RegularPolygon, Square, Circle
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from characters import PiCreature, Randolph, get_all_pi_creature_modes
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from helpers import *
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@ -170,7 +170,7 @@ class PentagonalPiCreatureFractal(PentagonalFractal):
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class PiCreatureFractal(VMobject):
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CONFIG = {
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"order" : 7,
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"scale_val" : 1.7,
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"scale_val" : 2.5,
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"start_mode" : "hooray",
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"height" : 6,
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"colors" : [
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@ -201,21 +201,24 @@ class PiCreatureFractal(VMobject):
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seed.scale_to_fit_height(self.height)
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seed.to_edge(DOWN)
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creatures = [seed]
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self.add(seed)
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self.add(VGroup(seed))
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for x in range(self.order):
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new_creatures = []
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for creature in creatures:
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for eye in creature.eyes:
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for eye, vect in zip(creature.eyes, [LEFT, RIGHT]):
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new_creature = PiCreature(
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mode = random.choice(modes)
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)
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new_creature.replace(eye)
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new_creature.scale(
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self.scale_val,
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about_point = new_creature.get_bottom()
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new_creature.scale_to_fit_height(
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self.scale_val*eye.get_height()
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)
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new_creature.next_to(
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eye, vect,
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buff = 0,
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aligned_edge = DOWN
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)
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new_creatures.append(new_creature)
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creature.blink()
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creature.look_at(random.choice(new_creatures))
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self.add_to_back(VGroup(*new_creatures))
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creatures = new_creatures
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@ -244,36 +247,74 @@ class WonkyHexagonFractal(SelfSimilarFractal):
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p5.move_to(p4.get_top(), DOWN+LEFT)
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p6.move_to(p4.get_bottom(), UP+LEFT)
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class CircularFractal(SelfSimilarFractal):
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CONFIG = {
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"num_subparts" : 3,
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"colors" : [GREEN, BLUE, GREY]
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}
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def get_seed_shape(self):
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return Circle()
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def arrange_subparts(self, *subparts):
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if not hasattr(self, "been_here"):
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self.num_subparts = 3+self.order
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self.been_here = True
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for i, part in enumerate(subparts):
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theta = np.pi/self.num_subparts
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part.next_to(
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ORIGIN, UP,
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buff = self.height/(2*np.tan(theta))
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)
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part.rotate(i*2*np.pi/self.num_subparts)
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self.num_subparts -= 1
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######## Space filling curves ############
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class JaggedCurvePiece(VMobject):
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def insert_n_anchor_points(self, n):
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if self.get_num_anchor_points() == 0:
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self.points = np.zeros((1, 3))
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anchors = self.get_anchors()
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indices = np.linspace(0, len(anchors)-1, n+len(anchors)).astype('int')
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self.set_points_as_corners(anchors[indices])
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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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"num_submobjects" : 20,
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"monochromatic" : False,
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"stroke_width" : 3,
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"order_to_stroke_width_map" : {
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3 : 3,
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4 : 2,
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5 : 1,
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},
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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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points = self.get_anchor_points()
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if self.monochromatic:
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self.set_points_as_corners(points)
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else:
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for triplet in zip(points, points[1:], points[2:]):
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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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self.set_points_as_corners(points)
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if not self.monochromatic:
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alphas = np.linspace(0, 1, self.num_submobjects)
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for alpha_pair in zip(alphas, alphas[1:]):
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submobject = JaggedCurvePiece()
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submobject.pointwise_become_partial(
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self, *alpha_pair
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)
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self.add(submobject)
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self.points = np.zeros((0, 3))
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def init_colors(self):
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VMobject.init_colors(self)
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self.gradient_highlight(*self.colors)
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for order in sorted(self.order_to_stroke_width_map.keys()):
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if self.order >= order:
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self.set_stroke(width = self.order_to_stroke_width_map[order])
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def get_anchor_points(self):
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raise Exception("Not implemented")
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@ -513,7 +554,12 @@ class KochSnowFlake(LindenmayerCurve):
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"radius" : 4,
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"scale_factor" : 3,
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"start_step" : RIGHT,
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"angle" : np.pi/3
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"angle" : np.pi/3,
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"order_to_stroke_width_map" : {
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3 : 3,
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5 : 2,
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6 : 1,
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},
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}
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def __init__(self, **kwargs):
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@ -578,61 +624,6 @@ class SnakeCurve(FractalCurve):
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class SpaceFillingCurveScene(Scene):
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@staticmethod
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def args_to_string(CurveClass, order):
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return CurveClass.__name__ + "Order" + str(order)
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@staticmethod
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def string_to_args(arg_str):
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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(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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"%s is not a space filling curve"%curve_class_name
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)
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CurveClass = space_filling_curves[curve_class_name]
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return CurveClass, int(order_str)
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class TransformOverIncreasingOrders(SpaceFillingCurveScene):
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def setup(self, CurveClass):
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sample = CurveClass(order = 1)
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self.curve = Line(3*LEFT, 3*RIGHT)
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self.curve.gradient_highlight(
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sample.start_color,
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sample.end_color
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)
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self.CurveClass = CurveClass
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self.order = 0
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def construct(self, CurveClass, max_order):
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self.setup(CurveClass)
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while self.order < max_order:
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self.increase_order()
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self.dither()
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def increase_order(self, *other_anims):
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self.order += 1
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new_curve = self.CurveClass(order = self.order)
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self.play(
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Transform(self.curve, new_curve),
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*other_anims,
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run_time = 3/np.sqrt(self.order)
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)
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class DrawSpaceFillingCurve(SpaceFillingCurveScene):
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def construct(self, CurveClass, order):
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curve = CurveClass(order = order)
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self.play(ShowCreation(curve), run_time = 10)
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self.dither()
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