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676 lines
20 KiB
Python
676 lines
20 KiB
Python
from functools import reduce
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from manimlib.constants import *
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# from manimlib.for_3b1b_videos.pi_creature import PiCreature
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# from manimlib.for_3b1b_videos.pi_creature import Randolph
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# from manimlib.for_3b1b_videos.pi_creature import get_all_pi_creature_modes
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from manimlib.mobject.geometry import Circle
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from manimlib.mobject.geometry import Polygon
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from manimlib.mobject.geometry import RegularPolygon
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from manimlib.mobject.types.vectorized_mobject import VGroup
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from manimlib.mobject.types.vectorized_mobject import VMobject
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from manimlib.utils.bezier import interpolate
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from manimlib.utils.color import color_gradient
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from manimlib.utils.config_ops import digest_config
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from manimlib.utils.space_ops import center_of_mass
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from manimlib.utils.space_ops import compass_directions
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from manimlib.utils.space_ops import rotate_vector
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from manimlib.utils.space_ops import rotation_matrix
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def rotate(points, angle=np.pi, axis=OUT):
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if axis is None:
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return points
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matrix = rotation_matrix(angle, axis)
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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, dimension=1.05, num_inserted_anchors_range=list(range(1, 4))):
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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, 1 - 1. / num_points, 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 = get_norm(p1 - p2) * length_scaling_factor
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curr_length = get_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) / get_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.set_submobjects([
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fractalification_iteration(
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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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"order": 5,
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"num_subparts": 3,
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"height": 4,
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"colors": [RED, WHITE],
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"stroke_width": 1,
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"fill_opacity": 1,
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}
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def init_colors(self):
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VMobject.init_colors(self)
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self.set_color_by_gradient(*self.colors)
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def init_points(self):
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order_n_self = self.get_order_n_self(self.order)
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if self.order == 0:
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self.set_submobjects([order_n_self])
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else:
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self.set_submobjects(order_n_self.submobjects)
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return self
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def get_order_n_self(self, order):
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if order == 0:
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result = self.get_seed_shape()
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else:
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lower_order = self.get_order_n_self(order - 1)
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subparts = [
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lower_order.copy()
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for x in range(self.num_subparts)
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]
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self.arrange_subparts(*subparts)
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result = VGroup(*subparts)
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result.set_height(self.height)
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result.center()
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return result
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def get_seed_shape(self):
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raise Exception("Not implemented")
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def arrange_subparts(self, *subparts):
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raise Exception("Not implemented")
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class Sierpinski(SelfSimilarFractal):
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def get_seed_shape(self):
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return Polygon(
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RIGHT, np.sqrt(3) * UP, LEFT,
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)
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def arrange_subparts(self, *subparts):
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tri1, tri2, tri3 = subparts
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tri1.move_to(tri2.get_corner(DOWN + LEFT), UP)
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tri3.move_to(tri2.get_corner(DOWN + RIGHT), UP)
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class DiamondFractal(SelfSimilarFractal):
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CONFIG = {
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"num_subparts": 4,
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"height": 4,
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"colors": [GREEN_E, YELLOW],
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}
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def get_seed_shape(self):
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return RegularPolygon(n=4)
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def arrange_subparts(self, *subparts):
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# VGroup(*subparts).rotate(np.pi/4)
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for part, vect in zip(subparts, compass_directions(start_vect=UP + RIGHT)):
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part.next_to(ORIGIN, vect, buff=0)
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VGroup(*subparts).rotate(np.pi / 4, about_point=ORIGIN)
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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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"height": 6,
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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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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, about_point=ORIGIN)
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class PentagonalPiCreatureFractal(PentagonalFractal):
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def init_colors(self):
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SelfSimilarFractal.init_colors(self)
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internal_pis = [
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pi
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for pi in self.get_family()
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if isinstance(pi, PiCreature)
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]
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colors = color_gradient(self.colors, len(internal_pis))
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for pi, color in zip(internal_pis, colors):
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pi.init_colors()
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pi.body.set_stroke(color, width=0.5)
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pi.set_color(color)
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def get_seed_shape(self):
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return Randolph(mode="shruggie")
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def arrange_subparts(self, *subparts):
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for part in subparts:
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part.rotate(2 * np.pi / 5, about_point=ORIGIN)
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PentagonalFractal.arrange_subparts(self, *subparts)
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class PiCreatureFractal(VMobject):
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CONFIG = {
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"order": 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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BLUE_D, BLUE_B, MAROON_B, MAROON_D, GREY,
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YELLOW, RED, GREY_BROWN, RED, RED_E,
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],
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"random_seed": 0,
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"stroke_width": 0,
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}
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def init_colors(self):
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VMobject.init_colors(self)
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internal_pis = [
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pi
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for pi in self.get_family()
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if isinstance(pi, PiCreature)
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]
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random.seed(self.random_seed)
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for pi in reversed(internal_pis):
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color = random.choice(self.colors)
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pi.set_color(color)
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pi.set_stroke(color, width=0)
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def init_points(self):
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random.seed(self.random_seed)
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modes = get_all_pi_creature_modes()
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seed = PiCreature(mode=self.start_mode)
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seed.set_height(self.height)
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seed.to_edge(DOWN)
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creatures = [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, 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.set_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.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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# def init_colors(self):
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# VMobject.init_colors(self)
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# self.set_color_by_gradient(*self.colors)
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class WonkyHexagonFractal(SelfSimilarFractal):
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CONFIG = {
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"num_subparts": 7
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}
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def get_seed_shape(self):
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return RegularPolygon(n=6)
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def arrange_subparts(self, *subparts):
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for i, piece in enumerate(subparts):
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piece.rotate(i * np.pi / 12, about_point=ORIGIN)
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p1, p2, p3, p4, p5, p6, p7 = subparts
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center_row = VGroup(p1, p4, p7)
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center_row.arrange(RIGHT, buff=0)
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for p in p2, p3, p5, p6:
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p.set_width(p1.get_width())
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p2.move_to(p1.get_top(), DOWN + LEFT)
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p3.move_to(p1.get_bottom(), UP + LEFT)
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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, about_point=ORIGIN)
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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_curves(self, n):
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if self.get_num_curves() == 0:
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self.set_points(np.zeros((1, 3)))
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anchors = self.get_anchors()
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indices = np.linspace(
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0, len(anchors) - 1, n + len(anchors)
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).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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"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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}
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def init_points(self):
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points = self.get_anchor_points()
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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.set_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.set_color_by_gradient(*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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class LindenmayerCurve(FractalCurve):
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CONFIG = {
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"axiom": "A",
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"rule": {},
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"scale_factor": 2,
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"radius": 3,
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"start_step": RIGHT,
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"angle": np.pi / 2,
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}
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def expand_command_string(self, command):
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result = ""
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for letter in command:
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if letter in self.rule:
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result += self.rule[letter]
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else:
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result += letter
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return result
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def get_command_string(self):
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result = self.axiom
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for x in range(self.order):
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result = self.expand_command_string(result)
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return result
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def get_anchor_points(self):
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step = float(self.radius) * self.start_step
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step /= (self.scale_factor**self.order)
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curr = np.zeros(3)
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result = [curr]
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for letter in self.get_command_string():
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if letter == "+":
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step = rotate(step, self.angle)
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elif letter == "-":
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step = rotate(step, -self.angle)
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else:
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curr = curr + step
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result.append(curr)
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return np.array(result) - center_of_mass(result)
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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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"offset_to_rotation_axis": {},
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"scale_factor": 2,
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"radius_scale_factor": 0.5,
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}
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def transform(self, points, offset):
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"""
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How to transform the copy of points shifted by
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offset. Generally meant to be extended in subclasses
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"""
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copy = np.array(points)
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if str(offset) in self.offset_to_rotation_axis:
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copy = rotate(
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copy,
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axis=self.offset_to_rotation_axis[str(offset)]
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)
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copy /= self.scale_factor,
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copy += offset * self.radius * self.radius_scale_factor
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return copy
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def refine_into_subparts(self, points):
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transformed_copies = [
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self.transform(points, offset)
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for offset in self.offsets
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]
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return reduce(
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lambda a, b: np.append(a, b, axis=0),
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transformed_copies
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)
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def get_anchor_points(self):
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points = np.zeros((1, 3))
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for count in range(self.order):
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points = self.refine_into_subparts(points)
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return points
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def generate_grid(self):
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raise Exception("Not implemented")
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class HilbertCurve(SelfSimilarSpaceFillingCurve):
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CONFIG = {
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"offsets": [
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LEFT + DOWN,
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LEFT + UP,
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RIGHT + UP,
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RIGHT + DOWN,
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],
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"offset_to_rotation_axis": {
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str(LEFT + DOWN): RIGHT + UP,
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str(RIGHT + DOWN): RIGHT + DOWN,
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},
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}
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class HilbertCurve3D(SelfSimilarSpaceFillingCurve):
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CONFIG = {
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"offsets": [
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RIGHT + DOWN + IN,
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LEFT + DOWN + IN,
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LEFT + DOWN + OUT,
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RIGHT + DOWN + OUT,
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RIGHT + UP + OUT,
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LEFT + UP + OUT,
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LEFT + UP + IN,
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RIGHT + UP + IN,
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],
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"offset_to_rotation_axis_and_angle": {
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str(RIGHT + DOWN + IN): (LEFT + UP + OUT, 2 * np.pi / 3),
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str(LEFT + DOWN + IN): (RIGHT + DOWN + IN, 2 * np.pi / 3),
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str(LEFT + DOWN + OUT): (RIGHT + DOWN + IN, 2 * np.pi / 3),
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str(RIGHT + DOWN + OUT): (UP, np.pi),
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str(RIGHT + UP + OUT): (UP, np.pi),
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str(LEFT + UP + OUT): (LEFT + DOWN + OUT, 2 * np.pi / 3),
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str(LEFT + UP + IN): (LEFT + DOWN + OUT, 2 * np.pi / 3),
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str(RIGHT + UP + IN): (RIGHT + UP + IN, 2 * np.pi / 3),
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},
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}
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# Rewrote transform method to include the rotation angle
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def transform(self, points, offset):
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copy = np.array(points)
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copy = rotate(
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copy,
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axis=self.offset_to_rotation_axis_and_angle[str(offset)][0],
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angle=self.offset_to_rotation_axis_and_angle[str(offset)][1],
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)
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copy /= self.scale_factor,
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copy += offset * self.radius * self.radius_scale_factor
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return copy
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class PeanoCurve(SelfSimilarSpaceFillingCurve):
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CONFIG = {
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"colors": [PURPLE, TEAL],
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"offsets": [
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LEFT + DOWN,
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LEFT,
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LEFT + UP,
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UP,
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ORIGIN,
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DOWN,
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RIGHT + DOWN,
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RIGHT,
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RIGHT + UP,
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],
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"offset_to_rotation_axis": {
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str(LEFT): UP,
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str(UP): RIGHT,
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str(ORIGIN): LEFT + UP,
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str(DOWN): RIGHT,
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str(RIGHT): UP,
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},
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"scale_factor": 3,
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"radius_scale_factor": 2.0 / 3,
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}
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class TriangleFillingCurve(SelfSimilarSpaceFillingCurve):
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CONFIG = {
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"colors": [MAROON, YELLOW],
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"offsets": [
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LEFT / 4. + DOWN / 6.,
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ORIGIN,
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RIGHT / 4. + DOWN / 6.,
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UP / 3.,
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],
|
|
"offset_to_rotation_axis": {
|
|
str(ORIGIN): RIGHT,
|
|
str(UP / 3.): UP,
|
|
},
|
|
"scale_factor": 2,
|
|
"radius_scale_factor": 1.5,
|
|
}
|
|
|
|
# class HexagonFillingCurve(SelfSimilarSpaceFillingCurve):
|
|
# CONFIG = {
|
|
# "start_color" : WHITE,
|
|
# "end_color" : BLUE_D,
|
|
# "axis_offset_pairs" : [
|
|
# (None, 1.5*DOWN + 0.5*np.sqrt(3)*LEFT),
|
|
# (UP+np.sqrt(3)*RIGHT, 1.5*DOWN + 0.5*np.sqrt(3)*RIGHT),
|
|
# (np.sqrt(3)*UP+RIGHT, ORIGIN),
|
|
# ((UP, RIGHT), np.sqrt(3)*LEFT),
|
|
# (None, 1.5*UP + 0.5*np.sqrt(3)*LEFT),
|
|
# (None, 1.5*UP + 0.5*np.sqrt(3)*RIGHT),
|
|
# (RIGHT, np.sqrt(3)*RIGHT),
|
|
# ],
|
|
# "scale_factor" : 3,
|
|
# "radius_scale_factor" : 2/(3*np.sqrt(3)),
|
|
# }
|
|
|
|
# def refine_into_subparts(self, points):
|
|
# return SelfSimilarSpaceFillingCurve.refine_into_subparts(
|
|
# self,
|
|
# rotate(points, np.pi/6, IN)
|
|
# )
|
|
|
|
|
|
class UtahFillingCurve(SelfSimilarSpaceFillingCurve):
|
|
CONFIG = {
|
|
"colors": [WHITE, BLUE_D],
|
|
"axis_offset_pairs": [
|
|
|
|
],
|
|
"scale_factor": 3,
|
|
"radius_scale_factor": 2 / (3 * np.sqrt(3)),
|
|
}
|
|
|
|
|
|
class FlowSnake(LindenmayerCurve):
|
|
CONFIG = {
|
|
"colors": [YELLOW, GREEN],
|
|
"axiom": "A",
|
|
"rule": {
|
|
"A": "A-B--B+A++AA+B-",
|
|
"B": "+A-BB--B-A++A+B",
|
|
},
|
|
"radius": 6, # TODO, this is innaccurate
|
|
"scale_factor": np.sqrt(7),
|
|
"start_step": RIGHT,
|
|
"angle": -np.pi / 3,
|
|
}
|
|
|
|
def __init__(self, **kwargs):
|
|
LindenmayerCurve.__init__(self, **kwargs)
|
|
self.rotate(-self.order * np.pi / 9, about_point=ORIGIN)
|
|
|
|
|
|
class SierpinskiCurve(LindenmayerCurve):
|
|
CONFIG = {
|
|
"colors": [RED, WHITE],
|
|
"axiom": "B",
|
|
"rule": {
|
|
"A": "+B-A-B+",
|
|
"B": "-A+B+A-",
|
|
},
|
|
"radius": 6, # TODO, this is innaccurate
|
|
"scale_factor": 2,
|
|
"start_step": RIGHT,
|
|
"angle": -np.pi / 3,
|
|
}
|
|
|
|
|
|
class KochSnowFlake(LindenmayerCurve):
|
|
CONFIG = {
|
|
"colors": [BLUE_D, WHITE, BLUE_D],
|
|
"axiom": "A--A--A--",
|
|
"rule": {
|
|
"A": "A+A--A+A"
|
|
},
|
|
"radius": 4,
|
|
"scale_factor": 3,
|
|
"start_step": RIGHT,
|
|
"angle": np.pi / 3,
|
|
"order_to_stroke_width_map": {
|
|
3: 3,
|
|
5: 2,
|
|
6: 1,
|
|
},
|
|
}
|
|
|
|
def __init__(self, **kwargs):
|
|
digest_config(self, kwargs)
|
|
self.scale_factor = 2 * (1 + np.cos(self.angle))
|
|
LindenmayerCurve.__init__(self, **kwargs)
|
|
|
|
|
|
class KochCurve(KochSnowFlake):
|
|
CONFIG = {
|
|
"axiom": "A--"
|
|
}
|
|
|
|
|
|
class QuadraticKoch(LindenmayerCurve):
|
|
CONFIG = {
|
|
"colors": [YELLOW, WHITE, MAROON_B],
|
|
"axiom": "A",
|
|
"rule": {
|
|
"A": "A+A-A-AA+A+A-A"
|
|
},
|
|
"radius": 4,
|
|
"scale_factor": 4,
|
|
"start_step": RIGHT,
|
|
"angle": np.pi / 2
|
|
}
|
|
|
|
|
|
class QuadraticKochIsland(QuadraticKoch):
|
|
CONFIG = {
|
|
"axiom": "A+A+A+A"
|
|
}
|
|
|
|
|
|
class StellarCurve(LindenmayerCurve):
|
|
CONFIG = {
|
|
"start_color": RED,
|
|
"end_color": BLUE_E,
|
|
"rule": {
|
|
"A": "+B-A-B+A-B+",
|
|
"B": "-A+B+A-B+A-",
|
|
},
|
|
"scale_factor": 3,
|
|
"angle": 2 * np.pi / 5,
|
|
}
|
|
|
|
|
|
class SnakeCurve(FractalCurve):
|
|
CONFIG = {
|
|
"start_color": BLUE,
|
|
"end_color": YELLOW,
|
|
}
|
|
|
|
def get_anchor_points(self):
|
|
result = []
|
|
resolution = 2**self.order
|
|
step = 2.0 * self.radius / resolution
|
|
lower_left = ORIGIN + \
|
|
LEFT * (self.radius - step / 2) + \
|
|
DOWN * (self.radius - step / 2)
|
|
|
|
for y in range(resolution):
|
|
x_range = list(range(resolution))
|
|
if y % 2 == 0:
|
|
x_range.reverse()
|
|
for x in x_range:
|
|
result.append(
|
|
lower_left + x * step * RIGHT + y * step * UP
|
|
)
|
|
return result
|