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End of fractal_dimension project
This commit is contained in:
Grant Sanderson
167
fractal_charm.py
Normal file
167
fractal_charm.py
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@ -0,0 +1,167 @@
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from helpers import *
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from mobject.tex_mobject import TexMobject
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from mobject import Mobject
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from mobject.image_mobject import ImageMobject
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from mobject.vectorized_mobject import *
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from animation.animation import Animation
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from animation.transform import *
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from animation.simple_animations import *
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from animation.playground import *
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from topics.geometry import *
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from topics.characters import *
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from topics.functions import *
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from topics.fractals import *
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from topics.number_line import *
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from topics.combinatorics import *
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from topics.numerals import *
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from topics.three_dimensions import *
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from scene import Scene
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from camera import Camera
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from mobject.svg_mobject import *
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from mobject.tex_mobject import *
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class FractalCreation(Scene):
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CONFIG = {
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"fractal_class" : PentagonalFractal,
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"max_order" : 5,
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"transform_kwargs" : {
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"path_arc" : np.pi/6,
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"submobject_mode" : "lagged_start",
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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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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(
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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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self.play(Transform(
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fractal, new_fractal,
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**self.transform_kwargs
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))
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self.dither()
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self.dither()
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self.fractal = fractal
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class PentagonalFractalCreation(FractalCreation):
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pass
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class DiamondFractalCreation(FractalCreation):
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CONFIG = {
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"fractal_class" : DiamondFractal,
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"max_order" : 6,
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"fractal_kwargs" : {"height" : 6}
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}
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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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"fractal_kwargs" : {"height" : 6},
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"transform_kwargs" : {
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"submobject_mode" : "all_at_once",
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"run_time" : 2,
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},
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}
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def construct(self):
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FractalCreation.construct(self)
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fractal = self.fractal
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smallest_pi = fractal[0][0]
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zoom_factor = 0.1/smallest_pi.get_height()
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fractal.generate_target()
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fractal.target.shift(-smallest_pi.get_corner(UP+LEFT))
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fractal.target.scale(zoom_factor)
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self.play(MoveToTarget(fractal, run_time = 10))
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self.dither()
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class QuadraticKochFractalCreation(FractalCreation):
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CONFIG = {
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"fractal_class" : QuadraticKoch,
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"max_order" : 5,
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"fractal_kwargs" : {"radius" : 10},
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# "transform_kwargs" : {
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# "submobject_mode" : "all_at_once",
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# "run_time" : 2,
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# },
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}
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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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"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 WonkyHexagonFractalCreation(FractalCreation):
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CONFIG = {
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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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@ -1,5 +1,3 @@
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#!/usr/bin/env python
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from helpers import *
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from mobject.tex_mobject import TexMobject
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@ -24,6 +22,8 @@ from camera import Camera
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from mobject.svg_mobject import *
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from mobject.tex_mobject import *
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from fractal_charm import FractalCreation
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from eoc.graph_scene import GraphScene
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from eoc.chapter1 import PatreonThanks
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@ -82,26 +82,7 @@ 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" : 5,
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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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@ -2312,7 +2293,7 @@ class IntroduceLogLogPlot(GraphScene):
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class ManyBritainCounts(BoxCountingWithBritain):
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CONFIG = {
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"box_width" : 0.1,
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"num_boundary_check_points" : 5000,
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"num_boundary_check_points" : 10000,
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"corner_rect_left_extension" : 1,
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}
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def construct(self):
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@ -2325,8 +2306,8 @@ class ManyBritainCounts(BoxCountingWithBritain):
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self.add(self.get_grid())
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self.add(britain)
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for width in range(1, 6):
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self.play(britain.scale_to_fit_width, width)
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for x in range(5):
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self.play(britain.scale, 2, britain.point_from_proportion(0.8))
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boxes = self.get_highlighted_boxes(britain)
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self.play(ShowCreation(boxes))
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self.dither()
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@ -2360,6 +2341,49 @@ class DefineFractal(TeacherStudentsScene):
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])
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self.dither(3)
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class RoughnessAndFractionalDimension(Scene):
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def construct(self):
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title = TextMobject(
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"Non-integer dimension $\\Leftrightarrow$ Roughness"
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)
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title.to_edge(UP)
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self.add(title)
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randy = Randolph().scale(2)
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randy.to_corner(DOWN+RIGHT)
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self.add(randy)
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target = randy.copy()
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target.change_mode("hooray")
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ponder_target = randy.copy()
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ponder_target.change_mode("pondering")
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for mob in target, ponder_target:
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fractalify(mob, order = 2)
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dimension_label = TextMobject("Boundary dimension = ", "1")
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dimension_label.to_edge(LEFT)
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one = dimension_label[1]
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one.highlight(BLUE)
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new_dim = TexMobject("1.2")
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new_dim.move_to(one, DOWN+LEFT)
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new_dim.highlight(one.get_color())
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self.add(dimension_label)
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self.play(Blink(randy))
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self.play(
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Transform(randy, target, run_time = 2),
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Transform(one, new_dim)
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)
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self.dither()
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self.play(Blink(randy))
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self.play(randy.look, DOWN+RIGHT)
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self.dither()
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self.play(randy.look, DOWN+LEFT)
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self.play(Blink(randy))
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self.dither()
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self.play(Transform(randy, ponder_target))
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self.dither()
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class DifferentSlopesAtDifferentScales(IntroduceLogLogPlot):
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def construct(self):
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self.setup_axes(animate = False)
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@ -2401,14 +2425,53 @@ class DifferentSlopesAtDifferentScales(IntroduceLogLogPlot):
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class HoldUpCoilExample(TeacherStudentsScene):
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def construct(self):
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point = UP+RIGHT
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self.play(
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self.get_teacher().change_mode, "raise_right_hand",
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self.get_teacher().look, UP+LEFT
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self.get_teacher().look_at, point
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)
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self.play(*[
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ApplyMethod(pi.look_at, point)
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for pi in self.get_students()
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])
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self.dither(5)
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self.change_student_modes(*["thinking"]*3)
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self.play(*[
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ApplyMethod(pi.look_at, point)
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for pi in self.get_students()
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])
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self.dither(5)
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class SmoothHilbertZoom(Scene):
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def construct(self):
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hilbert = HilbertCurve(
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order = 7,
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color = MAROON_B,
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monochromatic = True
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)
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hilbert.make_smooth()
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self.add(hilbert)
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two_d_title = TextMobject("2D at a distance...")
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one_d_title = TextMobject("1D up close")
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for title in two_d_title, one_d_title:
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title.to_edge(UP)
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self.add(two_d_title)
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self.dither()
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self.play(
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ApplyMethod(
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hilbert.scale, 100,
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hilbert.point_from_proportion(0.3),
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),
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Transform(
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two_d_title, one_d_title,
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rate_func = squish_rate_func(smooth)
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),
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run_time = 3
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)
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self.dither()
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class ListDimensionTypes(PiCreatureScene):
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CONFIG = {
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"use_morty" : False,
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@ -2777,7 +2840,7 @@ class FractalNonFractalFlowChart(Scene):
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class ShowPiCreatureFractalCreation(FractalCreation):
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CONFIG = {
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"fractal_class" : PiCreatureFractal,
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"fractal_class" : PentagonalPiCreatureFractal,
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"max_order" : 4,
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}
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@ -177,6 +177,17 @@ class PiCreature(SVGMobject):
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return self
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def get_all_pi_creature_modes():
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result = []
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prefix = "PiCreatures_"
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suffix = ".svg"
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for file in os.listdir(PI_CREATURE_DIR):
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if file.startswith(prefix) and file.endswith(suffix):
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result.append(
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file[len(prefix):-len(suffix)]
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)
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return result
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class Randolph(PiCreature):
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pass #Nothing more than an alternative name
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@ -3,8 +3,8 @@ 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
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from characters import PiCreature, Randolph
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from topics.geometry import Line, Polygon, RegularPolygon, Square
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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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@ -20,10 +20,7 @@ def fractalify(vmobject, order = 3, *args, **kwargs):
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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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def fractalification_iteration(vmobject, dimension = 1.05, num_inserted_anchors_range = 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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@ -147,7 +144,7 @@ class PentagonalFractal(SelfSimilarFractal):
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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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class PiCreatureFractal(PentagonalFractal):
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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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@ -170,6 +167,88 @@ class PiCreatureFractal(PentagonalFractal):
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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" : 1.7,
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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.submobject_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.highlight(color)
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pi.set_stroke(color, width = 0)
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def generate_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.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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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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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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)
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new_creatures.append(new_creature)
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creature.blink()
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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.gradient_highlight(*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)
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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_submobjects(RIGHT, buff = 0)
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for p in p2, p3, p5, p6:
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p.scale_to_fit_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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######## Space filling curves ############
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class FractalCurve(VMobject):
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Reference in New Issue
Block a user