Beginning fractal dimension project

fractal_dimension.py

@@ -25,6 +25,118 @@ from mobject.svg_mobject import *
 from mobject.tex_mobject import *
 
 
-class Test(Scene):
+class KochTest(Scene):
     def construct(self):
-        pass
+        koch = KochCurve(order = 5, stroke_width = 2)
+
+        self.play(ShowCreation(koch, run_time = 3))
+        self.play(
+            koch.scale, 3, koch.get_left(),
+            koch.set_stroke, None, 4
+        )
+        self.dither()
+
+class SierpinskiTest(Scene):
+    def construct(self):
+        sierp = Sierpinski(
+            order = 5,
+        )
+
+        self.play(FadeIn(
+            sierp, 
+            run_time = 5,
+            submobject_mode = "lagged_start",
+        ))
+        self.dither()
+        # self.play(sierp.scale, 2, sierp.get_top())
+        # self.dither(3)
+
+###################################
+
+
+class ZoomInOnFractal(PiCreatureScene):
+    CONFIG = {
+        "fractal_order" : 6,
+        "num_zooms" : 4,
+        "fractal_class" : Sierpinski,
+        "index_to_replace" : 0,
+    }
+    def construct(self):
+        morty = self.pi_creature
+        fractal = self.get_zoomable_fractal()
+
+        fractal.show()
+        
+        self.play(
+            ShowCreation(
+                fractal, 
+                run_time = 4, 
+                rate_func = rush_from
+            ),
+            morty.change_mode, "hooray",
+        )
+        self.dither()
+        self.play(
+            ApplyMethod(
+                fractal.scale, 2**self.num_zooms, 
+                self.zoom_in_about_point,
+                run_time = 8
+            ),
+            morty.change_mode, "thinking",
+            morty.look_at, fractal.get_corner(self.zoom_in_about_point),
+        )
+        self.play(Blink(morty))
+        self.dither()
+
+    def get_zoomable_fractal(self):
+        fractal = self.fractal_class(order = self.fractal_order)
+
+        to_be_tweaked = fractal
+        for x in range(self.num_zooms):
+            new_corner = self.fractal_class(order = self.fractal_order)
+            new_corner.replace(to_be_tweaked[self.index_to_replace])
+            self.tweak_subpart(new_corner)
+            to_be_tweaked.submobjects[self.index_to_replace] = new_corner
+            to_be_tweaked = new_corner
+        self.zoom_in_about_point = to_be_tweaked.get_center()
+
+        return fractal
+
+    def tweak_subpart(self, subpart):
+        pass
+
+
+class ZoomInOnDiamondFractal(ZoomInOnFractal):
+    CONFIG = {
+        "fractal_order" : 5,
+        "fractal_class" : DiamondFractal,
+    }
+    def construct(self):
+        high_res_fractal = self.fractal_class(order = self.fractal_order)
+        low_res_fractal = self.fractal_class(order = self.fractal_order-1)
+
+        high_res_fractal.scale(3, high_res_fractal.get_top())
+
+        self.add(low_res_fractal)
+        self.dither()
+        self.play(Transform(low_res_fractal, high_res_fractal))
+        self.dither(3)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+

mobject/vectorized_mobject.py

@@ -17,9 +17,6 @@ class VMobject(Mobject):
         "considered_smooth" : True,
         "propogate_style_to_family" : False,
     }
-    def __init__(self, *args, **kwargs):
-        Mobject.__init__(self, *args, **kwargs)
-        VMobject.init_colors(self)
 
     ## Colors
     def init_colors(self):

topics/characters.py

@@ -29,7 +29,9 @@ class PiCreature(SVGMobject):
     CONFIG = {
         "color" : BLUE_E,
         "stroke_width" : 0,
+        "stroke_color" : BLACK,
         "fill_opacity" : 1.0,
+        "propogate_style_to_family" : True,
         "initial_scale_factor" : 0.01,
         "corner_scale_factor" : 0.75,
         "flip_at_start" : False,
@@ -44,7 +46,6 @@ class PiCreature(SVGMobject):
         )
         digest_config(self, kwargs, locals())
         SVGMobject.__init__(self, file_name = svg_file, **kwargs)
-        self.init_colors()
         if self.flip_at_start:
             self.flip()
         if self.start_corner is not None:
@@ -66,7 +67,7 @@ class PiCreature(SVGMobject):
         self.parts_named = True
 
     def init_colors(self):
-        self.set_stroke(color = BLACK, width = self.stroke_width)
+        SVGMobject.init_colors(self)
         if not self.parts_named:
             self.name_parts()
         self.mouth.set_fill(BLACK, opacity = 1)

topics/fractals.py

@@ -3,7 +3,7 @@ from mobject.vectorized_mobject import VMobject, VGroup, VectorizedPoint
 from scene import Scene
 from animation.transform import Transform
 from animation.simple_animations import ShowCreation
-from topics.geometry import Line
+from topics.geometry import Line, Polygon, RegularPolygon
 
 from helpers import *
 
@@ -15,19 +15,92 @@ def rotate(points, angle = np.pi, axis = OUT):
     return points
 
 
+class SelfSimilarFractal(VMobject):
+    CONFIG = {
+        "order" : 5,
+        "num_subparts" : 3,
+        "height" : 4,
+        "colors" : [RED, WHITE],
+        "stroke_width" : 1,
+        "fill_opacity" : 1,
+        "propogate_style_to_family" : True,
+    }
+    def init_colors(self):
+        VMobject.init_colors(self)
+        self.gradient_highlight(*self.colors)
+
+    def generate_points(self):
+        self.submobjects = self.get_order_n_self(self.order).submobjects
+
+    def get_order_n_self(self, order):
+        if order == 0:
+            result = self.get_seed_shape()
+        else:
+            subparts = [
+                self.get_order_n_self(order - 1)
+                for x in range(self.num_subparts)
+            ]
+            self.arrange_subparts(*subparts)
+            result = VGroup(*subparts)
+
+        result.scale_to_fit_height(self.height)
+        result.center()
+        return result
+
+    def get_seed_shape(self):
+        raise Exception("Not implemented")
+
+    def arrange_subparts(self, *subparts):
+        raise Exception("Not implemented")
+
+
+class Sierpinski(SelfSimilarFractal):
+    def get_seed_shape(self):
+        return Polygon(
+            RIGHT, np.sqrt(3)*UP, LEFT,
+        )
+
+    def arrange_subparts(self, *subparts):
+        tri1, tri2, tri3 = subparts
+        tri1.move_to(tri2.get_corner(DOWN+LEFT), UP)
+        tri3.move_to(tri2.get_corner(DOWN+RIGHT), UP)
+
+
+class DiamondFractal(SelfSimilarFractal):
+    CONFIG = {
+        "num_subparts" : 4,
+        "height" : 6,
+    }
+    def get_seed_shape(self):
+        return RegularPolygon(n = 4)
+
+    def arrange_subparts(self, *subparts):
+        # VGroup(*subparts).rotate(np.pi/4)
+        for part, vect in zip(subparts, compass_directions(start_vect = UP+RIGHT)):
+            part.next_to(ORIGIN, vect, buff = 0)
+        VGroup(*subparts).rotate(np.pi/4)
+
+
+######## Space filling curves ############
+
 class SpaceFillingCurve(VMobject):
     CONFIG = {
         "radius"      : 3,
         "order"       : 5,
         "colors" : [RED, GREEN],
+        "monochromatic" : False,
+        "stroke_width" : 2,
     }
 
     def generate_points(self):
         points = self.get_anchor_points()
-        for triplet in zip(points, points[1:], points[2:]):
+        if self.monochromatic:
-            corner = VMobject()
+            self.set_points_as_corners(points)
-            corner.set_points_as_corners(triplet)
+        else:
-            self.add(corner)
+            for triplet in zip(points, points[1:], points[2:]):
+                corner = VMobject()
+                corner.set_points_as_corners(triplet)
+                self.add(corner)
         self.gradient_highlight(*self.colors)
 
     def get_anchor_points(self):
@@ -244,11 +317,10 @@ class FlowSnake(LindenmayerCurve):
         LindenmayerCurve.__init__(self, **kwargs)
         self.rotate(-self.order*np.pi/9)
 
-class Sierpinski(LindenmayerCurve):
+class SierpinskiCurve(LindenmayerCurve):
     CONFIG = {
-        "start_color" : RED,
+        "colors" : [RED, WHITE],
-        "end_color"   : WHITE,
+        "axiom" : "B",
-        "axiom"       : "A",
         "rule" : {
             "A" : "+B-A-B+",
             "B" : "-A+B+A-",
@@ -259,10 +331,9 @@ class Sierpinski(LindenmayerCurve):
         "angle"        : -np.pi/3,
     }
 
-class KochCurve(LindenmayerCurve):
+class KochSnowFlake(LindenmayerCurve):
     CONFIG = {
-        "start_color"  : BLUE_D,
+        "colors" : [BLUE_D, WHITE],
-        "end_color"    : WHITE,
         "axiom"        : "A--A--A--",
         "rule"         : {
             "A" : "A+A--A+A"
@@ -278,6 +349,12 @@ class KochCurve(LindenmayerCurve):
         self.scale_factor = 2*(1+np.cos(self.angle))
         LindenmayerCurve.__init__(self, **kwargs)
 
+class KochCurve(KochSnowFlake):
+    CONFIG = {
+        "axiom" : "A--"
+    }
+        
+
 
 class StellarCurve(LindenmayerCurve):
     CONFIG = {

topics/geometry.py

@@ -267,14 +267,14 @@ class Polygon(VMobject):
     def get_vertices(self):
         return self.get_anchors_and_handles()[0]
 
-class RegularPolygon(VMobject):
+class RegularPolygon(Polygon):
     CONFIG = {
         "start_angle" : 0
     }
     def __init__(self, n = 3, **kwargs):
         digest_config(self, kwargs, locals())
         start_vect = rotate_vector(RIGHT, self.start_angle)
-        vertices = compass_directions(n, start_angle)
+        vertices = compass_directions(n, start_vect)
         Polygon.__init__(self, *vertices, **kwargs)