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first variants of generalized Pascal's Triangle
This commit is contained in:
Ben Hambrecht
@ -1,201 +1,351 @@
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from big_ol_pile_of_manim_imports import *
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from once_useful_constructs.combinatorics import *
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nb_levels = 50
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nb_levels = 5
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dev_x_step = 2
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dev_y_step = 5
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def rainbow_color(alpha):
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nb_colors = 100
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rainbow = color_gradient([RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE], nb_colors)
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rainbow = np.append(rainbow,PURPLE)
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index = int(alpha * nb_colors)
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return rainbow[index]
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nb_colors = 100
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rainbow = color_gradient([RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE], nb_colors)
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rainbow = np.append(rainbow,PURPLE)
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index = int(alpha * nb_colors)
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return rainbow[index]
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def graded_color(n,k):
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if n != 0:
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alpha = float(k)/n
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else:
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alpha = 0.5
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color = interpolate_color(RED, BLUE, alpha)
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return color
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class SampleScene(Scene):
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def graded_square(n,k):
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return Square(
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side_length = 1,
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fill_color = graded_color(n,k),
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fill_opacity = 1,
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stroke_width = 1
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)
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def construct(self):
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def graded_binomial(n,k):
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return Integer(
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choose(n,k),
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color = graded_color(n,k)
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)
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triangle = Polygon()
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self.add(triangle)
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self.wait()
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def split_square(n,k):
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width = 1
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height = 1
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proportion = float(choose(n,k)) / 2**n
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lower_height = proportion * height
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upper_height = (1 - proportion) * height
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lower_rect = Rectangle(
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width = width,
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height = lower_height,
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fill_color = RED,
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fill_opacity = 1.0,
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stroke_color = WHITE,
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stroke_width = 3
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)
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upper_rect = Rectangle(
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width = width,
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height = upper_height,
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fill_color = BLUE,
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fill_opacity = 1.0,
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stroke_color = WHITE,
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stroke_width = 3
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)
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upper_rect.next_to(lower_rect,UP,buff = 0)
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square = VGroup(lower_rect, upper_rect).move_to(ORIGIN)
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return square
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class BuildNewPascalRow(Transform):
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def __init__(self,mobject, duplicate_row = None, **kwargs):
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if mobject.__class__ != GeneralizedPascalsTriangle and mobject.__class__ != PascalsTriangle:
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raise("Transform BuildNewPascalRow only works on members of (Generalized)PascalsTriangle!")
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n = mobject.nrows - 1
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lowest_row_copy1 = mobject.get_lowest_row()
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lowest_row_copy2 = duplicate_row
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start_mob = VGroup(lowest_row_copy1, lowest_row_copy2)
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new_pt = mobject.copy()
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new_pt.nrows += 1
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new_pt.generate_points()
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# align with original (copy got centered on screen)
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c1 = new_pt.coords_to_mobs[0][0].get_center()
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c2 = mobject.coords_to_mobs[0][0].get_center()
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print c1, c2
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v = c2 - c1
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new_pt.shift(v)
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new_row_left_copy = VGroup(*[
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new_pt.coords_to_mobs[n+1][k]
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for k in range(0,n+1)
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])
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new_row_right_copy = VGroup(*[
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new_pt.coords_to_mobs[n+1][k]
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for k in range(1,n+2)
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]).copy()
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target_mob = VGroup(new_row_left_copy, new_row_right_copy)
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Transform.__init__(self, start_mob, target_mob, **kwargs)
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class SimplePascal(Scene):
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def build_new_pascal_row(self,old_pt):
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lowest_row_copy = old_pt.get_lowest_row().copy()
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self.add(lowest_row_copy)
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n = old_pt.nrows - 1
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lowest_row_copy1 = old_pt.get_lowest_row()
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lowest_row_copy2 = lowest_row_copy1.copy()
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start_mob = VGroup(lowest_row_copy1, lowest_row_copy2)
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self.add(start_mob)
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new_pt = old_pt.copy()
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cell_height = old_pt.height / old_pt.nrows
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cell_width = old_pt.width / old_pt.nrows
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new_pt.nrows += 1
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new_pt.height = new_pt.nrows * cell_height
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new_pt.width = new_pt.nrows * cell_width
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new_pt.generate_points()
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# align with original (copy got centered on screen)
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c1 = new_pt.coords_to_mobs[0][0].get_center()
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c2 = old_pt.coords_to_mobs[0][0].get_center()
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v = c2 - c1
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new_pt.shift(v)
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new_row_left_copy = VGroup(*[
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new_pt.coords_to_mobs[n+1][k]
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for k in range(0,n+1)
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])
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new_row_right_copy = VGroup(*[
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new_pt.coords_to_mobs[n+1][k]
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for k in range(1,n+2)
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]).copy()
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target_mob = VGroup(new_row_left_copy, new_row_right_copy)
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self.play(Transform(start_mob, target_mob))
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return new_pt
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def construct(self):
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cell_height = 1
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cell_width = 1
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nrows = 1
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pt = GeneralizedPascalsTriangle(
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nrows = nrows,
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height = nrows * cell_height,
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width = nrows * cell_width,
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submob_class = graded_square,
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portion_to_fill = 0.9
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)
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pt.shift(3 * UP)
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self.add(pt)
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lowest_row_copy = pt.get_lowest_row().copy()
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self.add(lowest_row_copy)
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#self.play(BuildNewPascalRow(pt, duplicate_row = lowest_row_copy))
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for i in range(7):
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pt = self.build_new_pascal_row(pt)
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class PascalNetScene(Scene):
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def construct(self):
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def construct(self):
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unit_width = 0.25
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top_height = 4.0
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level_height = 2.0 * top_height / nb_levels
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unit_width = 0.25
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top_height = 4.0
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level_height = 2.0 * top_height / nb_levels
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start_points = np.array([top_height * UP])
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start_points = np.array([top_height * UP])
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dev_start = start_points[0]
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dev_start = start_points[0]
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j = 0
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j = 0
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for n in range(nb_levels):
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for n in range(nb_levels):
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half_width = 0.5 * (n + 0.5) * unit_width
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half_width = 0.5 * (n + 0.5) * unit_width
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stop_points_left = start_points.copy()
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stop_points_left[:,0] -= 0.5 * unit_width
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stop_points_left[:,1] -= level_height
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stop_points_left = start_points.copy()
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stop_points_left[:,0] -= 0.5 * unit_width
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stop_points_left[:,1] -= level_height
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stop_points_right = start_points.copy()
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stop_points_right[:,0] += 0.5 * unit_width
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stop_points_right[:,1] -= level_height
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for (p,q) in zip(start_points,stop_points_left):
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alpha = np.abs((p[0]+q[0])/2) / half_width
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color = rainbow_color(alpha)
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line = Line(p,q, stroke_color = color)
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self.add(line)
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stop_points_right = start_points.copy()
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stop_points_right[:,0] += 0.5 * unit_width
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stop_points_right[:,1] -= level_height
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for (p,q) in zip(start_points,stop_points_left):
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alpha = np.abs((p[0]+q[0])/2) / half_width
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color = rainbow_color(alpha)
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line = Line(p,q, stroke_color = color)
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self.add(line)
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for (i,(p,q)) in enumerate(zip(start_points,stop_points_right)):
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alpha = np.abs((p[0]+q[0])/2) / half_width
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color = rainbow_color(alpha)
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line = Line(p,q, stroke_color = color)
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self.add(line)
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for (i,(p,q)) in enumerate(zip(start_points,stop_points_right)):
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alpha = np.abs((p[0]+q[0])/2) / half_width
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color = rainbow_color(alpha)
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line = Line(p,q, stroke_color = color)
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self.add(line)
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if (n + 1) % dev_y_step == 0 and n != 1:
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j += dev_x_step
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dev_stop = stop_points_left[j]
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line = Line(dev_start,dev_stop,stroke_color = WHITE)
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self.add(line)
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dot = Dot(dev_stop, fill_color = WHITE)
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self.add_foreground_mobject(dot)
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dev_start = dev_stop
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if (n + 1) % dev_y_step == 0 and n != 1:
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j += dev_x_step
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dev_stop = stop_points_left[j]
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line = Line(dev_start,dev_stop,stroke_color = WHITE)
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self.add(line)
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dot = Dot(dev_stop, fill_color = WHITE)
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self.add_foreground_mobject(dot)
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dev_start = dev_stop
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start_points = np.append(stop_points_left,[stop_points_right[-1]], axis = 0)
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start_points = np.append(stop_points_left,[stop_points_right[-1]], axis = 0)
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self.wait()
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self.wait()
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class RescaledPascalNetScene(Scene):
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def construct(self):
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def construct(self):
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half_width = 3.0
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top_height = 4.0
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level_height = 2.0 * top_height / nb_levels
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half_width = 3.0
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top_height = 4.0
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level_height = 2.0 * top_height / nb_levels
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start_points = np.array([top_height * UP])
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left_edge = top_height * UP + half_width * LEFT
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right_edge = top_height * UP + half_width * RIGHT
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start_points = np.array([top_height * UP])
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left_edge = top_height * UP + half_width * LEFT
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right_edge = top_height * UP + half_width * RIGHT
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dev_start = start_points[0]
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dev_start = start_points[0]
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j = 0
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j = 0
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for n in range(nb_levels):
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for n in range(nb_levels):
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if n == 0:
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start_points_left_shift = np.array([left_edge])
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else:
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start_points_left_shift = start_points[:-1]
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start_points_left_shift = np.insert(start_points_left_shift,0,left_edge, axis = 0)
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stop_points_left = 0.5 * (start_points + start_points_left_shift)
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stop_points_left += level_height * DOWN
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if n == 0:
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start_points_left_shift = np.array([left_edge])
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else:
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start_points_left_shift = start_points[:-1]
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start_points_left_shift = np.insert(start_points_left_shift,0,left_edge, axis = 0)
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stop_points_left = 0.5 * (start_points + start_points_left_shift)
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stop_points_left += level_height * DOWN
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if n == 0:
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start_points_right_shift = np.array([right_edge])
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else:
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start_points_right_shift = start_points[1:]
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start_points_right_shift = np.append(start_points_right_shift,np.array([right_edge]), axis = 0)
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stop_points_right = 0.5 * (start_points + start_points_right_shift)
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stop_points_right += level_height * DOWN
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if n == 0:
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start_points_right_shift = np.array([right_edge])
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else:
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start_points_right_shift = start_points[1:]
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start_points_right_shift = np.append(start_points_right_shift,np.array([right_edge]), axis = 0)
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stop_points_right = 0.5 * (start_points + start_points_right_shift)
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stop_points_right += level_height * DOWN
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for (i,(p,q)) in enumerate(zip(start_points,stop_points_left)):
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color = LIGHT_GRAY
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for (i,(p,q)) in enumerate(zip(start_points,stop_points_left)):
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color = LIGHT_GRAY
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if n % 2 == 0 and i <= n/2:
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m = n/2 + 0.25
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jj = i
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alpha = 1 - float(jj)/m
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color = rainbow_color(alpha)
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if n % 2 == 0 and i <= n/2:
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m = n/2 + 0.25
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jj = i
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alpha = 1 - float(jj)/m
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color = rainbow_color(alpha)
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elif n % 2 == 0 and i > n/2:
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m = n/2 + 0.25
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jj = n - i + 0.5
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alpha = 1 - float(jj)/m
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color = rainbow_color(alpha)
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elif n % 2 == 0 and i > n/2:
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m = n/2 + 0.25
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jj = n - i + 0.5
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alpha = 1 - float(jj)/m
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color = rainbow_color(alpha)
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elif n % 2 == 1 and i <= n/2:
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m = n/2 + 0.75
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jj = i
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alpha = 1 - float(jj)/m
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color = rainbow_color(alpha)
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elif n % 2 == 1 and i <= n/2:
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m = n/2 + 0.75
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jj = i
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alpha = 1 - float(jj)/m
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color = rainbow_color(alpha)
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elif n % 2 == 1 and i > n/2:
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m = n/2 + 0.75
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jj = n - i + 0.5
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alpha = 1 - float(jj)/m
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color = rainbow_color(alpha)
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elif n % 2 == 1 and i > n/2:
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m = n/2 + 0.75
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jj = n - i + 0.5
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alpha = 1 - float(jj)/m
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color = rainbow_color(alpha)
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line = Line(p,q, stroke_color = color)
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self.add(line)
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line = Line(p,q, stroke_color = color)
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self.add(line)
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for (i,(p,q)) in enumerate(zip(start_points,stop_points_right)):
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color = LIGHT_GRAY
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for (i,(p,q)) in enumerate(zip(start_points,stop_points_right)):
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color = LIGHT_GRAY
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if n % 2 == 0 and i < n/2:
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m = n/2 + 0.25
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jj = i + 0.5
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alpha = 1 - float(jj)/m
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color = rainbow_color(alpha)
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if n % 2 == 0 and i < n/2:
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m = n/2 + 0.25
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jj = i + 0.5
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alpha = 1 - float(jj)/m
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color = rainbow_color(alpha)
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elif n % 2 == 0 and i >= n/2:
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m = n/2 + 0.25
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jj = n - i
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alpha = 1 - float(jj)/m
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color = rainbow_color(alpha)
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elif n % 2 == 0 and i >= n/2:
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m = n/2 + 0.25
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jj = n - i
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alpha = 1 - float(jj)/m
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color = rainbow_color(alpha)
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elif n % 2 == 1 and i <= n/2:
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m = n/2 + 0.75
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jj = i + 0.5
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alpha = 1 - float(jj)/m
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color = rainbow_color(alpha)
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elif n % 2 == 1 and i <= n/2:
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m = n/2 + 0.75
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jj = i + 0.5
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alpha = 1 - float(jj)/m
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color = rainbow_color(alpha)
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elif n % 2 == 1 and i > n/2:
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m = n/2 + 0.75
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jj = n - i
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alpha = 1 - float(jj)/m
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color = rainbow_color(alpha)
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elif n % 2 == 1 and i > n/2:
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m = n/2 + 0.75
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jj = n - i
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alpha = 1 - float(jj)/m
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color = rainbow_color(alpha)
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line = Line(p,q, stroke_color = color)
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self.add(line)
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line = Line(p,q, stroke_color = color)
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self.add(line)
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if (n + 1) % dev_y_step == 0 and n != 1:
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j += dev_x_step
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dev_stop = stop_points_left[j]
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line = Line(dev_start,dev_stop,stroke_color = WHITE)
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self.add(line)
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dot = Dot(dev_stop, fill_color = WHITE)
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self.add_foreground_mobject(dot)
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dev_start = dev_stop
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if (n + 1) % dev_y_step == 0 and n != 1:
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j += dev_x_step
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dev_stop = stop_points_left[j]
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line = Line(dev_start,dev_stop,stroke_color = WHITE)
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self.add(line)
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dot = Dot(dev_stop, fill_color = WHITE)
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self.add_foreground_mobject(dot)
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||||
dev_start = dev_stop
|
||||
|
||||
|
||||
|
||||
start_points = np.append(stop_points_left,[stop_points_right[-1]], axis = 0)
|
||||
|
||||
left_edge += level_height * DOWN
|
||||
right_edge += level_height * DOWN
|
||||
start_points = np.append(stop_points_left,[stop_points_right[-1]], axis = 0)
|
||||
|
||||
left_edge += level_height * DOWN
|
||||
right_edge += level_height * DOWN
|
||||
|
||||
|
||||
self.wait()
|
||||
self.wait()
|
||||
|
||||
|
||||
|
||||
|
||||
Reference in New Issue
Block a user