from big_ol_pile_of_manim_imports import * from once_useful_constructs.combinatorics import * nb_levels = 5 dev_x_step = 2 dev_y_step = 5 GRADE_COLOR_1 = RED GRADE_COLOR_2 = BLUE def graded_square(n,k): return Square( side_length = 1, fill_color = graded_color(n,k), fill_opacity = 1, stroke_width = 1 ) def graded_binomial(n,k): return Integer( choose(n,k), color = graded_color(n,k) ) def split_square(n,k): width = 1 height = 1 proportion = float(choose(n,k)) / 2**n lower_height = proportion * height upper_height = (1 - proportion) * height lower_rect = Rectangle( width = width, height = lower_height, fill_color = RED, fill_opacity = 1.0, stroke_color = WHITE, stroke_width = 3 ) upper_rect = Rectangle( width = width, height = upper_height, fill_color = BLUE, fill_opacity = 1.0, stroke_color = WHITE, stroke_width = 3 ) upper_rect.next_to(lower_rect,UP,buff = 0) square = VGroup(lower_rect, upper_rect).move_to(ORIGIN) return square class BuildNewPascalRow(Transform): def __init__(self,mobject, duplicate_row = None, **kwargs): if mobject.__class__ != GeneralizedPascalsTriangle and mobject.__class__ != PascalsTriangle: raise("Transform BuildNewPascalRow only works on members of (Generalized)PascalsTriangle!") n = mobject.nrows - 1 lowest_row_copy1 = mobject.get_lowest_row() lowest_row_copy2 = duplicate_row start_mob = VGroup(lowest_row_copy1, lowest_row_copy2) new_pt = mobject.copy() new_pt.nrows += 1 new_pt.generate_points() # align with original (copy got centered on screen) c1 = new_pt.coords_to_mobs[0][0].get_center() c2 = mobject.coords_to_mobs[0][0].get_center() print(c1, c2) v = c2 - c1 new_pt.shift(v) new_row_left_copy = VGroup(*[ new_pt.coords_to_mobs[n+1][k] for k in range(0,n+1) ]) new_row_right_copy = VGroup(*[ new_pt.coords_to_mobs[n+1][k] for k in range(1,n+2) ]).copy() target_mob = VGroup(new_row_left_copy, new_row_right_copy) Transform.__init__(self, start_mob, target_mob, **kwargs) class SimplePascal(Scene): def build_new_pascal_row(self,old_pt): lowest_row_copy = old_pt.get_lowest_row().copy() self.add(lowest_row_copy) n = old_pt.nrows - 1 lowest_row_copy1 = old_pt.get_lowest_row() lowest_row_copy2 = lowest_row_copy1.copy() start_mob = VGroup(lowest_row_copy1, lowest_row_copy2) self.add(start_mob) new_pt = old_pt.copy() cell_height = old_pt.height / old_pt.nrows cell_width = old_pt.width / old_pt.nrows new_pt.nrows += 1 new_pt.height = new_pt.nrows * cell_height new_pt.width = new_pt.nrows * cell_width new_pt.generate_points() # align with original (copy got centered on screen) c1 = new_pt.coords_to_mobs[0][0].get_center() c2 = old_pt.coords_to_mobs[0][0].get_center() v = c2 - c1 new_pt.shift(v) new_row_left_copy = VGroup(*[ new_pt.coords_to_mobs[n+1][k] for k in range(0,n+1) ]) new_row_right_copy = VGroup(*[ new_pt.coords_to_mobs[n+1][k] for k in range(1,n+2) ]).copy() target_mob = VGroup(new_row_left_copy, new_row_right_copy) self.play(Transform(start_mob, target_mob)) return new_pt def construct(self): cell_height = 1 cell_width = 1 nrows = 1 pt = GeneralizedPascalsTriangle( nrows = nrows, height = nrows * cell_height, width = nrows * cell_width, submob_class = graded_square, portion_to_fill = 0.9 ) pt.shift(3 * UP) self.add(pt) lowest_row_copy = pt.get_lowest_row().copy() self.add(lowest_row_copy) #self.play(BuildNewPascalRow(pt, duplicate_row = lowest_row_copy)) for i in range(7): pt = self.build_new_pascal_row(pt) class PascalNetScene(Scene): def construct(self): unit_width = 0.25 top_height = 4.0 level_height = 2.0 * top_height / nb_levels start_points = np.array([top_height * UP]) dev_start = start_points[0] j = 0 for n in range(nb_levels): half_width = 0.5 * (n + 0.5) * unit_width stop_points_left = start_points.copy() stop_points_left[:,0] -= 0.5 * unit_width stop_points_left[:,1] -= level_height stop_points_right = start_points.copy() stop_points_right[:,0] += 0.5 * unit_width stop_points_right[:,1] -= level_height for (p,q) in zip(start_points,stop_points_left): alpha = np.abs((p[0]+q[0])/2) / half_width color = rainbow_color(alpha) line = Line(p,q, stroke_color = color) self.add(line) for (i,(p,q)) in enumerate(zip(start_points,stop_points_right)): alpha = np.abs((p[0]+q[0])/2) / half_width color = rainbow_color(alpha) line = Line(p,q, stroke_color = color) self.add(line) if (n + 1) % dev_y_step == 0 and n != 1: j += dev_x_step dev_stop = stop_points_left[j] line = Line(dev_start,dev_stop,stroke_color = WHITE) self.add(line) dot = Dot(dev_stop, fill_color = WHITE) self.add_foreground_mobject(dot) dev_start = dev_stop start_points = np.append(stop_points_left,[stop_points_right[-1]], axis = 0) self.wait() class RescaledPascalNetScene(Scene): def construct(self): half_width = 3.0 top_height = 4.0 level_height = 2.0 * top_height / nb_levels start_points = np.array([top_height * UP]) left_edge = top_height * UP + half_width * LEFT right_edge = top_height * UP + half_width * RIGHT dev_start = start_points[0] j = 0 for n in range(nb_levels): if n == 0: start_points_left_shift = np.array([left_edge]) else: start_points_left_shift = start_points[:-1] start_points_left_shift = np.insert(start_points_left_shift,0,left_edge, axis = 0) stop_points_left = 0.5 * (start_points + start_points_left_shift) stop_points_left += level_height * DOWN if n == 0: start_points_right_shift = np.array([right_edge]) else: start_points_right_shift = start_points[1:] start_points_right_shift = np.append(start_points_right_shift,np.array([right_edge]), axis = 0) stop_points_right = 0.5 * (start_points + start_points_right_shift) stop_points_right += level_height * DOWN for (i,(p,q)) in enumerate(zip(start_points,stop_points_left)): color = LIGHT_GRAY if n % 2 == 0 and i <= n/2: m = n/2 + 0.25 jj = i alpha = 1 - float(jj)/m color = rainbow_color(alpha) elif n % 2 == 0 and i > n/2: m = n/2 + 0.25 jj = n - i + 0.5 alpha = 1 - float(jj)/m color = rainbow_color(alpha) elif n % 2 == 1 and i <= n/2: m = n/2 + 0.75 jj = i alpha = 1 - float(jj)/m color = rainbow_color(alpha) elif n % 2 == 1 and i > n/2: m = n/2 + 0.75 jj = n - i + 0.5 alpha = 1 - float(jj)/m color = rainbow_color(alpha) line = Line(p,q, stroke_color = color) self.add(line) for (i,(p,q)) in enumerate(zip(start_points,stop_points_right)): color = LIGHT_GRAY if n % 2 == 0 and i < n/2: m = n/2 + 0.25 jj = i + 0.5 alpha = 1 - float(jj)/m color = rainbow_color(alpha) elif n % 2 == 0 and i >= n/2: m = n/2 + 0.25 jj = n - i alpha = 1 - float(jj)/m color = rainbow_color(alpha) elif n % 2 == 1 and i <= n/2: m = n/2 + 0.75 jj = i + 0.5 alpha = 1 - float(jj)/m color = rainbow_color(alpha) elif n % 2 == 1 and i > n/2: m = n/2 + 0.75 jj = n - i alpha = 1 - float(jj)/m color = rainbow_color(alpha) line = Line(p,q, stroke_color = color) self.add(line) if (n + 1) % dev_y_step == 0 and n != 1: j += dev_x_step dev_stop = stop_points_left[j] line = Line(dev_start,dev_stop,stroke_color = WHITE) self.add(line) dot = Dot(dev_stop, fill_color = WHITE) self.add_foreground_mobject(dot) 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 self.wait()