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208 lines
4.6 KiB
Python
208 lines
4.6 KiB
Python
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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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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class SampleScene(Scene):
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def construct(self):
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triangle = Polygon()
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self.add(triangle)
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self.wait()
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class PascalNetScene(Scene):
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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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start_points = np.array([top_height * UP])
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dev_start = start_points[0]
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j = 0
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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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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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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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start_points = np.append(stop_points_left,[stop_points_right[-1]], axis = 0)
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self.wait()
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class RescaledPascalNetScene(Scene):
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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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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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j = 0
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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_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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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 == 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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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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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 == 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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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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start_points = np.append(stop_points_left,[stop_points_right[-1]], axis = 0)
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left_edge += level_height * DOWN
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right_edge += level_height * DOWN
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self.wait()
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