Playing with Pascal

active_projects/eop/pascal.py

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+from helpers import *
+from mobject import Mobject
+from mobject.vectorized_mobject import *
+from animation.animation import Animation
+from animation.transform import *
+from animation.simple_animations import *
+from topics.geometry import *
+from scene import Scene
+from camera import *
+
+nb_levels = 50
+
+dev_x_step = 2
+dev_y_step = 5
+
+def rainbow_color(alpha):
+	nb_colors = 100
+	rainbow = color_gradient([RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE], nb_colors)
+	rainbow = np.append(rainbow,PURPLE)
+	index = int(alpha * nb_colors)
+	return rainbow[index]
+
+
+
+
+
+
+class PascalScene(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 RescaledPascalScene(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()
+
+
+
+
+
+
+
+
+