1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
|
# -*- coding: utf-8 -*-
import sys, os, math
sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
from manim import *
from tiktok import *
X0, X1 = -3.75, 3.75
Y0, Y1 = -1.30, 3.30
def seq(n):
s = [n]
while n != 1:
n = n // 2 if n % 2 == 0 else 3 * n + 1
s.append(n)
return s
def curva(sq, color=AMBAR, sw=5, mx=None, nx=None, log=False):
"""Trayectoria como poligonal. mx/nx permiten compartir escala entre curvas."""
mx = mx or max(sq)
nx = nx or len(sq)
if log:
f = lambda v: math.log(v) / math.log(mx)
else:
f = lambda v: v / mx
pts = [[X0 + (X1 - X0) * i / (nx - 1), Y0 + (Y1 - Y0) * f(sq[i]), 0]
for i in range(len(sq))]
m = VMobject(stroke_color=color, stroke_width=sw)
m.set_points_as_corners(pts)
return m, pts
def tile(v, col):
t = Text(str(v), font=FONT, font_size=44, weight=BOLD, color="#0B0F1A")
box = RoundedRectangle(corner_radius=0.16, width=max(0.95, t.width + 0.45),
height=0.88, stroke_width=0, fill_color=col, fill_opacity=1)
return VGroup(box, t)
class Collatz(TikTok):
NAME = "collatz"
def construct(self):
self.prepare()
chip = self.chip("Abierto desde 1937", ROSA)
with self.beat(0) as b:
n = self.big("27", 150, AMBAR).move_to(UP * 1.9)
cap = self.fit(Text("agarrá cualquier número", font=FONT, font_size=50,
weight=BOLD, color=WHITE), 8.2).move_to(DOWN * 0.3)
b.play(FadeIn(chip, shift=DOWN * 0.3), run_time=0.45)
b.play(FadeIn(n, scale=0.6), run_time=0.45)
for v in ("6", "19", "41"):
b.play(Transform(n, self.big(v, 150, AMBAR).move_to(UP * 1.9)), run_time=0.26)
b.play(FadeIn(cap, shift=UP * 0.15), run_time=0.5)
def regla(txt, op, col):
a = Text(txt, font=FONT, font_size=46, weight=BOLD, color=col)
fl = Arrow(ORIGIN, RIGHT * 0.85, buff=0, color=GRIS, stroke_width=6,
max_tip_length_to_length_ratio=0.35)
c = Text(op, font=FONT, font_size=52, weight=BOLD, color=WHITE)
return VGroup(a, fl, c).arrange(RIGHT, buff=0.35)
with self.beat(1) as b:
b.play(FadeOut(VGroup(n, cap)), run_time=0.3)
r1 = regla("es PAR", "÷ 2", CELESTE)
r2 = regla("es IMPAR", "× 3 + 1", AMBAR)
rr = VGroup(r1, r2).arrange(DOWN, buff=0.7).move_to(UP * 1.6)
self.fit(rr, 8.2)
b.play(FadeIn(r1, shift=UP * 0.2), run_time=0.7)
b.play(FadeIn(r2, shift=UP * 0.2), run_time=0.7)
s6 = seq(6)
with self.beat(2) as b:
b.play(rr.animate.scale(0.72).move_to(UP * 5.2), run_time=0.5)
seis = self.big("6", 140, VERDE).move_to(UP * 1.0)
b.play(FadeIn(seis, scale=0.6), run_time=0.6)
with self.beat(3) as b:
b.play(FadeOut(seis), run_time=0.25)
tiles = VGroup(*[tile(v, VERDE if v == 1 else (CELESTE if v % 2 == 0 else AMBAR))
for v in s6])
fila1 = VGroup(*tiles[:5]).arrange(RIGHT, buff=0.28)
fila2 = VGroup(*tiles[5:]).arrange(RIGHT, buff=0.28)
grid = VGroup(fila1, fila2).arrange(DOWN, buff=0.45).move_to(UP * 1.4)
self.fit(grid, 8.2)
b.play(LaggedStart(*[FadeIn(t, scale=0.6) for t in tiles],
lag_ratio=0.5), run_time=max(1.4, b.floor - 0.4))
with self.beat(4) as b:
b.play(Circumscribe(tiles[-1], color=VERDE, buff=0.12, stroke_width=6),
run_time=0.7)
b.play(FadeOut(grid), run_time=0.35)
siete = self.big("7", 140, AMBAR).move_to(UP * 1.0)
b.play(FadeIn(siete, scale=0.6), run_time=0.5)
base = Line([X0 - 0.25, Y0, 0], [X1 + 0.25, Y0, 0], stroke_width=4, color="#33405C")
uno = Text("1", font=FONT, font_size=32, weight=BOLD, color=VERDE)
uno.next_to(base.get_start(), LEFT, buff=0.12)
s7 = seq(7)
with self.beat(5) as b:
b.play(FadeOut(siete), run_time=0.25)
c7, p7 = curva(s7, AMBAR, 6)
pico = Text("52", font=FONT, font_size=34, weight=BOLD, color=AMBAR)
pico.next_to([p7[s7.index(max(s7))][0], Y1, 0], UP, buff=0.12)
b.play(FadeIn(base), FadeIn(uno), run_time=0.35)
b.play(Create(c7), run_time=max(1.2, b.floor - 1.1))
b.play(FadeIn(pico), run_time=0.4)
s27 = seq(27)
with self.beat(6) as b:
b.play(FadeOut(VGroup(c7, pico)), run_time=0.3)
c27, p27 = curva(s27, ROSA, 5)
k = s27.index(max(s27))
top = Text("9.232", font=FONT, font_size=40, weight=BOLD, color=ROSA)
top.next_to([p27[k][0], Y1, 0], UP, buff=0.12)
lab = Text("27", font=FONT, font_size=40, weight=BOLD, color=ROSA)
lab.move_to([X0 - 0.05, Y1 + 0.45, 0])
b.play(FadeIn(lab), run_time=0.3)
b.play(Create(c27), run_time=max(1.3, b.floor - 1.0))
b.play(FadeIn(top), run_time=0.4)
with self.beat(7) as b:
fin = Dot([p27[-1][0], Y0, 0], radius=0.14, color=VERDE)
pasos = self.fit(Text("111 pasos y cae al 1", font=FONT, font_size=48,
weight=BOLD, color=VERDE), 8.0).move_to(DOWN * 2.6)
b.play(FadeIn(fin, scale=0.4), run_time=0.4)
b.play(Flash(fin, color=VERDE, line_length=0.35, num_lines=14,
flash_radius=0.8), run_time=0.6)
b.play(FadeIn(pasos, shift=UP * 0.15), run_time=0.6)
with self.beat(8) as b:
b.play(FadeOut(VGroup(c27, top, lab, fin, pasos)), run_time=0.4)
todos = [seq(k) for k in range(2, 80)]
MX = max(max(s) for s in todos)
NX = max(len(s) for s in todos)
cols = [AMBAR, CELESTE, ROSA, VERDE]
gr = VGroup(*[curva(s, cols[i % 4], 2.4, mx=MX, nx=NX, log=True)[0]
for i, s in enumerate(todos)])
gr.set_stroke(opacity=0.65)
b.play(LaggedStart(*[Create(c) for c in gr], lag_ratio=0.02),
run_time=max(1.6, b.floor - 0.9))
marca = self.fit(Text("todos terminan en 1", font=FONT, font_size=46,
weight=BOLD, color=VERDE), 8.0).move_to(DOWN * 2.6)
b.play(FadeIn(marca, shift=UP * 0.15), run_time=0.6)
with self.beat(9) as b:
b.play(FadeOut(VGroup(gr, marca, base, uno, rr)), run_time=0.45)
t = VGroup(
self.fit(Text("nadie pudo demostrar", font=FONT, font_size=50,
weight=BOLD, color=WHITE), 8.2),
self.fit(Text("que pasa SIEMPRE", font=FONT, font_size=54,
weight=BOLD, color=ROSA), 8.2),
).arrange(DOWN, buff=0.35).move_to(UP * 1.2)
b.play(FadeIn(t[0], shift=UP * 0.15), run_time=0.6)
b.play(FadeIn(t[1], scale=0.8), run_time=0.7)
with self.beat(10) as b:
b.play(FadeOut(t), run_time=0.35)
cta = VGroup(
self.fit(Text("conjetura de Collatz", font=FONT, font_size=56,
weight=BOLD, color=AMBAR), 8.0),
self.fit(Text("dejá tu número abajo", font=FONT, font_size=46,
weight=BOLD, color=WHITE), 8.0),
).arrange(DOWN, buff=0.38).move_to(UP * 0.8)
b.play(Write(cta[0]), run_time=0.9)
b.play(FadeIn(cta[1], shift=UP * 0.15), run_time=0.6)
self.finish()
|
