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冰雹猜想是指：一个正整数，如果是奇数就乘以3再加1，如果是偶数就除以2，在经过若干次的变换之后也必然会到4-2-1的循环。

以下是我在看到 这道看似简单的数学题没有人解得出来【官方双语】【Veritasium真喵素】_哔哩哔哩_bilibili 这个视频后突发奇想写了的代码（第一次发作品帖，见谅）。

import turtle
import math

mypen_1 = turtle.Pen()
mypen_2 = turtle.Pen()
mypen_w = turtle.Pen()
mypen = turtle.Pen()
pen = [mypen_1, mypen_2, mypen, mypen_w]
for i in pen:
    i.speed(0)
    i.pencolor('#f5f5f7')
myscreen = turtle.Screen()
myscreen.bgcolor('#1d1d1f')
mypen_w.hideturtle()

# 调整窗口大小
height = 800
width = 1200
myscreen.setup(width, height)

# 画坐标系
mypen_w.penup()
mypen_w.goto(width/2-700, height/2-100)
mypen_w.pendown()
mypen_w.write('"3n+1"问题可视化', font=('等线', 20))

mypen_1.penup()
mypen_1.goto(-(width/2-120), height/2-125)
mypen_1.pendown()
mypen_1.write('y', font=('等线', 20))
mypen_1.penup()
mypen_1.goto(-(width/2-50), 0)
mypen_1.pendown()
mypen_1.write('f(n)', font=('等线', 20))
mypen_1.penup()
mypen_1.goto(0, -(height/2-50))
mypen_1.pendown()
mypen_1.write('n', font=('等线', 20))

mypen_1.penup()
mypen_1.goto(-(width/2-150), height/2-125)
mypen_2.left(90)
mypen_2.penup()
mypen_2.goto(-(width/2-150), height/2-125)
mypen_2.pendown()
mypen_1.pendown()
mypen_1.goto(-(width/2-150), -(height/2-100))
mypen_1.goto(width/2-125, -(height/2-100)) 
mypen_1.write('x', font=('等线', 20))


# 输入
num = int(myscreen.textinput('3n+1', "请输入一个数字"))
num_1 = num
i = 0; x = 0
num_list = []
num_l = []
while num != 1:
    if num % 2 == 1:
        num = 3*num+1
        num_l.append(1)
    elif num % 2 != 1:
        num = num // 2
        num_l.append(0)
    i += 1
    if x < num:
        x = num
    num_list.append(num)
print('"3n+1"问题可视化'.format(num_1))
print('\n')
print(num_list)
print('\n')
print('n初始值：{}'.format(num_1))
print('f(n)最大值：{}'.format(x))
print('步骤数：{}'.format(i))

# 文字
mypen_w.penup()
mypen_w.goto(width/2-175, height/2-125)
mypen_w.pendown()
mypen_w.write('n初始值：{}'.format(num_1), font=('等线', 13))
mypen_w.penup()
mypen_w.goto(width/2-175, height/2-150)
mypen_w.pendown()
mypen_w.write('f(n)最大值：{}'.format(x), font=('等线', 13))
mypen_w.penup()
mypen_w.goto(width/2-175, height/2-175)
mypen_w.pendown()
mypen_w.write('步骤数：{}'.format(i), font=('等线', 13))


x_1 = x
i_1 = i
p = 1
p_1 = 1
if x > 15:
    l = len(str(x))
    p = int(math.pow(10, l-1))
    m = x/p
    x = math.ceil(m)
if i > 15:
    l_1 = len(str(i))
    p_1 = int(math.pow(10, l_1-1))
    m_1 = i/p_1
    i = math.ceil(m_1)

x_list = []
y_list = []

#单位长度
mypen.left(90)
for z in range(i) :
    mypen.penup()
    n = 855/i*z
    mypen.goto(-(width/2-150-855/i-n), -(height/2-100))
    x_list.append(-(width/2-150-855/i-n))
    mypen.pendown()
    mypen.forward(5) 
    mypen.penup()
    mypen.goto(-(width/2-150+3-855/i-n), -(height/2-80))
    mypen.pendown()  
    if (z+1)*p_1 > 99999:
        mypen.penup()
        mypen.backward(11)
        mypen.pendown()
        u = (z+1)*p_1
        u = len(list(str(u))) -1
        mypen.write('{}*10^{}'.format(z+1,u), font=('等线', 12))
    else:
        mypen.write((z+1)*p_1, font=('等线', 12))

mypen.right(90)
for z in range(x) :
    mypen.penup()
    n = 580/(x+1)*z
    mypen.goto(-(width/2-150), -(height/2-100)+580/(x+1)+n)
    y_list.append(-(height/2-100)+580/(x+1)+n)
    mypen.pendown()
    mypen.forward(5) 
    mypen.penup()
    mypen.goto(-(width/2-110), -(height/2-100)+580/(x+1)+n-7)
    mypen.pendown()
    if (z+1)*p > 99999:
        mypen.penup()
        mypen.backward(11)
        mypen.pendown()
        u = (z+1)*p
        u = len(list(str(u))) -1
        mypen.write('{}*10^{}'.format(z+1,u), font=('等线', 12))
    else:
        mypen.write((z+1)*p, font=('等线', 12))

# 数据可视化
mypen.penup()
mypen.goto(-(width/2-150), -(height/2-100)+580/(x+1)*num_1/p)
for n in range (i_1):
    mypen.pendown()
    mypen.goto(-(width/2-150)+855/i*(n+1)/p_1, -(height/2-100)+580/(x+1)*num_list[n]/p)

turtle.done()