如何让 python 乌龟在折线图中绘制 collatz 序列的输出？答案

【问题标题】：How does one make a python turtle to draw outputs of the collatz sequence in a line graph?如何让 python 乌龟在折线图中绘制 collatz 序列的输出？
【发布时间】：2020-06-13 21:38:47
【问题描述】：

def next_term(num):
    if num<=0:
        print("Zero or negative numbers are not even, nor Odd.","Enter number >",num)
    else:
        print(int(num))
        while num!=1:               #number is even
            if num%2==0:
                num=num/2
            else:
                num=(num*3)+1        #number is odd
            print(int(num))
def main():
    nani=int(input("Please enter number: "))
    next_term(nani)

if __name__=="__main__":
    main()

【问题讨论】：

标签： python turtle-graphics linegraph collatz

【解决方案1】：

所有你需要的只是一些调整，所有的调整都是评论：

import turtle # Import turtle
size = 20 # Set the size of each number
def next_term(num):
    if num<=0:
        print("Zero or negative numbers are not even, nor Odd.","Enter number >",num)
    else:
        print(int(num))
        while num!=1:        
            if num%2==0:
                num=num/2
            else:
                num=(num*3)+1     
            turtle.write(int(num),font=("Arial",size,"normal")) # Instead of print(), use turtle.write()
            turtle.forward(len(str(int(num)))*size) # After writing the number, go forward by the amount of digits in the number multiplied by a unit
def main():
    nani=int(input("Please enter number: "))
    next_term(nani)

if __name__=="__main__":
    main()

输出：

>>> 
Please enter number: 10
10
>>>

这是一种更简洁的方法：

import turtle

size = 20
def collatz(num):
    while num != 1:
        if num % 2:
            num = num*3+1
        else:
            num = num // 2
        turtle.write(num,font=("Arial",size,"normal"))
        turtle.forward(len(str(num))*size)


def main():
    nani = int(input("Please enter number: "))
    collatz(nani)

if __name__=="__main__":
    main()

【讨论】：

【解决方案2】：

您的问题需要更加具体，因为有很多种方法可以绘制 Collatz 数。例如，下面的代码绘制了一个输入值在到达1 的过程中所经过的各种数字的折线图：

from turtle import Screen, Turtle

def collatz(number):
    yield number

    while number != 1:
        if number % 2 == 0:  # number is even
            number //= 2
        else:
            number = number * 3 + 1  # number is odd

        yield number

def graph_terms(generator):
    screen = Screen()
    turtle = Turtle()
    turtle.hideturtle()

    terms = [n for n in generator]  # exhaust generator as we need len() and max()

    x_max, y_max = len(terms), max(terms)
    x_step = screen.window_width() / 2 / x_max
    y_step = screen.window_height() / 2 / y_max

    turtle.setheading(90)
    turtle.forward(y_max * y_step)
    turtle.backward(y_max * y_step)
    turtle.setheading(0)

    for _ in range(2):
        turtle.pendown()
        turtle.forward(x_max * x_step)
        turtle.backward(x_max * x_step)

        turtle.penup()
        turtle.color('red')
        turtle.sety(y_step)

    turtle.home()
    turtle.color('black')

    for step, term in enumerate(terms):
        turtle.goto(step * x_step, term * y_step)
        turtle.pendown()
        turtle.dot()

    screen.exitonclick()

def main():
    number = int(input("Please enter number: "))

    try:
        generator = collatz(number)
        graph_terms(generator)
    except StopIteration:
        pass

if __name__ == "__main__":
    main()

这是数字25的图表：

在我的代码中，我将您的 Collatz 数字函数重新设计为一个看起来像它想要的样子的生成器。但是，出于绘图目的，我会立即耗尽生成器，因为我需要序列的长度和最大值，因此在这种情况下生成器不会得到回报。

如果这是您正在寻找的折线图样式，那么完成这个极简代码对您来说仍然是一个练习：它需要在屏幕上居中；它需要在其轴上打印数字；等等

【讨论】：