Fibonacci Sunflower Tkinter

Question

我正试图用tkinter绘制出一个斐波纳契向日葵。它绘制正确，但我希望能够绘制螺旋。但是，我无法弄清楚如何正确连接它们。有什么想法吗？

这是我的代码：

import math
from tkinter import *

def s5(n,r): #works better for first direction
    spirals = []
    for i in range(n+1):
        spirals.append(((r*(i**0.5),((i*(360)/(((5**0.5)+1)/2))%360))))
    return spirals

# convert to cartesian to plot
def pol2cart(r,theta):
    x = r * math.cos(math.radians(theta))
    y = r * math.sin(math.radians(theta))
    return x,y

# set size of fib sun
num_points = 200
distance = 15

# do the cartesian conversion
coordinates = [pol2cart(r,t) for r,t in s5(num_points,distance)]

# center for the canvas
coordinates = [(x+250,y+250) for x,y in coordinates]

# create gui
master = Tk()
canvas = Canvas(master,width = 500,height=500)
canvas.pack()



# plot points 
h= 1
for x,y in coordinates:
    canvas.create_oval(x+7,y+7,x-7,y-7)
    canvas.create_text(x,y,text=h)
    h += 1

mainloop()

这是我想要实现的结果：

Answer 1

这是一个有趣的问题，我刚刚勾画出一个可能的解决方案。您可以从1到20开始，然后将每个数字添加到21。意思是你应该连接1到22,22到43,43到64，...... 再次连接2到23,23到44，......

这为您提供了一个方向的踏板。

对于另一个方向，您可以执行相同的操作，但从1到34开始，并为每个数字添加34。意思是从1开始并向其添加34。 1,35,69，...... 2,36,70，...

这两个图显示了这些螺旋的外观：

事实上这些数字并不神奇，这些数字来自斐波那契数字，并且基于螺旋层，您应该检测它。因此，您总是有数字差异，如：0,1,1,2,3,5,8,13,21,34,55 ......

Answer 2

你的程序的以下版本实际上绘制了线条，但我还没有找到21和34步骤的动机。我怀疑这与你在s5函数中使用的数字有关（'5'）。

import math
from Tkinter import *

class Fibonacci():
    def s5(self, n, r): # works better for first direction
        spirals = []
        for i in range(n+1):
            spirals.append(((r*(i**0.5),((i*(360)/(((5**0.5)+1)/2))%360))))
        return spirals

    def pol2cart(self, r, theta):
        x = r * math.cos(math.radians(theta))
        y = r * math.sin(math.radians(theta))
        return x,y

    def calculate_coordinates(self, num_points = 200, distance = 15):
        # do the cartesian conversion
        self.coordinates = [self.pol2cart(r, t) for r, t in self.s5(num_points, distance)]

        # center for the canvas
        self.coordinates = [(x+250,y+250) for x, y in self.coordinates]

    def plot_numbers(self, canvas):
        h = 1
        self.calculate_coordinates(num_points = 200, distance = 15)
        for x, y in self.coordinates:
            canvas.create_oval(x+7, y+7, x-7, y-7)
            canvas.create_text(x, y, text = h)
            h += 1

    def plot_lines(self, canvas):
        for delta in [21, 34]:
            for start in range(34):
                x0, y0 = self.coordinates[0]
                i = start
                while i < len(self.coordinates):
                    x1, y1 = self.coordinates[i]
                    canvas.create_line(x0, y0, x1, y1)
                    x0 = x1; y0 = y1
                    i += delta

    def create_gui(self):
        master = Tk()
        canvas = Canvas(master, width = 500, height = 500)
        canvas.pack()

        self.plot_numbers(canvas)
        self.plot_lines(canvas)

        mainloop()

def main():
    f = Fibonacci()
    f.create_gui()
    return 0

if __name__ == '__main__':
    main()

要消除中心作为起点，请修改plot_lines，如下所示：

def plot_lines(self, canvas):
    for delta in [21, 34]:
        for start in range(34):
            x0, y0 = self.coordinates[start]
            print x0, y0
            i = start + delta
            while i < len(self.coordinates):
                x1, y1 = self.coordinates[i]
                canvas.create_line(x0, y0, x1, y1)
                x0 = x1; y0 = y1
                i += delta

这给出：