本节书摘来自异步社区《Python极客项目编程 》一书中的第2章，第2.4节，作者 [美] Mahesh Venkitachalam，王海鹏 译，更多章节内容可以访问云栖社区“异步社区”公众号查看。
下面是完整的万花尺程序。也可以从https://github.com/electronut/pp/blob/master/ spirograph/spiro.py 下载该项目的代码。
import sys, random, argparse import numpy as np import math import turtle import random from PIL import Image from datetime import datetime from fractions import gcd # a class that draws a Spirograph class Spiro: # constructor def __init__(self, xc, yc, col, R, r, l): # create the turtle object self.t = turtle.Turtle() # set the cursor shape self.t.shape('turtle') # set the step in degrees self.step = 5 # set the drawing complete flag self.drawingComplete = False # set the parameters self.setparams(xc, yc, col, R, r, l) # initialize the drawing self.restart() # set the parameters def setparams(self, xc, yc, col, R, r, l): # the Spirograph parameters self.xc = xc self.yc = yc self.R = int(R) self.r = int(r) self.l = l self.col = col # reduce r/R to its smallest form by dividing with the GCD gcdVal = gcd(self.r, self.R) self.nRot = self.r//gcdVal # get ratio of radii self.k = r/float(R) # set the color self.t.color(*col) # store the current angle self.a = 0 # restart the drawing def restart(self): # set the flag self.drawingComplete = False # show the turtle self.t.showturtle() # go to the first point self.t.up() R, k, l = self.R, self.k, self.l a = 0.0 x = R*((1-k)*math.cos(a) + l*k*math.cos((1-k)*a/k)) y = R*((1-k)*math.sin(a) - l*k*math.sin((1-k)*a/k)) self.t.setpos(self.xc + x, self.yc + y) self.t.down() # draw the whole thing def draw(self): # draw the rest of the points R, k, l = self.R, self.k, self.l for i in range(0, 360*self.nRot + 1, self.step): a = math.radians(i) x = R*((1-k)*math.cos(a) + l*k*math.cos((1-k)*a/k)) y = R*((1-k)*math.sin(a) - l*k*math.sin((1-k)*a/k)) self.t.setpos(self.xc + x, self.yc + y) # drawing is now done so hide the turtle cursor self.t.hideturtle() # update by one step def update(self): # skip the rest of the steps if done if self.drawingComplete: return # increment the angle self.a += self.step # draw a step R, k, l = self.R, self.k, self.l # set the angle a = math.radians(self.a) x = self.R*((1-k)*math.cos(a) + l*k*math.cos((1-k)*a/k)) y = self.R*((1-k)*math.sin(a) - l*k*math.sin((1-k)*a/k)) self.t.setpos(self.xc + x, self.yc + y) # if drawing is complete, set the flag if self.a >= 360*self.nRot: self.drawingComplete = True # drawing is now done so hide the turtle cursor self.t.hideturtle() # clear everything def clear(self): self.t.clear() # a class for animating Spirographs class SpiroAnimator: # constructor def __init__(self, N): # set the timer value in milliseconds self.deltaT = 10 # get the window dimensions self.width = turtle.window_width() self.height = turtle.window_height() # create the Spiro objects self.spiros = [] for i in range(N): # generate random parameters rparams = self.genRandomParams() # set the spiro parameters spiro = Spiro(*rparams) self.spiros.append(spiro) # call timer turtle.ontimer(self.update, self.deltaT) # restart spiro drawing def restart(self): for spiro in self.spiros: # clear spiro.clear() # generate random parameters rparams = self.genRandomParams() # set the spiro parameters spiro.setparams(*rparams) # restart drawing spiro.restart() # generate random parameters def genRandomParams(self): width, height = self.width, self.height R = random.randint(50, min(width, height)//2) r = random.randint(10, 9*R//10) l = random.uniform(0.1, 0.9) xc = random.randint(-width//2, width//2) yc = random.randint(-height//2, height//2) col = (random.random(), random.random(), random.random()) return (xc, yc, col, R, r, l) def update(self): # update all spiros nComplete = 0 for spiro in self.spiros: # update spiro.update() # count completed spiros if spiro.drawingComplete: nComplete += 1 # restart if all spiros are complete if nComplete == len(self.spiros): self.restart() # call the timer turtle.ontimer(self.update, self.deltaT) # toggle turtle cursor on and off def toggleTurtles(self): for spiro in self.spiros: if spiro.t.isvisible(): spiro.t.hideturtle() else: spiro.t.showturtle() # save drawings as PNG files def saveDrawing(): # hide the turtle cursor turtle.hideturtle() # generate unique filenames dateStr = (datetime.now()).strftime("%d%b%Y-%H%M%S") fileName = 'spiro-' + dateStr print('saving drawing to %s.eps/png' % fileName) # get the tkinter canvas canvas = turtle.getcanvas() # save the drawing as a postscipt image canvas.postscript(file = fileName + '.eps') # use the Pillow module to convert the poscript image file to PNG img = Image.open(fileName + '.eps') img.save(fileName + '.png', 'png') # show the turtle cursor turtle.showturtle() # main() function def main(): # use sys.argv if needed print('generating spirograph...') # create parser descStr = """This program draws Spirographs using the Turtle module. When run with no arguments, this program draws random Spirographs. Terminology: R: radius of outer circle r: radius of inner circle l: ratio of hole distance to r """ parser = argparse.ArgumentParser(description=descStr) # add expected arguments parser.add_argument('--sparams', nargs=3, dest='sparams', required=False, help="The three arguments in sparams: R, r, l.") # parse args args = parser.parse_args() # set the width of the drawing window to 80 percent of the screen width turtle.setup(width=0.8) # set the cursor shape to turtle turtle.shape('turtle') # set the title to Spirographs! turtle.title("Spirographs!") # add the key handler to save our drawings turtle.onkey(saveDrawing, "s") # start listening turtle.listen() # hide the main turtle cursor turtle.hideturtle() # check for any arguments sent to --sparams and draw the Spirograph if args.sparams: params = [float(x) for x in args.sparams] # draw the Spirograph with the given parameters col = (0.0, 0.0, 0.0) spiro = Spiro(0, 0, col, *params) spiro.draw() else: # create the animator object spiroAnim = SpiroAnimator(4) # add a key handler to toggle the turtle cursor turtle.onkey(spiroAnim.toggleTurtles, "t") # add a key handler to restart the animation turtle.onkey(spiroAnim.restart, "space") # start the turtle main loop turtle.mainloop() # call main if __name__ == '__main__': main() 相关资源：Python算法教程_中文版.pdf