上一篇《Turtle库画一棵对称勾股树，美丽惊艳的分形世界！》中描绘了一棵对称的双色勾股树，详情见：
Python Turtle库画一棵对称勾股树，美丽惊艳的分形世界！_汉阳Hann's Home-CSDN博客 分形，具有以非整数维形式充填空间的形态特征。通常被定义为“一个粗糙或零碎的几何形状，可以分成数个部分，且每一部分都（至少近似地）是整体缩小后的形状”，即具有自相似的性质。分形（Fractal）一词，是芒德勃罗创造出来的，其原意具有不规则、支离破碎等意义。
1973年，芒德勃罗（B.B.Mandelbrot）在法兰西学院讲课时，首次提出了分维和分形的设想。 分形是一个数学术语，也是一套以分形特征为研究主题的数学理论。分形理论既是非线性科学的前沿和重要分支，又是一门新兴的横断学科，是研究一类现象特征的
新.https://blog.csdn.net/boysoft2002/article/details/120466255
修改一
简单的，加上一随机取色的函数，就能画出彩色树来。颜色取值方法有很多，常用的如下：
方法一：随机产生一个6位十六进制数
>>> from random import choice >>> def rndColor(): color,strColor = '#','0123456789ABCDEF' for _ in range(6): color += choice(strColor) return color >>> print([rndColor() for _ in range(7)]) ['#47922E', '#540621', '#AEA706', '#263CAC', '#2F346E', '#067BAC', '#4D295B'] >>>
方法二：在给定预定义颜色单词中取值，颜色数相对少但也够用
>>> def rndColor(): from random import choice colors = ('black', 'navy', 'darkblue', 'mediumblue', 'blue', 'darkgreen', 'green', 'teal', 'darkcyan', 'deepskyblue', 'darkturquoise', 'mediumspringgreen', 'lime', 'springgreen', 'aqua', 'cyan', 'midnightblue', 'dodgerblue', 'lightseagreen', 'forestgreen', 'seagreen', 'darkslategray', 'limegreen', 'mediumseagreen', 'turquoise', 'royalblue', 'steelblue', 'darkslateblue', 'mediumturquoise', 'indigo', 'darkolivegreen', 'cadetblue', 'cornflowerblue', 'mediumaquamarine', 'dimgray', 'slateblue', 'olivedrab', 'slategray', 'lightslategray', 'mediumslateblue', 'lawngreen', 'chartreuse', 'aquamarine', 'maroon', 'purple', 'olive', 'gray', 'skyblue', 'lightskyblue', 'blueviolet', 'darkred', 'darkmagenta', 'saddlebrown', 'darkseagreen', 'lightgreen', 'mediumpurple', 'darkviolet', 'palegreen', 'darkorchid', 'yellowgreen', 'sienna', 'brown', 'darkgray', 'lightblue', 'greenyellow', 'paleturquoise', 'lightsteelblue', 'powderblue', 'firebrick', 'darkgoldenrod', 'mediumorchid', 'rosybrown', 'darkkhaki', 'silver', 'mediumvioletred', 'indianred', 'peru', 'chocolate', 'tan', 'lightgray', 'thistle', 'orchid', 'goldenrod', 'palevioletred', 'crimson', 'gainsboro', 'plum', 'burlywood', 'lightcyan', 'lavender', 'darksalmon', 'violet', 'palegoldenrod', 'lightcoral', 'khaki', 'aliceblue', 'honeydew', 'azure', 'wheat', 'beige', 'whitesmoke', 'mintcream', 'ghostwhite', 'salmon', 'sandybrown', 'antiquewhite', 'linen', 'lightgoldenrodyellow', 'oldlace', 'red', 'fuchsia', 'magenta', 'deeppink', 'orangered', 'tomato', 'hotpink', 'coral', 'darkorange', 'lightsalmon', 'orange', 'lightpink', 'pink', 'gold', 'peachpuff', 'navajowhite', 'moccasin', 'bisque', 'mistyrose', 'blanchedalmond', 'papayawhip', 'lavenderblush', 'seashell', 'cornsilk', 'lemonchiffon', 'floralwhite', 'snow', 'yellow', 'lightyellow', 'ivory', 'white') return choice(colors) >>> print([rndColor() for _ in range(7)]) ['whitesmoke', 'dodgerblue', 'sandybrown', 'wheat', 'mediumorchid', 'goldenrod', 'tan'] >>> print([rndColor() for _ in range(7)]) ['darkblue', 'slateblue', 'aliceblue', 'salmon', 'seashell', 'darkgray', 'bisque'] >>>
就用方法一来取色，上一篇中的对称勾股树经填色后，效果如下：
源代码如下，填色语句已用#号注释掉了（效果上图左上）：
from turtle import * from random import choice def rndColor(): color,strColor = '#','0123456789ABCDEF' for _ in range(6): color += choice(strColor) return color def Square(self,length): self.color(rndColor()) #self.begin_fill() for _ in range(5): self.forward(length) self.right(90) #self.end_fill() def Triangle(self,length): self.color(rndColor()) #self.begin_fill() self.left(45) self.forward(length/2**0.5) self.right(90) self.forward(length/2**0.5) self.right(135) self.forward(length) #self.end_fill() def Move2Right(self,length): self.back(length) self.right(45) self.forward(length/2**0.5) self.right(90) def Recursive(n, tracer, length): if n<1: return tracers = [] for left in tracer: left.pencolor(rndColor()) Square(left, length) Triangle(left, length) right = left.clone() left.right(45) Move2Right(right, length) tracers.append(left) tracers.append(right) Recursive(n-1, tracers, length/2**0.5) def Setup(self, length, speed): self.hideturtle() self.speed(speed) self.penup() self.goto(-length*0.5, -length*1.8) self.seth(90) self.pensize(2) self.pendown() def main(level, length, speed=-1): setup(800,600) title('Fractal Tree') if speed==-1: tracer(0) else: tracer(1) t = Turtle() Setup(t, length, speed) from time import sleep sleep(2) Recursive(level, list([t]), length) done() bye() if __name__ == '__main__': main(9,135,-1)
修改二
左右偏向角都是45度勾股树就是对称的，那么角度指定从列表[i for i in range(5,86)]中抽取，勾股树的“树枝”就能任意角度生长了。参考网上的代码，增加了 onclick 事件，这样就可以反复观察效果。类似于 tkinter 库中用 .bind(<事件>,方法) 绑定函数来增加对象的事件动作，当然turtle窗口中也能使用bind方法(之后再作研究讨论)。经过修改后效果如下：
源代码如下：
import turtle from random import choice from math import sin,cos,radians def rndColor(flag=True): colorTuple=( ('navy', '#000080'), ('darkblue', '#00008B'), ('mediumblue', '#0000CD'), ('blue', '#0000FF'), ('darkgreen', '#006400'), ('green', '#008000'), ('teal', '#008080'), ('darkcyan', '#008B8B'), ('deepskyblue', '#00BFFF'), ('darkturquoise', '#00CED1'), ('mediumspringgreen', '#00FA9A'), ('lime', '#00FF00'), ('springgreen', '#00FF7F'), ('aqua', '#00FFFF'), ('cyan', '#00FFFF'), ('midnightblue', '#191970'), ('dodgerblue', '#1E90FF'), ('lightseagreen', '#20B2AA'), ('forestgreen', '#228B22'), ('seagreen', '#2E8B57'), ('darkslategray', '#2F4F4F'), ('limegreen', '#32CD32'), ('mediumseagreen', '#3CB371'), ('turquoise', '#40E0D0'), ('royalblue', '#4169E1'), ('steelblue', '#4682B4'), ('darkslateblue', '#483D8B'), ('mediumturquoise', '#48D1CC'), ('indigo', '#4B0082'), ('darkolivegreen', '#556B2F'), ('cadetblue', '#5F9EA0'), ('cornflowerblue', '#6495ED'), ('mediumaquamarine', '#66CDAA'), ('dimgray', '#696969'), ('slateblue', '#6A5ACD'), ('olivedrab', '#6B8E23'), ('slategray', '#708090'), ('lightslategray', '#778899'), ('mediumslateblue', '#7B68EE'), ('lawngreen', '#7CFC00'), ('chartreuse', '#7FFF00'), ('aquamarine', '#7FFFD4'), ('maroon', '#800000'), ('purple', '#800080'), ('olive', '#808000'), ('gray', '#808080'), ('skyblue', '#87CEEB'), ('lightskyblue', '#87CEFA'), ('blueviolet', '#8A2BE2'), ('darkred', '#8B0000'), ('darkmagenta', '#8B008B'), ('saddlebrown', '#8B4513'), ('darkseagreen', '#8FBC8F'), ('lightgreen', '#90EE90'), ('mediumpurple', '#9370DB'), ('darkviolet', '#9400D3'), ('palegreen', '#98FB98'), ('darkorchid', '#9932CC'), ('yellowgreen', '#9ACD32'), ('sienna', '#A0522D'), ('brown', '#A52A2A'), ('darkgray', '#A9A9A9'), ('lightblue', '#ADD8E6'), ('greenyellow', '#ADFF2F'), ('paleturquoise', '#AFEEEE'), ('lightsteelblue', '#B0C4DE'), ('powderblue', '#B0E0E6'), ('firebrick', '#B22222'), ('darkgoldenrod', '#B8860B'), ('mediumorchid', '#BA55D3'), ('rosybrown', '#BC8F8F'), ('darkkhaki', '#BDB76B'), ('silver', '#C0C0C0'), ('mediumvioletred', '#C71585'), ('indianred', '#CD5C5C'), ('peru', '#CD853F'), ('chocolate', '#D2691E'), ('tan', '#D2B48C'), ('lightgray', '#D3D3D3'), ('thistle', '#D8BFD8'), ('orchid', '#DA70D6'), ('goldenrod', '#DAA520'), ('palevioletred', '#DB7093'), ('crimson', '#DC143C'), ('gainsboro', '#DCDCDC'), ('plum', '#DDA0DD'), ('burlywood', '#DEB887'), ('lightcyan', '#E0FFFF'), ('lavender', '#E6E6FA'), ('darksalmon', '#E9967A'), ('violet', '#EE82EE'), ('palegoldenrod', '#EEE8AA'), ('lightcoral', '#F08080'), ('khaki', '#F0E68C'), ('aliceblue', '#F0F8FF'), ('honeydew', '#F0FFF0'), ('azure', '#F0FFFF'), ('wheat', '#F5DEB3'), ('beige', '#F5F5DC'), ('whitesmoke', '#F5F5F5'), ('mintcream', '#F5FFFA'), ('ghostwhite', '#F8F8FF'), ('salmon', '#FA8072'), ('sandybrown', '#FAA460'), ('antiquewhite', '#FAEBD7'), ('linen', '#FAF0E6'), ('lightgoldenrodyellow', '#FAFAD2'), ('oldlace', '#FDF5E6'), ('red', '#FF0000'), ('fuchsia', '#FF00FF'), ('magenta', '#FF00FF'), ('deeppink', '#FF1493'), ('orangered', '#FF4500'), ('tomato', '#FF6347'), ('hotpink', '#FF69B4'), ('coral', '#FF7F50'), ('darkorange', '#FF8C00'), ('lightsalmon', '#FFA07A'), ('orange', '#FFA500'), ('lightpink', '#FFB6C1'), ('pink', '#FFC0CB'), ('gold', '#FFD700'), ('peachpuff', '#FFDAB9'), ('navajowhite', '#FFDEAD'), ('moccasin', '#FFE4B5'), ('bisque', '#FFE4C4'), ('mistyrose', '#FFE4E1'), ('blanchedalmond', '#FFEBCD'), ('papayawhip', '#FFEFD5'), ('lavenderblush', '#FFF0F5'), ('seashell', '#FFF5EE'), ('cornsilk', '#FFF8DC'), ('lemonchiffon', '#FFFACD'), ('floralwhite', '#FFFAF0'), ('snow', '#FFFAFA'), ('yellow', '#FFFF00'), ('lightyellow', '#FFFFE0'), ('ivory', '#FFFFF0'), ) # 已去掉black和white color,strColor = '#','0123456789ABCD' #去掉EF调节颜色 for _ in range(6): color += choice(strColor) if flag: return color return choice(colorTuple)[1] def Square(length): t.color(rndColor()) # 参数改为Flase换colorTuple中的颜色 t.begin_fill() for i in range(4): t.fd(length) t.right(90) t.end_fill() def biTree(length): if length<0.08*Length: return xy = t.position() if abs(xy[0])>Width/2-2*length: return if xy[1]>Half_H-length*3: return if xy[1]<-Half_H+length*0.5: return # 以上四行尽可能约束树枝不超出可视范围 Square(length) Angle = choice([i for i in range(5,86)]) #左右偏向角度，不宜过大或过小 t.forward(length) t.left(Angle) biTree(length * cos(radians(Angle))) Square(length * cos(radians(Angle))) t.right(90) t.forward(length * cos(radians(Angle))) biTree(length * sin(radians(Angle))) Square(length * sin(radians(Angle))) t.right(90) t.forward(length * sin(radians(Angle))) t.right(Angle) t.forward(length) t.right(90) t.forward(length) t.right(90) def main(x=None,y=None): x,y = -Half_L, Half_L-Half_H t.clear() t.up() t.goto(x,y) t.down() #t.pensize(2) t.setheading(90) biTree(Length) t.penup() t.goto(Length*0.8,-Half_H+Half_L) t.pencolor('red') t.write("Click to refresh......") t.hideturtle() if __name__ == '__main__': Width,Height = 1200,800 #屏幕宽高 Length = 100 #第一层正方形的边长 Half_L,Half_H = Length/2,Height/2 turtle.setup(Width,Height) turtle.title('随机勾股树') turtle.tracer(0) t = turtle.Turtle() #t.speed(0) main() ts = turtle.Screen() ts.onclick(main) turtle.mainloop()
代码执行后，不停点击屏幕的动态效果如下：
本篇完！
