Python 再说勾股树，这次整一棵五彩的任意“生长”的分形树！

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 choicedef 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 turtlefrom random import choicefrom math import sin,cos,radiansdef 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！