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Python 再说勾股树,这次整一棵五彩的任意“生长”的分形树!

绿色资源网  技术教程  2021-9-29  153  0评论
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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! 

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