Mandelbrot设置显示不正确

Question

这是我尝试使用Pygame模块对Python 3.5中的Mandelbrot集进行编程.

import math, pygame
pygame.init()

def mapMandelbrot(c,r,dim,xRange,yRange):
    x = (dim-c)/dim
    y = (dim-r)/dim
    #print([x,y])
    x = x*(xRange[1]-xRange[0])
    y = y*(yRange[1]-yRange[0])
    x = xRange[0] + x
    y = yRange[0] + y
    return [x,y]

def checkDrawBox(surface):
    for i in pygame.event.get():
        if i.type == pygame.QUIT:
            pygame.quit()
        elif i.type == pygame.MOUSEBUTTONDOWN:
            startXY = pygame.mouse.get_pos()
            boxExit = False
            while boxExit == False:
                for event in pygame.event.get():
                    if event.type == pygame.MOUSEBUTTONUP:
                        boxExit = True
                if boxExit == True:
                    return [startXY,pygame.mouse.get_pos()]
                pygame.draw.rect(surface,[255,0,0],[startXY,[pygame.mouse.get_pos()[0]-startXY[0],pygame.mouse.get_pos()[1]-startXY[1]]],1)
                pygame.display.update()

def setup():
    dimensions = 500
    white = [255,255,255]
    black = [0,0,0]
    checkIterations = 100
    canvas = pygame.display.set_mode([dimensions,dimensions])
    canvas.fill(black)
    xRange = [-2,2]
    yRange = [-2,2]
    xRangePrev = [0,0]
    yRangePrev = [0,0]
    newxRange = [0,0]
    newyRange = [0,0]
    while True:
        if not ([xRange,yRange] == [xRangePrev,yRangePrev]):
            draw(dimensions, canvas, xRange, yRange, checkIterations)
            pygame.display.update()
            xRangePrev = xRange
            yRangePrev = yRange
        box = checkDrawBox(canvas)
        if box != None:
            maxX = max([box[0][0],box[1][0]])
            maxY = max([box[0][1],box[1][1]])
            newxRange[0] = mapMandelbrot(box[0][0],0,dimensions,xRange,yRange)[0]
            newxRange[1] = mapMandelbrot(box[1][0],0,dimensions,xRange,yRange)[0]
            newyRange[0] = mapMandelbrot(0,box[0][1],dimensions,xRange,yRange)[1]
            newyRange[1] = mapMandelbrot(0,box[1][1],dimensions,xRange,yRange)[1]
            xRange = newxRange
            yRange = newyRange

def draw(dim, surface, xRange, yRange, checkIterations):
    for column in range(dim):
        for row in range(dim):
            greyVal = iteration(0,0,mapMandelbrot(column,row,dim,xRange,yRange),checkIterations,checkIterations)    
            surface.set_at([dim-column,row],greyVal)

def iteration(a, b, c, iterCount, maxIter):
    a = (a*a) - (b*b) + c[0]
    b = (2*a*b) + c[1]
    iterCount = iterCount - 1
    if iterCount == 0:
        return [0,0,0]
    elif abs(a+b) > 17:
        b = (iterCount/maxIter)*255
        return [b,b,b]
    else:
        return iteration(a,b,c,iterCount,maxIter)


setup()

我相信迭代算法是正确的,但输出看起来不正确:

想知道可能是什么问题？很抱歉代码转储,只是不确定哪个部分可能会导致它看起来像那样.

Answer 1

迷人的bug - 它看起来像一个被压扁的bug :)

问题在于两条线:

a = (a*a) - (b*b) + c[0]
b = (2*a*b) + c[1]

您正在更改a第一行中的含义,因此a在第二行中使用了错误.

修复很简单:

a, b  = (a*a) - (b*b) + c[0], (2*a*b) + c[1]

这将导致a在计算右侧时使用相同的值.

弄清楚你的bug产生了什么会很有趣.即使它不是Mandelbrot集合,它本身似乎也是一个有趣的分形.从这个意义上说,你有一个非常幸运的错误.百分之九十九的时间,虫子会导致垃圾,但不时会产生一些非常有趣的东西,但这些都是无意识的.

在编辑:

Mandelbrot集基于迭代复数多项式:

f(z) = z^2 + c

此错误产生的伪Mandelbrot集基于迭代函数

f(z) = Re(z^2 + c) + i*[2*Re(z^2 + c)*Im(z) + Im(c)]

其中Re()和Im()是其提取复数的实部和虚部的运算符.这不是多项式z,尽管很容易看出它是多项式z,z*(其中z*是复数的共轭z).由于这是一个相当自然的错误,几乎可以肯定,这已经出现在Mandelbrot集的文献中,尽管我不记得曾经看过它.