math - 为什么这会产生拉伸(stretch)的分形？

Question

下面是我如何设置表示 MandelBrot 集的数组的伪代码，但当纵横比为 1:1 时，它会变得可怕地拉伸(stretch)。

xStep = (maxX - minX) / width;
yStep = (maxY - minY) / height;

for(i = 0; i < width; i++)
 for(j = 0; j < height; j++)
  {
   constantReal = minReal + xStep * i;
   constantImag = minImag + yStep * j;
   image[i][j] = inSet(constantReal, constantImag);
  }

谢谢!

Answer 1

Here is pseudo-code of how I setup an array representing the MandelBrot set, yet it becomes horribly stretched when leaving an aspect ratio of 1:1.

xStep = (maxX - minX) / width;
yStep = (maxY - minY) / height;

啊哈!这是因为您必须为要绘制的图像和要绘制的复杂平面区域保持相同的纵横比。换句话说，它必须保持

 width     maxX - minX
---------- = ---------------------
 height    maxY - minY

(因此 xStep == yStep。)您的代码可能不强制执行此要求。