绘制分形图像

根据Mandelbrot集绘制分形图像。Mandelbrot集由一个复变函数f(z) = z² + c生成，其中c为当前坐标点，z从0开始迭代。

Draw fractal image using Mandelbrot set. The Mandelbrot set is generated by a complex function f(z) = z² + c, where c is current coordinate point, and z iterates from 0.

根据Julia集绘制分形图像。Julia集由一个复变函数f(z) = z² + c生成，其中c为常数，z从当前坐标点开始迭代。

Draw fractal images using Julia set. The Julia set is generated by a complex function f(z) = z² + c, where c is a constant, and z iterates from current coordinate point.

一个边长为1的等边三角形，取每边中间的三分之一，接上去一个形状完全相似的但边长为其三分之一的三角形，结果是一个六角形。取六角形的每个边做同样的变换，即在中间三分之一接上更小的三角形，以此重复，直至无穷。

The Koch snowflake can be constructed by starting with an equilateral triangle, then recursively altering each line segment as follows:

1. divide the line segment into three segments of equal length.
2. draw an equilateral triangle that has the middle segment from step 1 as its base and points outward.
3. remove the line segment that is the base of the triangle from step 2.

将一个实心正方形划分为的9个小正方形，去掉中间的小正方形，再对余下的小正方形重复这一操作便能得到谢尔宾斯基地毯。

Divide a solid square into 9 small squares, remove the middle square, and repeat the operation for remaining small squares to get the Sierpinski carpet.