Another pre-Mandelbrot classic, this one found by W. Sierpinski around World War I. It is generated by dividing a triangle into four congruent smaller triangles, doing the same to each of them, and so on, yea, even unto infinity. (Notice how hard we try to avoid reiterating "iterating"?)
If you think of the interior triangles as "holes", they occupy more and more of the total area, while the "solid" portion becomes as hopelessly fragile as that gasket you HAD to remove without damaging it -- you remember, that Sunday afternoon when all the parts stores were closed? There's a three-dimensional equivalent using nested tetrahedrons instead of triangles, but it generates too much pyramid power to be safely unleashed yet.
There are no parameters for this type. We were able to implement it with integer math routines, so it runs fairly quickly even without an FPU.