From Kuenwoo Lee (may not be original) ...
The state of being wrong at every conceivable scale of resolution. That is, from a distance, a fractally wrong person's worldview is incorrect; and furthermore, if you zoom in on any small part of that person's worldview, that part is just as wrong as the whole worldview.
Debating with a person who is fractally wrong leads to infinite regress, as every refutation you make of that person's opinions will lead to a rejoinder, full of half-truths, leaps of logic, and outright lies, that requires just as much refutation to debunk as the first one. It is as impossible to convince a fractally wrong person of anything as it is to walk around the edge of the Mandelbrot set in finite time.
If you ever get embroiled in a discussion with a fractally wrong person on the Internet--in mailing lists, newsgroups, or website forums--your best bet is to say your piece once and ignore any replies, thus saving yourself time.
The image is "borrowed" from Jeffrey Shallit's blog Recursivity [Fractal Wrongness]