  Pattern formation is one of the most fundamental problems in distributed
computing, which has recently received much attention. In this paper, we
initiate the study of distributed pattern formation in situations when some
robots can be \textit{faulty}. In particular, we consider the well-established
\textit{look-compute-move} model with oblivious, anonymous robots. We first
present lower bounds and show that any deterministic algorithm takes at least
two rounds to form simple patterns in the presence of faulty robots. We then
present distributed algorithms for our problem which match this bound,
\textit{for conic sections}: in at most two rounds, robots form lines, circles
and parabola tolerating $f=2,3$ and $4$ faults, respectively. For $f=5$, the
target patterns are parabola, hyperbola and ellipse. We show that the resulting
pattern includes the $f$ faulty robots in the pattern of $n$ robots, where $n
\geq 2f+1$, and that $f < n < 2f+1$ robots cannot form such patterns. We
conclude by discussing several relaxations and extensions.
