  We study some aspects of conformal transformations in the context of twistor
theory, leading to the definition of a frustrated conformal transformation.
This equation relies on two instantons for the left and right copies of
$Sp(1)$, one being self-dual and the other anti-self-dual. Solutions to this
equation naturally generate maps on ambitwistor space due to an analog of the
Penrose-Ward correspondence. A solution based on the BPST instanton is
presented.
