  The creation of synthetic systems that emulate the defining properties of
living matter, such as motility, gradient-sensing, signalling and replication,
is a grand challenge of biomimetics. Such imitations of life crucially contain
active components that transform chemical energy into directed motion. These
artificial realizations of motility point in the direction of a new paradigm in
en- gineering, through the design of emergent behavior by manipulating
properties at the scale of the individual components. Catalytic colloidal
swimmers are a particularly promising example of such systems. Here we present
a comprehensive theoretical description of gradient-sensing of an individual
swimmer, leading controllably to chemotactic or anti-chemotactic behavior, and
use it to construct a framework for studying their collective behavior. We find
that both the positional and the orientational degrees of freedom of the active
colloids can exhibit condensation, signalling formation of clusters and asters.
The kinetics of catalysis introduces a natural control parameter for the range
of the interaction mediated by the diffusing chemical species. For various
regimes in parameter space in the long-ranged limit our system displays precise
analogs to gravitational collapse, plasma oscillations and electrostatic
screening. We present prescriptions for how to tune the surface properties of
the colloids during fabrication to achieve each type of behavior.
