  We demonstrate that diffusiophoretic, thermophoretic and chemotactic
phenomena in turbulence lead to clustering of particles on multi-fractal sets
that can be described using one single framework, valid when the particle size
is much smaller than the smallest length scale of turbulence $l_0$. To quantify
the clustering, we derive positive pair correlations and fractal dimensions
that hold for scales smaller than $l_0$. Statistics of the number of particles
in a small volume are non-Poissonian manifesting deviations from the case of
uncorrelated particles. For scales larger than $l_0$ we predict a stretched
exponential decay to 1 of the pair correlation function. For the case of
inhomogeneous turbulence we find that the fractal dimension depends on the
inhomogeneous direction. By performing experiments of clustering of
diffusiophoretic particles induced by salinity gradients in a turbulent gravity
current we demonstrate clustering in conformity to the theory. The particle
size in the experiment is comparable to $l_0$, outside the strict validity
region of the theory, suggesting that the theoretical predictions transfer to
this practically relevant regime. This clustering mechanism can provide the key
to the understanding of a multitude of processes such as formation of marine
snow in the ocean and population dynamics of chemotactic bacteria.
