**Liouville quantum gravity and quantum Loewner evolution**

Graph approximations to Liouville quantum gravity.

A random quadrangulation generated with the Hamburger-Cheeseburger bijection embedded into the plane using circle packing. Animation.

The Eden model on a Liouville quantum gravity surface. Animation 1. Animation 2.

The Eden model on a Liouville quantum gravity surface with gamma=sqrt(8/3) and different multiples of the log.

Diffusion limited aggregation on a Liouville quantum gravity surface.

Diffusion limited aggregation on a graph approximation to a Liouville quantum gravity surface with different log singularities at the origin.