Humans communicate with graphical sketches apart from symbolic languages (Fay et al., 2014). Primarily focusing on the latter, recent studies of emergent communication (Lazaridou and Baroni, 2020) overlook the sketches; they do not account for the evolution process through which symbolic sign systems emerge in the trade-off between iconicity and symbolicity. In this work, we take the very first step to model and simulate this process via two neural agents playing a visual communication game; the sender communicates with the receiver by sketching on a canvas. We devise a novel reinforcement learning method such that agents are evolved jointly towards successful communication and abstract graphical conventions. To inspect the emerged conventions, we define three fundamental properties—iconicity, symbolicity, and semanticity—and design evaluation methods accordingly. Our experimental results under different controls are consistent with the observation in studies of human graphical conventions (Hawkins et al., 2019; Fay et al., 2010). Of note, we find that evolved sketches can preserve the continuum of semantics (Mikolov et al., 2013) under proper environmental pressures. More interestingly, co-evolved agents can switch between conventionalized and iconic communication based on their familiarity with referents. We hope the present research can pave the path for studying emergent communication with the modality of sketches.