Fluvial fans are large, low-gradient depositional systems that occur in sedimentary basins worldwide. Fluvial fans can represent much of the geologic record of foreland basins, create hazards, and record paleoclimate and tectonic signals. However, we lack an understanding of how fluvial fans grow into the variety of shapes observed around the world. We explored this aspect using a cellular model of foreland basin landscape evolution with rules for sediment transport, river avulsion, and floodplain processes. We tested the hypothesis that avulsion dynamics, namely, avulsion trigger period and abandoned channel dynamics, are a primary control on fluvial fan development. We found that shorter trigger periods lead to rounder planform fluvial fan shapes because, between avulsions, channel aggradation (and thus avulsion setup) propagates shorter distances from the upstream boundary along channel pathways. This prioritizes lateral sediment dispersion, creating shorter, rounder fans, over sediment delivery further into the basin, which would create elongated fans. Modeled fans with abandoned channel attraction (but not repulsion) generated a commonly observed abrupt fan boundary marked by a transition from distributary to tributary channel patterns. While fluvial fans are thought to be linked to climate, they can occur anywhere that rivers aggrade, lose lateral confinement, and preserve alluvial topography. Instead, fluvial fans might be more recognizable in environments that frequently trigger avulsions and preserve abandoned channels that capture future avulsions.